High Temperature Excitonic Insulator and Possible Superfluid Based on Two-Dimensional Diamond

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Herein, we realize excitonic insulator based on two-dimensional (2D) wide band gap diamond with transition temperature as high as 220K. The resistance rises dramatically by more than three orders, which can be explained by the Bose-Einstein condensation (BEC) of excitons. While cooling down below transition temperature, the wavelength of the bounded exciton caused by boron and nitrogen centers becomes highly overlapped, leading to BEC process. Furthermore, the variable hopping mechanism is confirmed in agreement with the exciton transport process. When temperature drops down further, a sudden drop of resistance over three orders was observed around 60K, possibly due to the formation of excitonic superfluid resulting from highly overlap of wavelength of the large density bounded excitons at lower temperature. This study provides evidences for excitonic insulator and possible superfluid phase based on wide bandgap semiconductor. Physical sciences/Physics/Condensed-matter physics/Phase transitions and critical phenomena Physical sciences/Materials science/Condensed-matter physics/Phase transitions and critical phenomena Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Introduction Excitonic insulator is a crucial state of matter, the gap of which is related to the binding energy of excitons and their collective ground state, rather than the band structure of the material itself 1 . Instead of electrons and holes moving independently as in standard conductors or insulators, excitons can behave as composite bosons and condense into a neutral ground state that spans the entire material, especially in two-dimensional (2D) system 2 – 6 . The condensed excitons can exhibit quantum coherence over macroscopic distance, similar to the coherence observed in superfluid helium and Bose-Einstein condensation (BEC), which is attractive since it has many important applications such as polariton laser and quantum computing 7 , 8 .Additionally, by transforming doped electrons into cooper pairs through exciton-electron interaction, excitonic insulator acts as the parent material of exciton-mediated superconductor, a promising candidate for realizing high temperature superconductivity as predicted by many scientists including John Bardeen 9 – 14 . However, the search for materials that can sustain an excitonic insulating phase is challenging, requiring systems with a strong interaction between excitons. Compared with bulk materials, larger binding energy of exciton tends to be achieved in low dimensional systems due to quantum confinement effect, providing larger possibility to realize excitonic insulator 15 , 16 . Normally, heterostructures made from layering different 2D materials can exhibit strong excitonic effect due to their unique electronic properties. Layered InAs/GaSb has been adapted to explore excitonic insulator as the electron and hole have a binding energy larger than energy band gap of InAs or GaSb 17 , 18 . Recently, Ta 2 NiSe 5 has attracted much attention as a potential excitonic insulator, and many evidences indicate that it has a transition temperature as high as about 325K 19 . However, most of the research above mainly focused on narrow bandgap materials or semimetal, achieving excitonic insulating phase by opening or expanding an external gap introduced by excitons 20 , 21 . There is rare research on excitonic insulator based on wide bandgap materials such as diamond, which possesses an exciton binding energy as large as several hundred meV while being fabricated into 2D thin film due to quantum confinement 22 , 23 . Herein, by co-doping boron acceptors with nitrogen donors, we realized excitonic insulator in 2D single crystal diamond with thickness of 9nm. The resistance can rise dramatically by more than three orders with a transition temperature of 220K. We successfully described the transition and insulating phase with variable range hopping (VRH) model, pointing out that excitons will condense into ground state below critical temperature T C . The rise of resistance is due to the lower hopping possibility for carriers in low temperature with strong quantum confinement effect of bounded excitons in 2D diamond. When temperature crosses 61.1K, the resistance quickly drops down to 2.5kΩ, possibly marks the second phase transition from excitonic insulator to superfluid of bounded excitons, and the resistance behaves as an inversed linear function with the biased current at temperature below 20K. This research provides the evidence for excitonic insulating phase and possible superfluid phase in wide bandgap system, opening the avenue of high temperature superconductor or superfluid through exciton designment. Result And Discussion Figure 1 A shows the HRTEM image of a boron-nitrogen co-doped diamond sample. The sample was grown by homoepitaxial growth technology from a single crystal diamond substrate, and the thickness of the film is about 9.5nm, as marked in the figure. Four gold electrodes have been sputtered in parallel on the surface for four-probe measurement and the size of each sample is about 6mm×6mm. Figure 1 B shows the HRTEM image of the diamond along direction, where the clear atomic structure demonstrates the high crystal quality and long-range uniformity of the diamond film, laying the foundation for BEC of excitons. HRTEM image of the cross section and along direction with its FFT result for another sample are shown in fig. S1 . Figure 1 C shows the schematic illustration of the nitrogen deep donor centers in diamond, where the holes are localized or shared by the nitrogen centers, forming the bounded excitons. The possibility of excitonic ground state formation is enhanced in 2D system due to reduced screening. The fabrication of 2D diamond increases the possibility of realization of excitonic insulator by utilization of the bounded excitons. Figure 1 D shows the ultraviolet-visible spectroscopy of the sample 20240423-1 and its single crystal diamond substrate. The transmittance of the sample obviously increased compared with its substrate due to B-N co-doping, which means the absorption is mainly caused by the exciton-related process. Through linear extrapolation, we can easily derive that the bandgap of the diamond substrate is about 5.39eV, indicating the purity of single crystal diamond. By introducing dopants, the absorption edge increases to about 5.57eV, which should be ascribed to the formation of the 2D confined excitons formed by boron-nitrogen complexes inside diamond. The exciton formation and enlarged absorption edge mean that the binding energy of exciton is larger than the band gap of intrinsic diamond, which permits the formation of excitonic insulator similar with the case in narrow band gap semiconductors such as Ta 2 NiSe 5 24 . Another UV-Vis spectroscopy result is shown in fig. S2 for sample 20240411, where the absorption edge increases to about 5.54eV, similar with sample 20240423-1. From Fig. 1 E, two peaks around 2848.7cm − 1 and 2918.1cm − 1 in the infrared spectroscopy of the sample are clearly depicted, representing deep and shallow doped boron accepters respectively 25 . Figure 1 F shows the Raman spectrum of the diamond, where the 1332.47cm − 1 peak is ascribed to the first-order Raman scattering caused by the zero-center optical phonon mode, indicating no stress has been introduced into the epitaxial grown diamond. The peak around 1422.08cm − 1 is resulting from N-V color centers, obviously showing that nitrogen dopants were heavily introduced into the sample. All the data and figures highlight that based on high quality grown 2D diamond, boron and nitrogen were uniformly and heavily co-doped into the sample, laying the groundwork for the formation of bounded excitons. Figure 2 A shows the resistance as a function of temperature for sample 20240424-2-2 with a thickness of 9nm. As the temperature decreases, the resistance of the sample increases dramatically from 6kΩ at 300K to nearly 12MΩ at 61.1K. On one hand, lower temperature reduces thermal excitation of the carriers and makes boron accepters harder to be ionized, leading to lower conductivity. On the other hand, the wavelength of stable excitons formed in low temperature from boron and nitrogen centers becomes larger, causing the strong interaction among the neutral bosons and finally condensing into BEC status with higher resistance. The inset shows the derivation of Fig. 2 A, representing the rate of the increment of the resistance, restating the sharp change of the resistance. To confirm the results, we reproduced several samples and measured them in different instruments. It turns out that the results are repeatable and the resistance-temperature relation of other three samples 20240411, 20240319-2 and 20240318 are shown in Fig. 2 B-D, respectively. The thickness of all the samples is below 15nm, and the resistance increases more than three orders while cooling down for most of them. Another four diamond samples and their resistance as a function of temperature are shown in fig. S3, presenting similar feature with samples mentioned above. For comparison, we fabricated another three samples, named sample 20240409, 20240125 and 20250218, with thickness of 30nm, 90nm, and more than 1000nm, respectively. Figure 3 A shows the resistance of sample 20240409, which still behaves as an excitonic insulator with an increment of 2396 times from room temperature to about 22K. However, when sample becomes thicker, as shown in Fig. 3 B, the rate of increment of resistance is much lower than that case in 2D. In sample 20250218 heavily doped by boron and nitrogen with a thickness of more than 1000nm shown in Fig. 3 C, the resistance does not increase continuously with the decrement of temperature, and it changes less than 20% from 300K to 3K. The abovementioned comparative results indicate that with the increment of the thickness of the samples, the B-N co-doped diamond gradually lose the behavior of an excitonic insulator. From this point of view, the sharp increment of the resistance of 2D diamond should be ascribed to the formation of bounded excitons related with B-N complexes with large binding energy. As we pointed out above, 2D system tends to achieve larger exciton binding energy compared with 3D due to stronger quantum confinement effect, which enlarges the differences between the binding energy of exciton and band gap. We choose sample 20240424-2-2 and 20240411 for deeper analysis. Figure 4 A shows the resistance of the sample as a function of temperature in logarithmic form. It is easier to notice that the resistance of the sample rises from less than 10kΩ in room temperature to more than 10MΩ around 61.1K. A slight but clear change in the slope of resistance occurs around 220K, indicating when temperature crosses critical temperature T C , the conductive behavior of the sample is mainly caused by hopping behavior of the carriers due to excitons condensation. At temperature above T C , the transport characteristic fits pretty well with Arrhenius model 26 given by Eq. ( 1 ), as shown in Fig. 4 B. $$\:\rho\:={\rho\:}_{0}\text{e}\text{x}\text{p}\left(\frac{{E}_{A}}{{k}_{B}T}\right)$$ 1 Where ρ is the resistance of the sample, ρ 0 is a coefficient unrelated to temperature, E A is the activation energy, characterizing the difficulty for electrons to be thermally excited, k B is Boltzmann's constant and T stands for temperature. It is obvious that lnR-T − 1 function in Fig. 4 B possesses great linearity above 220K with a coefficient of determination ( R 2 ) closed to 1.0, indicating a complete thermal excitation behavior for electrons. When the temperature continuously decreases, the resistance curve of the sample 20240424-2-2 steepens significantly within a small temperature range around 220K, which marks the phase transition of the 2D diamond. Below 220K, the wavelength of the excitons becomes overlapped, thus free carriers are strongly localized by the excitons, leading to the excitonic insulator status. Additionally, lower temperature results in less ionization of boron acceptors, further reducing the carrier density. In low temperature area, due to carrier localization by bounded excitons contributed by randomly distributed boron and nitrogen atoms, carriers tend to hop between two localized bounded excitons in the material, which is well known as variable range hopping (VRH) model, as predicted by N. F. Mott 27 , 28 . In an interacting system like B-N co-dopped 2D diamond, VRH model indicates that the resistance will follow Efros and Shklovskii’s Law 29 , given by Eq. ( 2 ): $$\:\sigma\:\left(T\right)\propto\:\text{e}\text{x}\text{p}[-{\left(\frac{{T}_{0}}{T}\right)}^{\frac{1}{2}}]$$ 2 Where T 0 is the characteristic temperature given by Eq. (3) 30 : $$\:{T}_{0}=\frac{\beta\:{e}^{2}}{\epsilon\:{k}_{B}\xi\:}$$ 3 β is a coefficient and β = 6.5 for 2D system 31 , e stands for elementary charge, ε is the dielectric constant for material and ξ represents the localization length, which defines the spatial extent of the electron’s wavefunction. From Fig. 4 C, it is obvious that the resistance of the sample fits well with VRH model below T C with a big R 2 close to 1.0, confirming that carriers are confined by bounded excitons and begin to hop among the excitons, implying the stable presence of excitonic insulating phase for B-N co-doped 2D diamond. It is easy to calculate the localization length ξ ≈ 38.9nm, revealing the long-range and strong interactions among the excitons, leading to the possibility of BEC status. Additionally, the localization length is much larger than the Bohr radius of excitons in diamond (< 1nm) 32,33 , so that the electrons can interact with each other strongly in a large scale. Figure 4 D-F shows another sample 20240411 for repeated confirmation, with a resistance from 1.08Ω at room temperature to more than 3000Ω around 42K. The marked critical temperature is about 208.3K, and the localization length ξ is 49.8nm. Another two samples mentioned in Fig. 2 C and D and their fitting models are shown in fig. S4. Both of them exhibit similar and significant phase transition like sample 20240424-2-2 and 20240411, further confirming the excitonic insulating phase based on 2D diamond. It should be emphasized that the resistivity of the sample 20240424-2-2 drops very quickly while reaching the highest point, possibly pointing to the superfluid status of the BEC of bounded excitons in 2D diamond. As shown in Fig. 5 A, the resistance rises from 6kΩ to 12MΩ at around 61.1K, but when temperature continuously decreases, resistance suddenly drops to about 2.5kΩ at low temperature. This abnormal transport behavior can possibly due to the long-range formation of superfluid of bounded excitons, which spans the entire material, so that free carriers can pair up into cooper pairs mediated by strong interaction between excitons and electrons, leading to higher conductivity. Negative resistance occurs around 30K as shown in Fig. 5 B, possibly because some of the electrons or holes are pulled out by the strong interaction between the cooper pairs and excitons, resulting in a reversed current direction in the method of four-probe resistance measurement. At extremely low temperature area below 20K, as shown in Fig. 5 C and D, we find that the resistance remains stable relatively, and by increasing the flowing current through the sample at the value of 10µA, 100µA, 200µA, 500µA, 1000µA, 2000µA, 3000µA and 5000µA, respectively, the average resistance decreases linearly as a function of flowing current. When temperature lowers down to 20K, the superfluid status of excitons remains stable, providing stable and strong interaction between excitons and cooper pairs, so that exhibiting stable resistance with an unchanged current. However, as current increases, the formation of cooper pairs increases as a linear function of the current, leading to inversed linear function between resistance and biased current (Fig. 5 C and D). Another sample possibly behaves as a superfluid named 20240424-2-1 is presented in fig. S5, where similar transport characteristics occurs again with a resistance drops from 12MΩ to 2.4kΩ at 29.3K when the biased current is 10µA. Still negative resistance occurs at 16K and the average resistance decreases linearly as a function of flowing current below 10K. We have repeated the measurement on many B-N co-doped 2D diamond samples, which exhibit the similar behavior presented in Fig. 5 . Although the measurements on the mixed phased of exciton BEC superfluid and copper pairs induced superconductivity should be further investigated and standardized in the future, the repeated experimental results of the suddenly drop of the resistance at the highest value of the excitonic insulator state are confirmed. It should be noted that we have also repeated the measurements on three different Quantum design machines, where the same behavior can be reproduced. The conclusion of possible status of BEC superfluid of exciton in B-N co-doped diamond can be safely drawn herein. Conclusion In conclusion, we have demonstrated the existence of excitonic insulator and possible superfluid phase in B-N co-doped 2D diamond. The resistance rises dramatically by more than three orders and exhibits an obvious phase transition around 220K for one sample. Above T C , the carriers behave as the Arrhenius law predicted, with thermal excitation as the dominant excitation in the system. While temperature cooled down below T C , excitons condense to form BEC due to large exciton binding energy resulting from quantum confinement effect. The variable range hopping model can be applied to describe the transport behavior of the B-N co-doped diamond with a large localization length of 38.9nm, which is in accordance with the characteristic of excitonic insulator. A sharp transition occurs at 61.1K where resistance suddenly drop and even exhibits negative value, and the resistance decreases as an inversed linear function with biased current at extremely low temperature, which possibly indicating the formation of superfluid state of excitons. Our work opens the avenue for searching excitonic insulator in wide bandgap materials, which further promotes the exciton-mediated superconductor or superfluid. Declarations Competing interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Author contributions S. Lin designed and carried out the experiments, analyzed the data, conceived the study, and wrote the paper. S. Huang, carried out the experiments, analyzed the data, discussed the results and assisted writing the paper. M. Yang participated in the experiments, analyzed the data and discussed the mechanism, X. Chen participated the experiments and discussed the data, H. Bi and K. Xiong participated in the experiments. All authors contributed to the preparation of the manuscript. Acknowledgments S. Lin thanks the support from the National Natural Science Foundation of China (No. 51202216, 51551203, 61774135 and 62474161). S. Lin thanks for the kind discussion with Alexy Kavokin and many scientists or colleagues and those discussions are intriguing. References Jérome D, Rice TM, Kohn W (1967) Excitonic insulator. Phys Rev 158:462–475. https://doi.org/10.1103/PhysRev.158.462 Pieri P, Neilson D, Strinati GC (2007) Effects of density imbalance on the BCS-BEC crossover in semiconductor electron-hole bilayers. Phys Rev B Condens matter Mater Phys 75. https://doi.org/10.1103/PhysRevB.75.113301 Debnath B, Barlas Y, Wickramaratne D, Neupane MR, Lake RK (2017) Exciton condensate in bilayer transition metal dichalcogenides: Strong coupling regime. Phys Rev B 96. https://doi.org/10.1103/PhysRevB.96.174504 Gupta S, Kutana A, Yakobson BI (2020) Univ. of California, O. C. A. Heterobilayers of 2D materials as a platform for excitonic superfluidity. Nat Commun 11:2989–2989. https://doi.org/10.1038/s41467-020-16737-0 Fogler MM, Butov LV, Novoselov KS (2014) High-temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat Commun 5:4555–4555. https://doi.org/10.1038/ncomms5555 Lozovik YE, Kurbakov IL, Astrakharchik GE, Boronat J, Willander M (2007) Strong correlation effects in 2D Bose–Einstein condensed dipolar excitons. Solid State Commun 144:399–404. https://doi.org/10.1016/j.ssc.2007.07.041 Allen JF, Misener AD (1938) Flow of Liquid Helium II. Nature 141:75–75. https://doi.org/10.1038/141075a0 Kavokin A et al (2022) Polariton condensates for classical and quantum computing. Nat Reviews Phys 4:435–451. https://doi.org/10.1038/s42254-022-00447-1 Allender D, Bray J, Bardeen J (1973) Model for an exciton mechanism of superconductivity. Phys Rev B 7:1020–1029. https://doi.org/10.1103/PhysRevB.7.1020 Bardeen J, Excitonic superconductivity? (1978) J less-common Met 62:447–450. https://doi.org/10.1016/0022-5088(78)90058-9 Bardeen J, Cooper LN, Schrieffer JR (1957) Theory of Superconductivity. Phys Rev 108:1175–1204. https://doi.org/10.1103/PhysRev.108.1175 Laussy FP, Kavokin AV, Shelykh IA (2010) Exciton-polariton mediated superconductivity. Phys Rev Lett 104:106402–106402. https://doi.org/10.1103/PhysRevLett.104.106402 Yin DL, Han RS (1987) Possible electron-exciton (E-E) interaction and high Tc superconductivity in bulk semimetals. Solid State Commun 63:645–648. https://doi.org/10.1016/0038-1098(87)90871-4 Fogler MM, Butov LV, Novoselov KS (2014) High-temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat Commun 5. https://doi.org/10.1038/ncomms5555 Alivisatos AP (1996) Semiconductor clusters, nanocrystals, and quantum dots. Science 271:933–937. https://doi.org/10.1126/science.271.5251.933 Novoselov KS, Mishchenko A, Carvalho A, Neto AH (2016) C. 2D materials and van der Waals heterostructures. Science 353. https://doi.org/10.1126/science.aac9439 Du L et al (1971) (2017) Evidence for a topological excitonic insulator in InAs/GaSb bilayers. Nature Communications 8. https://doi.org/10.1038/s41467-017-01988-1 Wang R, Sedrakyan TA, Wang B, Du L, Du R-R (2023) Excitonic topological order in imbalanced electron–hole bilayers. Nature 619:57–62. https://doi.org/10.1038/s41586-023-06065-w Lu YF et al (2017) Zero-gap semiconductor to excitonic insulator transition in Ta2NiSe5. Nat Commun 8:14408. https://doi.org/10.1038/ncomms14408 Wang Z et al (2019) Evidence of high-temperature exciton condensation in two-dimensional atomic double layers. Nat (London) 574:76–80. https://doi.org/10.1038/s41586-019-1591-7 Kogar A et al (2017) Signatures of exciton condensation in a transition metal dichalcogenide. Sci (American Association Advancement Science) 358:1314–1317. https://doi.org/10.1126/science.aam6432 Jackson KA, Pederson MR (1991) New theoretical model for the diamond 1s core exciton. Phys Rev Lett 67:2521–2524. https://doi.org/10.1103/PhysRevLett.67.2521 Zhu Q, Karlsson KF, Pelucchi E, Kapon E (2007) Transition from Two-Dimensional to Three-Dimensional Quantum Confinement in Semiconductor Quantum Wires/Quantum Dots. Nano Lett 7:2227–2233. https://doi.org/10.1021/nl0706650 Seo Y-S et al (2018) Temperature-dependent excitonic superfluid plasma frequency evolution in an excitonic insulator, Ta2NiSe5. Sci Rep 8:1–9. https://doi.org/10.1038/s41598-018-30430-9 Wedepohl PT (1957) Electrical and Optical Properties of Type IIb Diamonds. Proceedings of the Physical Society. Section B 70, 177–185 https://doi.org/10.1088/0370-1301/70/2/303 Pearson GL, Bardeen J (1949) Electrical properties of pure silicon and silicon alloys containing boron and phosphorus. Phys Rev 75:865–883. https://doi.org/10.1103/PhysRev.75.865 Mott NF (1968) Conduction in glasses containing transition metal ions. J Non-cryst Solids 1:1–17. https://doi.org/10.1016/0022-3093(68)90002-1 Mott NF (1967) Electrons in disordered structures. Adv Phys 16:49–144. https://doi.org/10.1080/00018736700101265 Efros AL, Shklovskii BI (1975) Coulomb gap and low temperature conductivity of disordered systems. J Phys C Solid state Phys 8:L49–L51. https://doi.org/10.1088/0022-3719/8/4/003 Ortuño M, Estellés-Duart F, Somoza AM (2022) Numerical Simulations of Variable-Range Hopping. Physica Status Solidi (B) Basic Research 259, n/a-n/a https://doi.org/10.1002/pssb.202100340 Lien NV (1995) Crossovers in two-dimensional variable range hopping. Phys Lett A 207:379–384. https://doi.org/10.1016/0375-9601(95)00666-Q Gheeraert E, Koizumi S, Teraji T, Kanda H, Nesládek M (1999) Electronic States of Boron and Phosphorus in Diamond. Phys status solidi Appl Res 174:39–51. https://doi.org/10.1002/(SICI)1521-396X(199907)174:13.0.CO;2-E Sharp SJ, Collins AT, Davies G, Joyce GS (1997) Higher resolution studies of shallow bound exciton luminescence in diamond. J Phys Condens matter 9:L451–L455. https://doi.org/10.1088/0953-8984/9/33/003 Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryMaterial.docx Supplementary Material Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6807758","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":468825987,"identity":"72406b4e-aa35-48dd-bdff-7f6225750f9c","order_by":0,"name":"Shisheng Lin","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+klEQVRIiWNgGAWjYDACCcYGZhDNx8zA+ICBB8RMIFILGzMDswGRWhgYIFqASAIiRECL/Ozm5s8FFXfs2th5j1X+kDnMwM+eY8DwcwduLQZ3DrZJzzjzLLmNmS/thgTPYQbJnjcGjL1n8GiRSGxj5m07nMzGzGN2wwCoxeBGjgEzYxseh81IbP7M+w+ipSABqMWekBaGG4kN0rwNh+1AWhgOgGyRIKDF4EZimzTPscMJQC3Gkg086TwSZ54VHOzF67D0x595ag7b8/OfMfz4s8dajr89eeODn/gcBgWJDSCSsQcSmQcIa2BgsIdQP4hROwpGwSgYBSMNAAAefUmyCatdvQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-2782-9375","institution":"Zhejiang University","correspondingAuthor":true,"prefix":"","firstName":"Shisheng","middleName":"","lastName":"Lin","suffix":""},{"id":468825988,"identity":"fca15437-5d58-4d01-8509-640de2a6f465","order_by":1,"name":"Shaoqi Huang","email":"","orcid":"","institution":"Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Shaoqi","middleName":"","lastName":"Huang","suffix":""},{"id":468825989,"identity":"a4cfd0e1-453c-4d21-bdd3-ed1cead79887","order_by":2,"name":"Minhui Yang","email":"","orcid":"","institution":"Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Minhui","middleName":"","lastName":"Yang","suffix":""},{"id":468825990,"identity":"b10b556f-a74b-498e-883d-89dc3fc5d4df","order_by":3,"name":"Xin Chen","email":"","orcid":"","institution":"Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Xin","middleName":"","lastName":"Chen","suffix":""},{"id":468825991,"identity":"f52f631d-2e59-421b-8dc4-a03f19a6fffe","order_by":4,"name":"Hongjia Bi","email":"","orcid":"","institution":"Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Hongjia","middleName":"","lastName":"Bi","suffix":""},{"id":468825992,"identity":"26977ba1-ac51-4e7a-8c10-966424851837","order_by":5,"name":"Kangchen Xiong","email":"","orcid":"","institution":"Zhejiang University","correspondingAuthor":false,"prefix":"","firstName":"Kangchen","middleName":"","lastName":"Xiong","suffix":""}],"badges":[],"createdAt":"2025-06-03 06:45:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6807758/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6807758/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84394819,"identity":"eb16b737-258f-4d96-ac50-8b49cf6c0825","added_by":"auto","created_at":"2025-06-11 12:22:36","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":2388576,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eCharacterization of 2D diamond.\u003c/strong\u003e (\u003cstrong\u003eA\u003c/strong\u003e) HRTEM image of the cross section of 2D diamond and diamond substrate. (\u003cstrong\u003eB\u003c/strong\u003e) Atomic structure of diamond along \u0026lt;001\u0026gt; direction of the sample. (\u003cstrong\u003eC\u003c/strong\u003e) The schematic illustration of bounded excitons in B-N co-doped diamond. (\u003cstrong\u003eD\u003c/strong\u003e) Ultraviolet-visible (UV-Vis) spectroscopy of the sample 20240423-1 and pure diamond substrate. (\u003cstrong\u003eE\u003c/strong\u003e) Infrared (IR) spectroscopy of the sample. (\u003cstrong\u003eF\u003c/strong\u003e) Raman spectrum of the sample.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-6807758/v1/8e64f74b019887438116d82d.png"},{"id":84395868,"identity":"8a6c9ac4-7322-4e2c-8ba2-820d6b89c217","added_by":"auto","created_at":"2025-06-11 12:30:36","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":604537,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTransport characteristic of excitonic insulator based on 2D diamond.\u003c/strong\u003e (\u003cstrong\u003eA\u003c/strong\u003e)-(\u003cstrong\u003eD\u003c/strong\u003e)Four different samples of diamond excitonic insulator with thickness of 9nm, 4.5nm, 15nm, 15nm sequentially, and their resistance as a function of temperature. The insets show the rate of change of resistance.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-6807758/v1/553571a5fe7f61475fc1ac4e.png"},{"id":84394821,"identity":"7cf18932-6ddc-4cd3-8d62-68691d9d395f","added_by":"auto","created_at":"2025-06-11 12:22:36","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":221237,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eComparative diamond samples with different thickness.\u003c/strong\u003e(\u003cstrong\u003eA\u003c/strong\u003e) An obvious excitonic insulating behavior of the sample 20240409 with thickness of 30nm. (\u003cstrong\u003eB\u003c/strong\u003e) The rate of growth of resistance decreases significantly for sample 20240125 with thickness of 90nm. (\u003cstrong\u003eC\u003c/strong\u003e) Resistance does not increase severely as temperature lowers down for sample 20250218 with a thickness of more than 1000nm.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-6807758/v1/82321b0b13d8a3676f30514f.png"},{"id":84395870,"identity":"d6b2428e-d8d4-4bdf-a4e4-26eec9fa8f31","added_by":"auto","created_at":"2025-06-11 12:30:36","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":425399,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eResistance model of excitonic insulator based on 2D diamond. \u003c/strong\u003e(\u003cstrong\u003eA\u003c/strong\u003e) Resistance as a function of temperature in logarithmic form for sample 20240424-2-2. Critical temperature \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e = 220K is marked on the figure. (\u003cstrong\u003eB\u003c/strong\u003e) The change of resistance fits well with Arrhenius model for temperature above \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e. (\u003cstrong\u003eC\u003c/strong\u003e) The change of resistance fits well with variable range hopping model for temperature below \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e, where excitons condense into ground state. (\u003cstrong\u003eD\u003c/strong\u003e)-(\u003cstrong\u003eF\u003c/strong\u003e) Resistance in logarithmic form, fitting of Arrhenius model for temperature above \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e and fitting of variable range hopping model for temperature below \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e for sample 20240411, respectively. Critical temperature \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e = 208.3K is marked on each figure. Coefficient of determination (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e) for each fitting curve is closed to 1.0, indicating good linearity.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-6807758/v1/c2876c3bac27a5bc66349e3e.png"},{"id":84395871,"identity":"5977e9b8-6bb9-4d98-a20f-c3eac16fb0c9","added_by":"auto","created_at":"2025-06-11 12:30:36","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":770792,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePossible high temperature excitonic mediated superfluidity. \u003c/strong\u003e(\u003cstrong\u003eA\u003c/strong\u003e) Sharp drop of resistance for sample 20240424-2-2 at 61.1K. (\u003cstrong\u003eB\u003c/strong\u003e) The resistance crosses over zero near 30 K for applied current of 10μA, 50μA, 500μA and 700μA. (\u003cstrong\u003eC\u003c/strong\u003e) The dependence of resistance as a function of applied current below 20K, where the resistance is inverse proportion to the applied current. (\u003cstrong\u003eD\u003c/strong\u003e) The dependence of resistance as a function of the biased current, where an inverse linear function can be clearly clarified.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-6807758/v1/796225feb44de7a35e13d36d.png"},{"id":86969955,"identity":"0311a05c-467b-4291-aaef-51d4e748898c","added_by":"auto","created_at":"2025-07-17 18:39:08","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4866275,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6807758/v1/91ca672d-516e-4bce-b2f2-b727144cdf54.pdf"},{"id":84394825,"identity":"188283b1-cd91-4be0-b8db-98a7744f0665","added_by":"auto","created_at":"2025-06-11 12:22:36","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":2426956,"visible":true,"origin":"","legend":"Supplementary Material","description":"","filename":"SupplementaryMaterial.docx","url":"https://assets-eu.researchsquare.com/files/rs-6807758/v1/5481f0780d0b80432344e158.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"High Temperature Excitonic Insulator and Possible Superfluid Based on Two-Dimensional Diamond","fulltext":[{"header":"Introduction","content":"\u003cp\u003eExcitonic insulator is a crucial state of matter, the gap of which is related to the binding energy of excitons and their collective ground state, rather than the band structure of the material itself\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Instead of electrons and holes moving independently as in standard conductors or insulators, excitons can behave as composite bosons and condense into a neutral ground state that spans the entire material, especially in two-dimensional (2D) system\u003csup\u003e\u003cspan additionalcitationids=\"CR3 CR4 CR5\" citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. The condensed excitons can exhibit quantum coherence over macroscopic distance, similar to the coherence observed in superfluid helium and Bose-Einstein condensation (BEC), which is attractive since it has many important applications such as polariton laser and quantum computing\u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e.Additionally, by transforming doped electrons into cooper pairs through exciton-electron interaction, excitonic insulator acts as the parent material of exciton-mediated superconductor, a promising candidate for realizing high temperature superconductivity as predicted by many scientists including John Bardeen\u003csup\u003e\u003cspan additionalcitationids=\"CR10 CR11 CR12 CR13\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. However, the search for materials that can sustain an excitonic insulating phase is challenging, requiring systems with a strong interaction between excitons.\u003c/p\u003e \u003cp\u003eCompared with bulk materials, larger binding energy of exciton tends to be achieved in low dimensional systems due to quantum confinement effect, providing larger possibility to realize excitonic insulator\u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e,\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Normally, heterostructures made from layering different 2D materials can exhibit strong excitonic effect due to their unique electronic properties. Layered InAs/GaSb has been adapted to explore excitonic insulator as the electron and hole have a binding energy larger than energy band gap of InAs or GaSb\u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e,\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. Recently, Ta\u003csub\u003e2\u003c/sub\u003eNiSe\u003csub\u003e5\u003c/sub\u003e has attracted much attention as a potential excitonic insulator, and many evidences indicate that it has a transition temperature as high as about 325K\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. However, most of the research above mainly focused on narrow bandgap materials or semimetal, achieving excitonic insulating phase by opening or expanding an external gap introduced by excitons\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. There is rare research on excitonic insulator based on wide bandgap materials such as diamond, which possesses an exciton binding energy as large as several hundred meV while being fabricated into 2D thin film due to quantum confinement\u003csup\u003e\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e,\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eHerein, by co-doping boron acceptors with nitrogen donors, we realized excitonic insulator in 2D single crystal diamond with thickness of 9nm. The resistance can rise dramatically by more than three orders with a transition temperature of 220K. We successfully described the transition and insulating phase with variable range hopping (VRH) model, pointing out that excitons will condense into ground state below critical temperature \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e. The rise of resistance is due to the lower hopping possibility for carriers in low temperature with strong quantum confinement effect of bounded excitons in 2D diamond. When temperature crosses 61.1K, the resistance quickly drops down to 2.5kΩ, possibly marks the second phase transition from excitonic insulator to superfluid of bounded excitons, and the resistance behaves as an inversed linear function with the biased current at temperature below 20K. This research provides the evidence for excitonic insulating phase and possible superfluid phase in wide bandgap system, opening the avenue of high temperature superconductor or superfluid through exciton designment.\u003c/p\u003e"},{"header":"Result And Discussion","content":"\u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eA shows the HRTEM image of a boron-nitrogen co-doped diamond sample. The sample was grown by homoepitaxial growth technology from a single crystal diamond substrate, and the thickness of the film is about 9.5nm, as marked in the figure. Four gold electrodes have been sputtered in parallel on the surface for four-probe measurement and the size of each sample is about 6mm\u0026times;6mm. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eB shows the HRTEM image of the diamond along \u0026lt;\u0026thinsp;001\u0026thinsp;\u0026gt;\u0026thinsp;direction, where the clear atomic structure demonstrates the high crystal quality and long-range uniformity of the diamond film, laying the foundation for BEC of excitons. HRTEM image of the cross section and along \u0026lt;\u0026thinsp;001\u0026thinsp;\u0026gt;\u0026thinsp;direction with its FFT result for another sample are shown in fig. \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eC shows the schematic illustration of the nitrogen deep donor centers in diamond, where the holes are localized or shared by the nitrogen centers, forming the bounded excitons. The possibility of excitonic ground state formation is enhanced in 2D system due to reduced screening. The fabrication of 2D diamond increases the possibility of realization of excitonic insulator by utilization of the bounded excitons. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eD shows the ultraviolet-visible spectroscopy of the sample 20240423-1 and its single crystal diamond substrate. The transmittance of the sample obviously increased compared with its substrate due to B-N co-doping, which means the absorption is mainly caused by the exciton-related process. Through linear extrapolation, we can easily derive that the bandgap of the diamond substrate is about 5.39eV, indicating the purity of single crystal diamond. By introducing dopants, the absorption edge increases to about 5.57eV, which should be ascribed to the formation of the 2D confined excitons formed by boron-nitrogen complexes inside diamond. The exciton formation and enlarged absorption edge mean that the binding energy of exciton is larger than the band gap of intrinsic diamond, which permits the formation of excitonic insulator similar with the case in narrow band gap semiconductors such as Ta\u003csub\u003e2\u003c/sub\u003eNiSe\u003csub\u003e5\u003c/sub\u003e\u003csup\u003e24\u003c/sup\u003e. Another UV-Vis spectroscopy result is shown in fig. S2 for sample 20240411, where the absorption edge increases to about 5.54eV, similar with sample 20240423-1. From Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eE, two peaks around 2848.7cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and 2918.1cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e in the infrared spectroscopy of the sample are clearly depicted, representing deep and shallow doped boron accepters respectively\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eF shows the Raman spectrum of the diamond, where the 1332.47cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e peak is ascribed to the first-order Raman scattering caused by the zero-center optical phonon mode, indicating no stress has been introduced into the epitaxial grown diamond. The peak around 1422.08cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e is resulting from N-V color centers, obviously showing that nitrogen dopants were heavily introduced into the sample. All the data and figures highlight that based on high quality grown 2D diamond, boron and nitrogen were uniformly and heavily co-doped into the sample, laying the groundwork for the formation of bounded excitons.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA shows the resistance as a function of temperature for sample 20240424-2-2 with a thickness of 9nm. As the temperature decreases, the resistance of the sample increases dramatically from 6kΩ at 300K to nearly 12MΩ at 61.1K. On one hand, lower temperature reduces thermal excitation of the carriers and makes boron accepters harder to be ionized, leading to lower conductivity. On the other hand, the wavelength of stable excitons formed in low temperature from boron and nitrogen centers becomes larger, causing the strong interaction among the neutral bosons and finally condensing into BEC status with higher resistance. The inset shows the derivation of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eA, representing the rate of the increment of the resistance, restating the sharp change of the resistance. To confirm the results, we reproduced several samples and measured them in different instruments. It turns out that the results are repeatable and the resistance-temperature relation of other three samples 20240411, 20240319-2 and 20240318 are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eB-D, respectively. The thickness of all the samples is below 15nm, and the resistance increases more than three orders while cooling down for most of them. Another four diamond samples and their resistance as a function of temperature are shown in fig. S3, presenting similar feature with samples mentioned above.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor comparison, we fabricated another three samples, named sample 20240409, 20240125 and 20250218, with thickness of 30nm, 90nm, and more than 1000nm, respectively. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eA shows the resistance of sample 20240409, which still behaves as an excitonic insulator with an increment of 2396 times from room temperature to about 22K. However, when sample becomes thicker, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eB, the rate of increment of resistance is much lower than that case in 2D. In sample 20250218 heavily doped by boron and nitrogen with a thickness of more than 1000nm shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eC, the resistance does not increase continuously with the decrement of temperature, and it changes less than 20% from 300K to 3K. The abovementioned comparative results indicate that with the increment of the thickness of the samples, the B-N co-doped diamond gradually lose the behavior of an excitonic insulator. From this point of view, the sharp increment of the resistance of 2D diamond should be ascribed to the formation of bounded excitons related with B-N complexes with large binding energy. As we pointed out above, 2D system tends to achieve larger exciton binding energy compared with 3D due to stronger quantum confinement effect, which enlarges the differences between the binding energy of exciton and band gap.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe choose sample 20240424-2-2 and 20240411 for deeper analysis. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eA shows the resistance of the sample as a function of temperature in logarithmic form. It is easier to notice that the resistance of the sample rises from less than 10kΩ in room temperature to more than 10MΩ around 61.1K. A slight but clear change in the slope of resistance occurs around 220K, indicating when temperature crosses critical temperature \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e, the conductive behavior of the sample is mainly caused by hopping behavior of the carriers due to excitons condensation. At temperature above \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e, the transport characteristic fits pretty well with Arrhenius model\u003csup\u003e\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e given by Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\rho\\:={\\rho\\:}_{0}\\text{e}\\text{x}\\text{p}\\left(\\frac{{E}_{A}}{{k}_{B}T}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eρ\u003c/em\u003e is the resistance of the sample, ρ\u003csub\u003e0\u003c/sub\u003e is a coefficient unrelated to temperature, \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003eA\u003c/em\u003e\u003c/sub\u003e is the activation energy, characterizing the difficulty for electrons to be thermally excited, k\u003csub\u003eB\u003c/sub\u003e is Boltzmann's constant and \u003cem\u003eT\u003c/em\u003e stands for temperature. It is obvious that \u003cem\u003elnR-T\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u0026minus;\u0026thinsp;1\u003c/em\u003e\u003c/sup\u003e function in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eB possesses great linearity above 220K with a coefficient of determination (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e) closed to 1.0, indicating a complete thermal excitation behavior for electrons. When the temperature continuously decreases, the resistance curve of the sample 20240424-2-2 steepens significantly within a small temperature range around 220K, which marks the phase transition of the 2D diamond. Below 220K, the wavelength of the excitons becomes overlapped, thus free carriers are strongly localized by the excitons, leading to the excitonic insulator status. Additionally, lower temperature results in less ionization of boron acceptors, further reducing the carrier density. In low temperature area, due to carrier localization by bounded excitons contributed by randomly distributed boron and nitrogen atoms, carriers tend to hop between two localized bounded excitons in the material, which is well known as variable range hopping (VRH) model, as predicted by N. F. Mott\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e,\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. In an interacting system like B-N co-dopped 2D diamond, VRH model indicates that the resistance will follow Efros and Shklovskii\u0026rsquo;s Law\u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e, given by Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e):\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:\\sigma\\:\\left(T\\right)\\propto\\:\\text{e}\\text{x}\\text{p}[-{\\left(\\frac{{T}_{0}}{T}\\right)}^{\\frac{1}{2}}]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is the characteristic temperature given by Eq.\u0026nbsp;(3)\u003csup\u003e30\u003c/sup\u003e:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{T}_{0}=\\frac{\\beta\\:{e}^{2}}{\\epsilon\\:{k}_{B}\\xi\\:}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cem\u003eβ\u003c/em\u003e is a coefficient and \u003cem\u003eβ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;6.5 for 2D system\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e, \u003cem\u003ee\u003c/em\u003e stands for elementary charge, \u003cem\u003eε\u003c/em\u003e is the dielectric constant for material and \u003cem\u003eξ\u003c/em\u003e represents the localization length, which defines the spatial extent of the electron\u0026rsquo;s wavefunction. From Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eC, it is obvious that the resistance of the sample fits well with VRH model below \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e with a big \u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/em\u003e\u003c/sup\u003e close to 1.0, confirming that carriers are confined by bounded excitons and begin to hop among the excitons, implying the stable presence of excitonic insulating phase for B-N co-doped 2D diamond. It is easy to calculate the localization length \u003cem\u003eξ\u003c/em\u003e\u0026thinsp;\u0026asymp;\u0026thinsp;38.9nm, revealing the long-range and strong interactions among the excitons, leading to the possibility of BEC status. Additionally, the localization length is much larger than the Bohr radius of excitons in diamond (\u0026lt;\u0026thinsp;1nm)\u003csup\u003e32,33\u003c/sup\u003e, so that the electrons can interact with each other strongly in a large scale. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eD-F shows another sample 20240411 for repeated confirmation, with a resistance from 1.08Ω at room temperature to more than 3000Ω around 42K. The marked critical temperature is about 208.3K, and the localization length \u003cem\u003eξ\u003c/em\u003e is 49.8nm. Another two samples mentioned in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eC and D and their fitting models are shown in fig. S4. Both of them exhibit similar and significant phase transition like sample 20240424-2-2 and 20240411, further confirming the excitonic insulating phase based on 2D diamond.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIt should be emphasized that the resistivity of the sample 20240424-2-2 drops very quickly while reaching the highest point, possibly pointing to the superfluid status of the BEC of bounded excitons in 2D diamond. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eA, the resistance rises from 6kΩ to 12MΩ at around 61.1K, but when temperature continuously decreases, resistance suddenly drops to about 2.5kΩ at low temperature. This abnormal transport behavior can possibly due to the long-range formation of superfluid of bounded excitons, which spans the entire material, so that free carriers can pair up into cooper pairs mediated by strong interaction between excitons and electrons, leading to higher conductivity. Negative resistance occurs around 30K as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eB, possibly because some of the electrons or holes are pulled out by the strong interaction between the cooper pairs and excitons, resulting in a reversed current direction in the method of four-probe resistance measurement. At extremely low temperature area below 20K, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eC and D, we find that the resistance remains stable relatively, and by increasing the flowing current through the sample at the value of 10\u0026micro;A, 100\u0026micro;A, 200\u0026micro;A, 500\u0026micro;A, 1000\u0026micro;A, 2000\u0026micro;A, 3000\u0026micro;A and 5000\u0026micro;A, respectively, the average resistance decreases linearly as a function of flowing current. When temperature lowers down to 20K, the superfluid status of excitons remains stable, providing stable and strong interaction between excitons and cooper pairs, so that exhibiting stable resistance with an unchanged current. However, as current increases, the formation of cooper pairs increases as a linear function of the current, leading to inversed linear function between resistance and biased current (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003eC and D). Another sample possibly behaves as a superfluid named 20240424-2-1 is presented in fig. S5, where similar transport characteristics occurs again with a resistance drops from 12MΩ to 2.4kΩ at 29.3K when the biased current is 10\u0026micro;A. Still negative resistance occurs at 16K and the average resistance decreases linearly as a function of flowing current below 10K. We have repeated the measurement on many B-N co-doped 2D diamond samples, which exhibit the similar behavior presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. Although the measurements on the mixed phased of exciton BEC superfluid and copper pairs induced superconductivity should be further investigated and standardized in the future, the repeated experimental results of the suddenly drop of the resistance at the highest value of the excitonic insulator state are confirmed. It should be noted that we have also repeated the measurements on three different Quantum design machines, where the same behavior can be reproduced. The conclusion of possible status of BEC superfluid of exciton in B-N co-doped diamond can be safely drawn herein.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn conclusion, we have demonstrated the existence of excitonic insulator and possible superfluid phase in B-N co-doped 2D diamond. The resistance rises dramatically by more than three orders and exhibits an obvious phase transition around 220K for one sample. Above \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e, the carriers behave as the Arrhenius law predicted, with thermal excitation as the dominant excitation in the system. While temperature cooled down below \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003eC\u003c/em\u003e\u003c/sub\u003e, excitons condense to form BEC due to large exciton binding energy resulting from quantum confinement effect. The variable range hopping model can be applied to describe the transport behavior of the B-N co-doped diamond with a large localization length of 38.9nm, which is in accordance with the characteristic of excitonic insulator. A sharp transition occurs at 61.1K where resistance suddenly drop and even exhibits negative value, and the resistance decreases as an inversed linear function with biased current at extremely low temperature, which possibly indicating the formation of superfluid state of excitons. Our work opens the avenue for searching excitonic insulator in wide bandgap materials, which further promotes the exciton-mediated superconductor or superfluid.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor contributions\u003c/h2\u003e \u003cp\u003eS. Lin designed and carried out the experiments, analyzed the data, conceived the study, and wrote the paper. S. Huang, carried out the experiments, analyzed the data, discussed the results and assisted writing the paper. M. Yang participated in the experiments, analyzed the data and discussed the mechanism, X. Chen participated the experiments and discussed the data, H. Bi and K. Xiong participated in the experiments. All authors contributed to the preparation of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgments\u003c/h2\u003e \u003cp\u003eS. Lin thanks the support from the National Natural Science Foundation of China (No. 51202216, 51551203, 61774135 and 62474161). S. Lin thanks for the kind discussion with Alexy Kavokin and many scientists or colleagues and those discussions are intriguing.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eJ\u0026eacute;rome D, Rice TM, Kohn W (1967) Excitonic insulator. Phys Rev 158:462\u0026ndash;475. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRev.158.462\u003c/span\u003e\u003cspan address=\"10.1103/PhysRev.158.462\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePieri P, Neilson D, Strinati GC (2007) Effects of density imbalance on the BCS-BEC crossover in semiconductor electron-hole bilayers. Phys Rev B Condens matter Mater Phys 75. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevB.75.113301\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevB.75.113301\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDebnath B, Barlas Y, Wickramaratne D, Neupane MR, Lake RK (2017) Exciton condensate in bilayer transition metal dichalcogenides: Strong coupling regime. Phys Rev B 96. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevB.96.174504\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevB.96.174504\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGupta S, Kutana A, Yakobson BI (2020) Univ. of California, O. C. A. Heterobilayers of 2D materials as a platform for excitonic superfluidity. Nat Commun 11:2989\u0026ndash;2989. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41467-020-16737-0\u003c/span\u003e\u003cspan address=\"10.1038/s41467-020-16737-0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFogler MM, Butov LV, Novoselov KS (2014) High-temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat Commun 5:4555\u0026ndash;4555. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/ncomms5555\u003c/span\u003e\u003cspan address=\"10.1038/ncomms5555\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLozovik YE, Kurbakov IL, Astrakharchik GE, Boronat J, Willander M (2007) Strong correlation effects in 2D Bose\u0026ndash;Einstein condensed dipolar excitons. Solid State Commun 144:399\u0026ndash;404. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ssc.2007.07.041\u003c/span\u003e\u003cspan address=\"10.1016/j.ssc.2007.07.041\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAllen JF, Misener AD (1938) Flow of Liquid Helium II. Nature 141:75\u0026ndash;75. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/141075a0\u003c/span\u003e\u003cspan address=\"10.1038/141075a0\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKavokin A et al (2022) Polariton condensates for classical and quantum computing. Nat Reviews Phys 4:435\u0026ndash;451. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s42254-022-00447-1\u003c/span\u003e\u003cspan address=\"10.1038/s42254-022-00447-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAllender D, Bray J, Bardeen J (1973) Model for an exciton mechanism of superconductivity. Phys Rev B 7:1020\u0026ndash;1029. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevB.7.1020\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevB.7.1020\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBardeen J, Excitonic superconductivity? (1978) J less-common Met 62:447\u0026ndash;450. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/0022-5088(78)90058-9\u003c/span\u003e\u003cspan address=\"10.1016/0022-5088(78)90058-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBardeen J, Cooper LN, Schrieffer JR (1957) Theory of Superconductivity. Phys Rev 108:1175\u0026ndash;1204. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRev.108.1175\u003c/span\u003e\u003cspan address=\"10.1103/PhysRev.108.1175\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLaussy FP, Kavokin AV, Shelykh IA (2010) Exciton-polariton mediated superconductivity. Phys Rev Lett 104:106402\u0026ndash;106402. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevLett.104.106402\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevLett.104.106402\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYin DL, Han RS (1987) Possible electron-exciton (E-E) interaction and high Tc superconductivity in bulk semimetals. Solid State Commun 63:645\u0026ndash;648. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/0038-1098(87)90871-4\u003c/span\u003e\u003cspan address=\"10.1016/0038-1098(87)90871-4\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFogler MM, Butov LV, Novoselov KS (2014) High-temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat Commun 5. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/ncomms5555\u003c/span\u003e\u003cspan address=\"10.1038/ncomms5555\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAlivisatos AP (1996) Semiconductor clusters, nanocrystals, and quantum dots. Science 271:933\u0026ndash;937. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1126/science.271.5251.933\u003c/span\u003e\u003cspan address=\"10.1126/science.271.5251.933\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eNovoselov KS, Mishchenko A, Carvalho A, Neto AH (2016) C. 2D materials and van der Waals heterostructures. Science 353. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1126/science.aac9439\u003c/span\u003e\u003cspan address=\"10.1126/science.aac9439\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDu L et al (1971) (2017) Evidence for a topological excitonic insulator in InAs/GaSb bilayers. \u003cem\u003eNature Communications\u003c/em\u003e 8. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41467-017-01988-1\u003c/span\u003e\u003cspan address=\"10.1038/s41467-017-01988-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang R, Sedrakyan TA, Wang B, Du L, Du R-R (2023) Excitonic topological order in imbalanced electron\u0026ndash;hole bilayers. Nature 619:57\u0026ndash;62. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41586-023-06065-w\u003c/span\u003e\u003cspan address=\"10.1038/s41586-023-06065-w\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLu YF et al (2017) Zero-gap semiconductor to excitonic insulator transition in Ta2NiSe5. Nat Commun 8:14408. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/ncomms14408\u003c/span\u003e\u003cspan address=\"10.1038/ncomms14408\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWang Z et al (2019) Evidence of high-temperature exciton condensation in two-dimensional atomic double layers. Nat (London) 574:76\u0026ndash;80. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41586-019-1591-7\u003c/span\u003e\u003cspan address=\"10.1038/s41586-019-1591-7\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKogar A et al (2017) Signatures of exciton condensation in a transition metal dichalcogenide. Sci (American Association Advancement Science) 358:1314\u0026ndash;1317. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1126/science.aam6432\u003c/span\u003e\u003cspan address=\"10.1126/science.aam6432\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eJackson KA, Pederson MR (1991) New theoretical model for the diamond 1s core exciton. Phys Rev Lett 67:2521\u0026ndash;2524. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRevLett.67.2521\u003c/span\u003e\u003cspan address=\"10.1103/PhysRevLett.67.2521\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhu Q, Karlsson KF, Pelucchi E, Kapon E (2007) Transition from Two-Dimensional to Three-Dimensional Quantum Confinement in Semiconductor Quantum Wires/Quantum Dots. Nano Lett 7:2227\u0026ndash;2233. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1021/nl0706650\u003c/span\u003e\u003cspan address=\"10.1021/nl0706650\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSeo Y-S et al (2018) Temperature-dependent excitonic superfluid plasma frequency evolution in an excitonic insulator, Ta2NiSe5. Sci Rep 8:1\u0026ndash;9. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41598-018-30430-9\u003c/span\u003e\u003cspan address=\"10.1038/s41598-018-30430-9\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWedepohl PT (1957) Electrical and Optical Properties of Type IIb Diamonds. \u003cem\u003eProceedings of the Physical Society. Section B\u003c/em\u003e 70, 177\u0026ndash;185 \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1088/0370-1301/70/2/303\u003c/span\u003e\u003cspan address=\"10.1088/0370-1301/70/2/303\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePearson GL, Bardeen J (1949) Electrical properties of pure silicon and silicon alloys containing boron and phosphorus. Phys Rev 75:865\u0026ndash;883. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1103/PhysRev.75.865\u003c/span\u003e\u003cspan address=\"10.1103/PhysRev.75.865\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMott NF (1968) Conduction in glasses containing transition metal ions. J Non-cryst Solids 1:1\u0026ndash;17. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/0022-3093(68)90002-1\u003c/span\u003e\u003cspan address=\"10.1016/0022-3093(68)90002-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMott NF (1967) Electrons in disordered structures. Adv Phys 16:49\u0026ndash;144. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1080/00018736700101265\u003c/span\u003e\u003cspan address=\"10.1080/00018736700101265\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEfros AL, Shklovskii BI (1975) Coulomb gap and low temperature conductivity of disordered systems. J Phys C Solid state Phys 8:L49\u0026ndash;L51. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1088/0022-3719/8/4/003\u003c/span\u003e\u003cspan address=\"10.1088/0022-3719/8/4/003\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eOrtu\u0026ntilde;o M, Estell\u0026eacute;s-Duart F, Somoza AM (2022) Numerical Simulations of Variable-Range Hopping. \u003cem\u003ePhysica Status Solidi (B) Basic Research\u003c/em\u003e 259, n/a-n/a \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/pssb.202100340\u003c/span\u003e\u003cspan address=\"10.1002/pssb.202100340\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eLien NV (1995) Crossovers in two-dimensional variable range hopping. Phys Lett A 207:379\u0026ndash;384. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/0375-9601(95)00666-Q\u003c/span\u003e\u003cspan address=\"10.1016/0375-9601(95)00666-Q\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGheeraert E, Koizumi S, Teraji T, Kanda H, Nesl\u0026aacute;dek M (1999) Electronic States of Boron and Phosphorus in Diamond. Phys status solidi Appl Res 174:39\u0026ndash;51. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1002/(SICI)1521-396X(199907)174:1\u0026lt;39::AID-PSSA39\u0026gt;3.0.CO;2-E\u003c/span\u003e\u003cspan address=\"10.1002/(SICI)1521-396X(199907)174:1%3C39::AID-PSSA39%3E3.0.CO;2-E\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSharp SJ, Collins AT, Davies G, Joyce GS (1997) Higher resolution studies of shallow bound exciton luminescence in diamond. J Phys Condens matter 9:L451\u0026ndash;L455. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1088/0953-8984/9/33/003\u003c/span\u003e\u003cspan address=\"10.1088/0953-8984/9/33/003\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6807758/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6807758/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eRecent research on excitonic insulator has progressed mainly based on narrow bandgap semiconductor or semimetal. Herein, we realize excitonic insulator based on two-dimensional (2D) wide band gap diamond with transition temperature as high as 220K. The resistance rises dramatically by more than three orders, which can be explained by the Bose-Einstein condensation (BEC) of excitons. While cooling down below transition temperature, the wavelength of the bounded exciton caused by boron and nitrogen centers becomes highly overlapped, leading to BEC process. Furthermore, the variable hopping mechanism is confirmed in agreement with the exciton transport process. When temperature drops down further, a sudden drop of resistance over three orders was observed around 60K, possibly due to the formation of excitonic superfluid resulting from highly overlap of wavelength of the large density bounded excitons at lower temperature. This study provides evidences for excitonic insulator and possible superfluid phase based on wide bandgap semiconductor.\u003c/p\u003e","manuscriptTitle":"High Temperature Excitonic Insulator and Possible Superfluid Based on Two-Dimensional Diamond","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-11 12:22:32","doi":"10.21203/rs.3.rs-6807758/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"communications-materials","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"commsmat","sideBox":"Learn more about [Communications Materials](https://www.nature.com/commsmat/)","snPcode":"","submissionUrl":"","title":"Communications Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Communications Series","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"3236849d-e85e-4c30-8a90-8948c88b1c9a","owner":[],"postedDate":"June 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":49776179,"name":"Physical sciences/Physics/Condensed-matter physics/Phase transitions and critical phenomena"},{"id":49776180,"name":"Physical sciences/Materials science/Condensed-matter physics/Phase transitions and critical phenomena"}],"tags":[],"updatedAt":"2025-09-11T08:02:14+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-11 12:22:32","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6807758","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6807758","identity":"rs-6807758","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}