Parity Breaking and Sublattice Dichotomy in Monolayer FeSe Superconductor

Parity Breaking and Sublattice Dichotomy in Monolayer FeSe Superconductor | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Parity Breaking and Sublattice Dichotomy in Monolayer FeSe Superconductor Lili Wang, Cui Ding, Zhipeng Xu, Xiaotong Jiao, Yinqi Hu, Wenxuan Zhao, and 5 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4705720/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract A unit cell represents the smallest repeating structure in solid-state physics and serves as the fundamental building block of a material. In iron-based superconductors, each unit cell contains two iron atoms, which form two distinct sublattices in the two-dimensional iron layers. Under normal circumstances, these sublattices are expected to have identical physical properties due to space inversion symmetry. However, we discover that this sublattice structure can introduce a novel degree of freedom for probing unconventional pairing mechanisms in iron-based superconductors. Through molecular-beam epitaxy, we have successfully grown monolayer FeSe films with atomically homogeneous (1 × 1) structures on SrTiO₃(001) substrates. In these films, we observe distinct dual tunneling spectra within pairing gap energy corresponding to the two sublattices, a phenomenon we term sublattice dichotomy . This dichotomy can be quantitatively explained by a parity-breaking superconducting state, characterized by the coexistence of conventional pairing and interband parity pairing. The interband singlet pairing arises due to the lacking of inversion symmetry, which is naturally broken from the interface coupling between FeSe and the SrTiO₃ surface. Physical sciences/Physics/Condensed-matter physics/Superconducting properties and materials Physical sciences/Physics/Condensed-matter physics/Surfaces, interfaces and thin films Figures Figure 1 Figure 2 Figure 3 Figure 4 Full Text Monolayer FeSe grown on SrTiO 3 (001) is one unique iron-based high-temperature superconductor that boosts Cooper pairs at a record temperature of above 65 K 1-4 ,greatly higher than its bulk counterpart value of 9-14 K and up to 48 K under heavy doping 5-10 . Since it was discovered in 2012 1 , tremendous efforts have been spent on reproducing, analyzing, and generalizing this unexpected finding 2-4,11-24 . The monolayer FeSe only contains Fermi surfaces around the Brillouin zone corner while the common iron superconductors have another group of Γ hole pockets 2,4,11-14 . How the superconducting features deviate from other iron-based superconductors is widely debated. However, owing to the diverse interface structures, the understanding of the physical properties of monolayer FeSe, especially their superconducting nature, remains elusive. The primitive unit cell of a single iron-based superconducting layer contains two Fe sublattices that bond alternately with upper-layer Se (Se + ) and bottom-layer Se (Se - ), i.e., α-Fe aligned in Se - -[100] and Se + -[010] and β-Fe otherwise as illustrated in Fig. 1(a). For the monolayer FeSe/SrTiO 3 , the distances between the Se + -Fe plane and the Se - -Fe plane become asymmetric due to interface coupling 25-27 , which leads to two inequivalent Fe sublattices. Moreover, as a result of interface charger transfer, there are simply only two Fermi surfaces around M points, as disclosed by angle-resolved photoemission spectroscopy (ARPES) measurement and presented in Fig. 1(b). In theoretical models for iron-based superconductors based on 1-Fe unit cells, there are two possible pairing schemes, the normal intraband pairing and the interband pairing, illustrated by the black and red double-arrows, respectively. The normal pairings are zero total momentum Cooper pairs between k and - k , while the interband pairings are Cooper pairs between k and - k + Q , which is allowed as the momentum vector Q = (π, π) is a reciprocal lattice vector for the genuine 2-Fe unit cell. Notice that, the normal pairing and the interband pairing have opposite parity values without mixing. The interband pairing between k and - k + Q was proposed and classified by Hu as the η- pairing in Ref. [ 28 ], while their consequences remain unexplored. The broken inversion symmetry at the FeSe/SrTiO 3 interface allows the coexistence of two types of pairings. Therefore, the monolayer FeSe offers an opportunity to explore possible novel pairings. In this work, we carry out a systematic investigation of molecular beam epitaxial (MBE) monolayer FeSe with an atomically homogeneous (1 × 1) surface structure on SrTiO 3 (001) using atomic-resolution scanning tunneling microscopy/spectroscopy (STM/STS). We find the tunneling spectra of α-Fe and β-Fe are significantly different, resulting in the sublattice dichotomy in tunneling spectra coherence peaks as illustrated in Fig. 1(c). More specifically, monolayer FeSe is one two-band system with dual-gap 1,16,22 , i.e., one pair of inner gap coherence peaks at ± V i and the other pair of outer gap coherence peaks at ± V o . We find the coherence peak at - V i for α-Fe is lower than β-Fe while the coherence peak at + V i for α-Fe is higher than β-Fe with a similar amount. Moreover, opposite intensity contrast at ± V o coherence peaks to those at ± V i for each sublattice. This sublattice dichotomy can only be explained by the substantial coexistence of both normal pairing and interband pairing in the superconducting state. To characterize the surface structure, we collect the bias-dependent atomic resolution topography of the monolayer FeSe and summarize the results in Fig. S1 in supplemental materials (SM). Plotted in Figs. 2 (a) and (b) are the atomic resolution topography images taken at sample bias V s = 80 meV and V s = -50 meV, respectively, presenting the Se + (001)-(1 × 1) surface, instead of the ubiquitous (2 × 1) orders observed previously 1,16,20 . In the inserted fast Fourier transformed (FFT) images, the sharp Q a and Q b Bragg spots corresponding to the (1 × 1) primitive unit cell give expanded in-plane lattice constants of 3.89 Å compared with the bulk value of 3.78 Å 6 , which shows that the FeSe monolayer is fully strained to the SrTiO 3 (001). As exemplified in Fig. 2(b), the density of states from Fe sites increases upon the tip in closer proximity to the surface; correspondingly, in addition to the sharp ( Q a , Q b )Bragg spots, the Q x and Q y Bragg spots of the 1-Fe sublattice emerge. With the differing tunneling currents in the triple-layer, Se - atom sites, Fe atom sites, and Se + atom sites are individually discerned. As depicted in the bottom inset zoom-in topography image, the apparent atomic contrast matches well with the superimposed lattice model. The direct atomic resolution probe of the perfect (1 × 1) surface is the foundation for exploring the intrinsic sublattice feature in the Fe-layer. We collect atomic-site-dependent tunneling spectra to extract the electronic structure. As summarized in Fig. 2(c), the typical large-bias tunneling spectra, taken at the four atomic sites in one 2-Fe unit cell (bottom panel), present the filled states below the Fermi level ( E F ) consistent with the specific orbitals (top panel) disclosed by ARPES, additionally, empty states above the E F . The tunneling conductance around E F ranging from -50 meV to 60 meV is quite low due to the low tunneling probability of the M -centered electron bands (inferred as δ), which is lower and flatter for Fe sites than for Se sites. The spectra upturn around -80 meV (σ) belongs to the Γ -centered t 2g hole band edge, while the unoccupied upturn around 100 meV (λ) and the occupied hump below -350 meV (ξ­) to the Γ -centered e g orbital. Compared with the common monolayer FeSe (2 × 1) surface 20 , the Γ -centered e g bands are shifted downward by ~ 100 meV. Plotted in Fig. 2(d) are the corresponding small-bias tunneling spectra within the bias range (-30, + 30) meV. The tunneling spectra present the standard dual-gap structures with the inner coherence peak ± V i around ±10 meV and the outer coherence peaks ± V o around ±(15-17) meV, which are also consistent with previous works 1,16,22 . Interestingly, all the pairing gaps exhibit strong particle-hole asymmetry, which can be categorized into α-Fe and Se - group and β-Fe and Se + group. The former group exhibits strikingly higher + V i coherence peaks than the latter one. To eliminate the tunneling matrix contrast for different layers, we then focus on the Fe layer and collect detailed low-energy tunneling spectra at each Fe site. The normalized tunneling spectra along the three [100]-running cuts marked in Fig. 3(a) are plotted in Fig. 3(c) (with the corresponding raw spectra and normalization process summarized in Fig. S2). These tunneling spectra along each cut are almost homogeneous, exhibiting the sharp ± V i coherence peaks around ±10 meV and widened ± V o coherence peaks wiggled within an energy range ±(15-17) meV. The outer gap variation is likely from the local electronic modulation owing to the SrTiO 3 substrate 29 . In contrast, the inner coherence peaks are close to the E F , resulting in a relatively small gap variation. One special point is that the tunneling spectra are particle-hole asymmetric. The spectra for the α-Fe along the yellow dashed-line cut-1 (left panel) consistently exhibit much higher inner gap coherence peaks on the hole sides + V i . The tunneling spectra of the α-Fe along the yellow dashed-line cut-2, as plotted in the middle panel, show similar behaviors: the hole side of the inner coherence peak + V i is still higher than the electron side - V i . Surprisingly, a new feature emerges from the asymmetric tunneling spectra at ± V i for β-Fe. As identified from the spectra taken along the green dashed-line cut-3 plotted in the right panel, the electron sideof the inner coherence peak - V i becomes higher than the hole side + V i . Hence, the tunneling spectra for the α-Fe and β-Fe are completely different, resulting in a sublattice dichotomy for the tunneling spectra. To further demonstrate this sublattice dichotomy feature, we take a complete scan of the area in Fig. 3(a) for the statistics. We define a ratio of inner-gap coherence peak intensity Z ( r , V i ) = g ( r , V i )/ g ( r , - V i ), where g ( r , V ) ≡ d I /d V ( r , V ), and plot the ratios Z ( r , V i ) at V i = 10 meV in Fig. 3(b). The Z ( r , V i ) is always larger than 1 for α-Fe but smaller than1 for β-Fe. This particle-hole intensity switching behavior at ± V i is the sublattice dichotomy defined in Fig. 1(c). On the other hand, the widening ± V o coherence peaks within ± (15-17) meV resulting in large errors in Z ( r , V o ). Hence, we try another strategy using g ( r , V ) mapping to show the sublattice dichotomy further and plot the g ( r , ± V o ) with V o = 15 meV in Fig. 3(d). Compared with the β-Fe sites, the α-Fe sites consistently show decreased intensities at the hole side + V o and increased intensities at the electron side - V o , which is exactly opposite to the electron-hole intensity contrast at ± V i summarized in Fig. 3(b). Therefore, the results shown in Fig. 3 completely present the Fe-sublattice dichotomy illustrated in Fig. 1(c). In the SM, we plot a series of g ( r , V ) mapping images at ± V i and ± V o obtained simultaneously and the corresponding phase-referenced FFT on another sample (Fig. S3), which shows the reproducibility and robustness of the sublattice dichotomy effect. In contrast, there are no sublattice dichotomy features above T c at liquid nitrogen temperature (Fig. S4). We briefly summarize our findings here. The distinct dual tunneling spectra corresponding to the two sublattices are presented by the two typical tunneling spectra of α-Fe and β-Fe plotted in Fig. 4(a). For the inner-gap coherence peaks, the α-Fe has a more pronounced hole peak at + V i while the β-Fe has a more pronounced electron peak at - V i . On the other hand, the outer-gap coherence peaks at ± V o show a reverse behavior to the inner-gap coherence peaks at ± V i . More precisely, the + V i tunneling weight at α-Fe is almost equal to the - V i tunneling weight at β-Fe and vice versa. Notably, we check the d I /d V tunneling spectra and g ( r , V ) mapping images of the common FeSe-(2 × 1) surface (Fig. S5) and observe the sublattice dichotomy features as well, though weakened due to the electronic modulation 30,31 . Furthermore, associated with the occurrence of checkerboard order under reduced in-plane anisotropy, this dichotomy feature is indiscernible 32 . This unexpected intrinsic phenomenon points to a highly unusual pairing function inside the monolayer FeSe. It is clear that the space inversion symmetry is broken if there is a sublattice dichotomy. As we have mentioned in the introduction, for the monolayer FeSe on SrTiO 3 (001), the space inversion symmetry is broken at the coherent interface. However, the effect of the symmetry breaking on the electronic physics is largely unclear and has been ignored in both theoretical modeling and experimental studies. The absence of the inversion symmetry allows the normal pairing and interband pairings to coexist. This odd parity interband pairing is known to produce the two-gap feature 28 . Therefore, it is natural to ask whether the combined action of interbandpairing and normal pairing can produce the dichotomy effect 33 . To capture the above physics and monolayer FeSe electronic structure, we follow the k · p model around the M point based on the symmetry of FeSe 34 , and then, add bothinterband pairing and normal pairing into the k · p model. The local density of states (DOSs) at two sublattice sites are further calculated respectively (See the model details in SM). The tunneling DOSs for α-Fe and β-Fe are plotted in Fig. 4(b). Our theoretical simulation captures the sublattice dichotomy effect nicely. Furthermore, in Fig. 4(b), the tunneling spectrum around zero bias at α-Fe slightly shifts towards the negative voltage while the tunneling spectrum at β-Fe shifts opposite towards the positive voltage. This is the local particle-hole symmetry feature of interband pairing 33 . This feature is also visible in the experimental findings shown in Fig. 4(a). It is important to note that neither the normal pairing nor the interbandpairing individually can produce the dichotomy effect (Figs. S6(c, d)). It is also possible that the normal state already contains the symmetry-breaking effects. However, this normal state with normal pairing can only lead to sublattice difference without particle-hole asymmetry (Fig. S6(e)) rather than the sublattice dichotomy found here. Hence, the interbandpairing is an essential component of the sublattice dichotomy that we observed. In summary, we perform a systematic investigation on the sublattice degree of freedom of the monolayer FeSe. We successfully grow monolayer FeSe with an exclusive (1 × 1) surface on the SrTiO 3 (001) substrate by MBE and then analyze the electronic structure by STS in combination with ARPES. We successfully identify dual-gap superconducting coherence peaks at ± V i and ± V o . By comparing the tunneling spectra at α-Fe and β-Fe, we find sublattice dichotomy effects. More precisely, the coherence peak of α-Fe at + V i is higher than β-Fe while the coherence peak of β-Fe at - V i is also higher than α-Fe with a similar difference. We also observe a reversed contrast at ± V o . We have shown that the coexistence of the normal pairing between k and - k and the interbandpairing between k and - k + Q is the key mechanism for this sublattice dichotomy. This interband pairing is also the extension of the η- pairing classified in Refs. [ 28, 35, 36 ]. The exceptionally high superconducting transition temperature in the monolayer FeSe remains a central unresolved question in the field of iron-based superconductors. Deciphering the pairing structure in monolayer FeSe is key to addressing this mystery. Our research discovers a novel superconducting state in the monolayer FeSe on SrTiO₃, placing significant constraints on possible pairing configurations, as well as pairing mechanisms. Specifically, our findings suggest that the T c enhancement arises from the activation of a new pairing channel, namely, the interband pairing. Traditionally, the interband pairing is not expected to dominate over the intraband pairing as the primary instability; however, our observation of sublattice dichotomy requires a strong interband pairing, which cannot be simply understood as a conventional Fermi surface instability. The T c enhancement in the monolayer FeSe has generated intriguing conjectures on the pairing mechanisms including interfacial electron-phonon enhancement 13,23,24 and incipient pairing mechanism 37-40 . However, all of these proposals have not specified such a large interband pairing component. Therefore, our results offer fresh insights to examine the pairing mechanisms in monolayer FeSe and underscore the complex and rich physics associated with sublattice degrees of freedom. Sample preparation Our experiments were carried out in a Createc ultrahigh vacuum (1.0 × 10 -10 mbar) low-temperature (4.8 K) STM system equipped with an MBE chamber. The Nb-doped SrTiO 3 (001) (0.05 wt.%) substrates were annealed above 1000 ◦ Cto obtain dual-TiO 2-δ -termination. Monolayer FeSe films were prepared by standard co-evaporating and post-annealing, with a deposition rate of ∼0.02 monolayer per minute at a substrate temperature of 470 ◦ C. STM experiments All STM measurements were performed in a constant current mode (tunneling current set point I t = 500 pA) with the bias voltage applied to the sample ( V s ), using a polycrystalline PtIr tip. The differential conductance d I /d V spectra, characterizing the local density of states around the E F , are measured by disabling the feedback circuit, sweeping the sample voltage V s , and then extracting the differential tunneling current d I /d V using a standard lock-in technique with a small bias modulation (∼1% of the sweeping range) at 937 Hz. ARPES experiments The FeSe/SrTiO 3 sample was in-situ transferred to the ARPES chamber and measured under an ultrahigh vacuum below 1.5 × 10 -10 mbar. Data were collected using a DA30 analyzer and a Scienta VUV 5050 helium lamp at 80 K. The energy and angular resolutions were set to 10 meV and 0.2 ◦ , respectively. The Fermi surfaces, deduced from our ARPES measurements, consist of two overlapped ellipse-like electron pockets around each Brillouin zone (BZ) corner ( M x and M y ), consistent with the previous ARPES results 2,4,11-14 . Declarations Competing Interests The authors declare no competing interests. Author Contributions C. D. and X. J. carried out the STM experiments; Q. H., W. Z. and L. Y. performed the ARPES experiments; L. W., J-F. J. and Q-K. X. designed and coordinated the experiments; Z-P. X, K. J. and J-P. H. performed the theoretical analysis. K. J., L. W. and J-P. H. wrote the manuscript with comments from all authors. Acknowledgment The work is supported by the National Natural Science Foundation of China (Grant No. 92477204, No. 52388201, No. 1888101, No. 12174428, No. 11920101005), the National Key Research and Development Program of China (Grant No. 2022YFA1403100 and No. 2022YFA1403900), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB28000000 and No. XDB33000000), the New Cornerstone Investigator Program, the Chinese Academy of Sciences Project for Young Scientists in Basic Research (2022YSBR-048). References Wang, Q.-Y. et al. Interface-induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO 3 . Chin. Phys. 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Chen, X., Maiti, S., Linscheid, A. & Hirschfeld, P. J. Electron pairing in the presence of incipient bands in iron-based superconductors. Phys. Rev. B 92, 224514 (2015). Linscheid, A., Maiti, S., Wang, Y., Johnston, S. & Hirschfeld, P. J. High T c via spin fluctuations from incipient bands: application to monolayers and intercalates of FeSe. Phys. Rev. Lett. 117, 077003 (2016). Kreisel, A., Hirschfeld, P. J. & Andersen, B. M. On the remarkable superconductivity of FeSe and its close cousins. Symmetry 12, 1402 (2020). Additional Declarations There is NO Competing Interest. Supplementary Files FeSeSM0122.docx Supplementary materials Cite Share Download PDF Status: Posted 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. 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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-4705720","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":414169096,"identity":"29316e0d-15be-4fdf-81c6-c80e52eee593","order_by":0,"name":"Lili Wang","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0001-6035-1660","institution":"Tsinghua University","correspondingAuthor":true,"prefix":"","firstName":"Lili","middleName":"","lastName":"Wang","suffix":""},{"id":414169097,"identity":"76145175-23a1-4b5a-a467-3df8c7a03c5a","order_by":1,"name":"Cui Ding","email":"","orcid":"","institution":"Tsinghua University","correspondingAuthor":false,"prefix":"","firstName":"Cui","middleName":"","lastName":"Ding","suffix":""},{"id":414169098,"identity":"f15c34c2-a04f-46e9-abb5-6646b55282ab","order_by":2,"name":"Zhipeng Xu","email":"","orcid":"","institution":"Institute of Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Zhipeng","middleName":"","lastName":"Xu","suffix":""},{"id":414169099,"identity":"4a0c42d5-7250-4b65-93e0-c6f2030bc0a7","order_by":3,"name":"Xiaotong Jiao","email":"","orcid":"","institution":"Tsinghua University","correspondingAuthor":false,"prefix":"","firstName":"Xiaotong","middleName":"","lastName":"Jiao","suffix":""},{"id":414169100,"identity":"2b89efab-cf2a-46b7-8988-5aa493dffeed","order_by":4,"name":"Yinqi Hu","email":"","orcid":"https://orcid.org/0009-0005-6277-6327","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Yinqi","middleName":"","lastName":"Hu","suffix":""},{"id":414169101,"identity":"df47bcb3-47db-4f31-9a64-7f195560a2d7","order_by":5,"name":"Wenxuan Zhao","email":"","orcid":"","institution":"Tsinghua University","correspondingAuthor":false,"prefix":"","firstName":"Wenxuan","middleName":"","lastName":"Zhao","suffix":""},{"id":414169102,"identity":"def8b44a-57ca-48e3-ba5f-789151e70d1a","order_by":6,"name":"Lexian Yang","email":"","orcid":"https://orcid.org/0000-0002-0078-1797","institution":"Tsinghua","correspondingAuthor":false,"prefix":"","firstName":"Lexian","middleName":"","lastName":"Yang","suffix":""},{"id":414169103,"identity":"40dab643-a599-4198-9652-bcdfa7931f6c","order_by":7,"name":"Kun Jiang","email":"","orcid":"https://orcid.org/0000-0003-1136-2472","institution":"Institute of Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Kun","middleName":"","lastName":"Jiang","suffix":""},{"id":414169104,"identity":"b7179db3-9483-4a98-9566-fd1acca6b297","order_by":8,"name":"Jinfeng Jia","email":"","orcid":"https://orcid.org/0000-0002-9900-281X","institution":"Shanghai Jiao Tong University","correspondingAuthor":false,"prefix":"","firstName":"Jinfeng","middleName":"","lastName":"Jia","suffix":""},{"id":414169105,"identity":"093129b3-1f66-4b64-9ac3-5f875b7a372f","order_by":9,"name":"Jiangping Hu","email":"","orcid":"https://orcid.org/0000-0002-4837-7742","institution":"Institute of Physics, Chinese Academy of Sciences","correspondingAuthor":false,"prefix":"","firstName":"Jiangping","middleName":"","lastName":"Hu","suffix":""},{"id":414169106,"identity":"391c4a96-b821-48a7-9949-77165e7f4be1","order_by":10,"name":"Qi-Kun Xue","email":"","orcid":"https://orcid.org/0000-0002-4129-1284","institution":"Southern University of Science and Technology","correspondingAuthor":false,"prefix":"","firstName":"Qi-Kun","middleName":"","lastName":"Xue","suffix":""}],"badges":[],"createdAt":"2024-07-08 12:56:57","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4705720/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4705720/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":76365672,"identity":"ebf4ee29-136f-4cbf-8ea9-507a8b3c94b1","added_by":"auto","created_at":"2025-02-15 15:52:22","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":291514,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic of the lattice of monolayer FeSe showing two inequivalent sublattices. The Fe atoms aligned in Se\u003csub\u003e-\u003c/sub\u003e-[100] and Se\u003csub\u003e+\u003c/sub\u003e-[010] are labeled as α-Fe (red balls), and the other ones as β-Fe (blue balls). The shaded square marks the primitive unit cell that contains two Fe sublattices, and the green dot labeled at the midpoint of the adjacent Fe sublattices indicates the position of the inversion operator for the bulk FeSe. (b) The Fermi surface and the systematic illustration of the normal pairing between (k↑,-k↓) (black double-arrow) and the interband pairing between (k↑,-k+Q↓) (red double-arrow), where \u003cem\u003eQ \u003c/em\u003e= (π, π) (red double-dot). The Fermi surface is represented by the photoemission intensity map around \u003cem\u003eM\u003c/em\u003e\u003csub\u003ex\u003c/sub\u003e\u003cem\u003e \u003c/em\u003eand \u003cem\u003eM\u003c/em\u003e\u003csub\u003ey\u003c/sub\u003e at the Fermi energy at 80 K, symmetrized with respect to the Γ point. The intensity was integrated over a window (\u003cem\u003eE\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e- 25 meV, \u003cem\u003eE\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e+ 15 meV). (c) Schematic tunneling spectra in α-Fe and β-Fe sublattices show the sublattice dichotomy.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-4705720/v1/378a273b7c58ce62eb804883.png"},{"id":76365669,"identity":"a1a44ca2-281e-4367-9f1b-c36966aef633","added_by":"auto","created_at":"2025-02-15 15:52:22","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":758370,"visible":true,"origin":"","legend":"\u003cp\u003e(a) and (b) Bias-dependent atomic resolution topography of monolayer FeSe, with the corresponding FFT patterns inserted showing exclusive (1 × 1) Bragg spots. The superimposed red (blue) balls mark α-Fe (β-Fe) sites, and dark (light) orange balls mark Se\u003csub\u003e+ \u003c/sub\u003e(Se\u003csub\u003e-\u003c/sub\u003e) sites. (c) Large-bias tunneling spectra taken at the four Fe/Se atom sites labeled in the inset, with the deduced electronic bands, in combination with ARPES results, plotted in the upper panel. (d) Small-bias tunneling spectra taken at the same sites. The spectra are offset for clarity, with horizontal dashed lines indicating zero conductance. The vertical dashed lines in (d) are eye guides for the coherence peaks ±\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e and ±\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e. Setpoint: (a), \u003cem\u003eV\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e= 80 mV; (b), \u003cem\u003eV\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e= -50 mV; (c), \u003cem\u003eV\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e= 500 mV; and (d), \u003cem\u003eV\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e= 50 mV.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4705720/v1/31d54ccceb4b451505003818.png"},{"id":76366532,"identity":"95c07b74-7c33-4462-a22b-3900348205d4","added_by":"auto","created_at":"2025-02-15 16:08:22","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":769452,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Atomic resolution topography of the monolayer FeSe on the SrTiO\u003csub\u003e3\u003c/sub\u003e(001) surface with the schematic of Fe sites overlaid. (b) Mosaic plots of \u003cem\u003eZ\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e) = \u003cem\u003eg\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, +\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e)/\u003cem\u003eg\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, -\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e) of Fe sites as depicted in (a). \u003cem\u003eZ\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e) \u0026gt; 1 for α-Fe and \u003cem\u003eZ\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e) \u0026lt; 1 for β-Fe. (c) Normalized d\u003cem\u003eI\u003c/em\u003e/d\u003cem\u003eV\u003c/em\u003e tunneling spectra taken along the [100]-running rows of α-Fe (line cuts #1 and #2) and β-Fe (line cut #3) highlighted in (a). (d) Atomic resolution \u003cem\u003eg\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, ±\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e) mapping images, showing sublattice-reversed intensity contrast that is opposite to the \u003cem\u003eZ\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e in (b). Setpoint: (a), \u003cem\u003eV\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e= -50 mV; (b, c), \u003cem\u003eV\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e= 50 mV; (d) \u003cem\u003eV\u003c/em\u003e\u003csub\u003es\u003c/sub\u003e\u003cem\u003e \u003c/em\u003e= ± 15 mV.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4705720/v1/f5f9d433adc709cdf35b956e.png"},{"id":76365673,"identity":"bd58b4e4-5dd6-4218-9dd5-50b4e8a88a41","added_by":"auto","created_at":"2025-02-15 15:52:22","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":61021,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Two typical tunneling spectra at α-Fe and β-Fe showing the sublattice dichotomy effect. (b) The calculated tunneling DOS at two Fe-sites based on the \u003cem\u003e\u003cstrong\u003ek\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e \u003c/em\u003e· \u003cem\u003e\u003cstrong\u003ep\u003c/strong\u003e\u003c/em\u003e\u003cem\u003e \u003c/em\u003emodel with both normal pairing and interband\u003cem\u003e \u003c/em\u003epairing.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4705720/v1/45787acde68e9ab33d81202d.png"},{"id":88879021,"identity":"14f59913-15a6-4c7c-9d5f-96643ec3e74b","added_by":"auto","created_at":"2025-08-12 10:44:37","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2258429,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4705720/v1/a42d7fc6-0078-4239-a5b0-2e9fb86de9d5.pdf"},{"id":76365687,"identity":"32e8b42e-e7c4-4ced-9df9-cfdfc0fa0d07","added_by":"auto","created_at":"2025-02-15 15:52:23","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":48474397,"visible":true,"origin":"","legend":"Supplementary materials","description":"","filename":"FeSeSM0122.docx","url":"https://assets-eu.researchsquare.com/files/rs-4705720/v1/4bca3aeba0f2a9beef422b60.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Parity Breaking and Sublattice Dichotomy in Monolayer FeSe Superconductor","fulltext":[{"header":"Full Text","content":"\u003cp\u003eMonolayer FeSe grown on SrTiO\u003csub\u003e3\u003c/sub\u003e(001) is one unique iron-based high-temperature superconductor that boosts Cooper pairs at a record temperature of above 65 K\u003csup\u003e1-4\u003c/sup\u003e,greatly higher than its bulk counterpart value of 9-14 K and up to 48 K under heavy doping\u003csup\u003e5-10\u003c/sup\u003e. Since it was discovered in 2012\u003csup\u003e1\u003c/sup\u003e, tremendous efforts have been spent on reproducing, analyzing, and generalizing this unexpected finding\u003csup\u003e2-4,11-24\u003c/sup\u003e. The monolayer FeSe only contains Fermi surfaces around the Brillouin zone corner while the common iron superconductors have another group of \u0026Gamma; hole pockets\u003csup\u003e2,4,11-14\u003c/sup\u003e. How the superconducting features deviate from other iron-based superconductors is widely debated. However, owing to the diverse interface structures, the understanding of the physical properties of monolayer FeSe, especially their superconducting nature, remains elusive.\u003c/p\u003e\n\u003cp\u003eThe primitive unit cell of a single iron-based superconducting layer contains two Fe sublattices that bond alternately with upper-layer Se (Se\u003csub\u003e+\u003c/sub\u003e) and bottom-layer Se (Se\u003csub\u003e-\u003c/sub\u003e), i.e., \u0026alpha;-Fe aligned in Se\u003csub\u003e-\u003c/sub\u003e-[100] and Se\u003csub\u003e+\u003c/sub\u003e-[010] and \u0026beta;-Fe otherwise as illustrated in Fig. 1(a). For the monolayer FeSe/SrTiO\u003csub\u003e3\u003c/sub\u003e, the distances between the Se\u003csub\u003e+\u003c/sub\u003e-Fe plane and the Se\u003csub\u003e-\u003c/sub\u003e-Fe plane become asymmetric due to interface coupling\u003csup\u003e25-27\u003c/sup\u003e, which leads to two inequivalent Fe sublattices. Moreover, as a result of interface charger transfer, there are simply only two Fermi surfaces around M points, as disclosed by angle-resolved photoemission spectroscopy (ARPES) measurement and presented in Fig. 1(b). In theoretical models for iron-based superconductors based on 1-Fe unit cells, there are two possible pairing schemes, the normal intraband pairing and the interband pairing, illustrated by the black and red double-arrows, respectively. The normal pairings are zero total momentum Cooper pairs between\u003cstrong\u003e\u003cem\u003e\u0026nbsp;k\u003c/em\u003e\u003c/strong\u003eand -\u003cstrong\u003e\u003cem\u003ek\u003c/em\u003e\u003c/strong\u003e, while the interband pairings are Cooper pairs between \u003cstrong\u003e\u003cem\u003ek\u003c/em\u003e\u003c/strong\u003eand -\u003cstrong\u003e\u003cem\u003ek\u003c/em\u003e\u003c/strong\u003e+ \u003cstrong\u003e\u003cem\u003eQ\u003c/em\u003e\u003c/strong\u003e, which is allowed as the momentum vector \u003cstrong\u003e\u003cem\u003eQ\u003c/em\u003e\u003c/strong\u003e = (\u0026pi;, \u0026pi;) is a reciprocal lattice vector for the genuine 2-Fe unit cell. Notice that, the normal pairing and the interband pairing have opposite parity values without mixing. The interband pairing between \u003cstrong\u003e\u003cem\u003ek\u003c/em\u003e\u003c/strong\u003eand -\u003cstrong\u003e\u003cem\u003ek\u003c/em\u003e\u003c/strong\u003e+ \u003cstrong\u003e\u003cem\u003eQ\u0026nbsp;\u003c/em\u003e\u003c/strong\u003ewas proposed and classified by Hu as the \u003cem\u003e\u0026eta;-\u003c/em\u003epairing in Ref. [\u003cem\u003e28\u003c/em\u003e], while their consequences remain unexplored. The broken inversion symmetry at the FeSe/SrTiO\u003csub\u003e3\u003c/sub\u003e interface allows the coexistence of two types of pairings. Therefore, the monolayer FeSe offers an opportunity to explore possible novel pairings.\u003c/p\u003e\n\u003cp\u003eIn this work, we carry out a systematic investigation of molecular beam epitaxial (MBE) monolayer FeSe with an atomically homogeneous (1 \u0026times; 1) surface structure on SrTiO\u003csub\u003e3\u003c/sub\u003e(001) using atomic-resolution scanning tunneling microscopy/spectroscopy (STM/STS). We find the tunneling spectra of \u0026alpha;-Fe and \u0026beta;-Fe are significantly different, resulting in the sublattice dichotomy in tunneling spectra coherence peaks as illustrated in Fig. 1(c). More specifically, monolayer FeSe is one two-band system with dual-gap\u003csup\u003e1,16,22\u003c/sup\u003e, i.e., one pair of inner gap coherence peaks at \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e and the other pair of outer gap coherence peaks at \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e. We find the coherence peak at -\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003efor \u0026alpha;-Fe is lower than \u0026beta;-Fe while the coherence peak at +\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003efor \u0026alpha;-Fe is higher than \u0026beta;-Fe with a similar amount. Moreover, opposite intensity contrast at \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e coherence peaks to those at \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e for each sublattice. This sublattice dichotomy can only be explained by the substantial coexistence of both normal pairing and\u0026nbsp;interband pairing\u0026nbsp;in the superconducting state.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo characterize the surface structure, we collect the bias-dependent atomic resolution topography of the monolayer FeSe and summarize the results in Fig. S1 in supplemental materials (SM). Plotted in Figs. 2 (a) and (b) are the atomic resolution topography images taken at sample bias \u003cem\u003eV\u003csub\u003es\u003c/sub\u003e\u003c/em\u003e = 80 meV and \u003cem\u003eV\u003csub\u003es\u003c/sub\u003e\u003c/em\u003e = -50 meV, respectively, presenting the Se\u003csub\u003e+\u003c/sub\u003e(001)-(1 \u0026times; 1) surface, instead of the ubiquitous (2 \u0026times; 1) orders observed previously\u003csup\u003e1,16,20\u003c/sup\u003e. In the inserted fast Fourier transformed (FFT) images, the sharp \u003cem\u003eQ\u003csub\u003ea\u0026nbsp;\u003c/sub\u003e\u003c/em\u003eand \u003cem\u003eQ\u003csub\u003eb\u003c/sub\u003e\u0026nbsp;\u003c/em\u003eBragg spots corresponding to the (1 \u0026times; 1) primitive unit cell give expanded in-plane lattice constants of 3.89 \u0026Aring; compared with the bulk value of 3.78 \u0026Aring;\u003csup\u003e6\u003c/sup\u003e, which shows that the FeSe monolayer is fully strained to the SrTiO\u003csub\u003e3\u003c/sub\u003e(001). As exemplified in Fig. 2(b), the density of states from Fe sites increases upon the tip in closer proximity to the surface; correspondingly, in addition to the sharp (\u003cem\u003eQ\u003c/em\u003e\u003csub\u003ea\u003c/sub\u003e, \u003cem\u003eQ\u003c/em\u003e\u003csub\u003eb\u003c/sub\u003e)Bragg spots, the \u003cem\u003eQ\u003csub\u003ex\u003c/sub\u003e\u0026nbsp;\u003c/em\u003eand \u003cem\u003eQ\u003csub\u003ey\u003c/sub\u003e\u0026nbsp;\u003c/em\u003eBragg spots of the 1-Fe sublattice emerge. With the differing tunneling currents in the triple-layer, Se\u003csub\u003e-\u003c/sub\u003e atom sites, Fe atom sites, and Se\u003csub\u003e+\u003c/sub\u003e atom sites are individually discerned. As depicted in the bottom inset zoom-in topography image, the apparent atomic contrast matches well with the superimposed lattice model. The direct atomic resolution probe of the perfect (1 \u0026times; 1) surface is the foundation for exploring the intrinsic sublattice feature in the Fe-layer.\u003c/p\u003e\n\u003cp\u003eWe collect atomic-site-dependent tunneling spectra to extract the electronic structure. As summarized in Fig. 2(c), the typical large-bias tunneling spectra, taken at the four atomic sites in one 2-Fe unit cell (bottom panel), present the filled states below the Fermi level (\u003cem\u003eE\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e) consistent with the specific orbitals (top panel) disclosed by ARPES, additionally, empty states above the \u003cem\u003eE\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e. The tunneling conductance around \u003cem\u003eE\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003eranging from -50 meV to 60 meV is quite low due to the low tunneling probability of the \u003cem\u003eM\u003c/em\u003e-centered electron bands (inferred as \u0026delta;), which is lower and flatter for Fe sites than for Se sites. The spectra upturn around -80 meV (\u0026sigma;) belongs to the \u003cem\u003e\u0026Gamma;\u003c/em\u003e-centered \u003cem\u003et\u003c/em\u003e\u003csub\u003e2g\u003c/sub\u003e hole band edge, while the unoccupied upturn around 100 meV (\u0026lambda;) and the occupied hump below -350 meV (\u0026xi;\u0026shy;) to the \u003cem\u003e\u0026Gamma;\u003c/em\u003e-centered \u003cem\u003ee\u003c/em\u003e\u003csub\u003eg\u003c/sub\u003e orbital. Compared with the common monolayer FeSe (2 \u0026times; 1) surface\u003csup\u003e20\u003c/sup\u003e, the \u003cem\u003e\u0026Gamma;\u003c/em\u003e-centered \u003cem\u003ee\u003c/em\u003e\u003csub\u003eg\u003c/sub\u003e bands are shifted downward by ~ 100 meV. Plotted in Fig. 2(d) are the corresponding small-bias tunneling spectra within the bias range (-30, + 30) meV. The tunneling spectra present the standard dual-gap structures with the inner coherence peak \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003earound \u0026plusmn;10 meV and the outer coherence peaks \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003earound \u0026plusmn;(15-17) meV, which are also consistent with previous works\u003csup\u003e1,16,22\u003c/sup\u003e. Interestingly, all the pairing gaps exhibit strong particle-hole asymmetry, which can be categorized into \u0026alpha;-Fe and Se\u003csub\u003e-\u003c/sub\u003e group and \u0026beta;-Fe and Se\u003csub\u003e+\u003c/sub\u003e group. The former group exhibits strikingly higher +\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e coherence peaks than the latter one.\u003c/p\u003e\n\u003cp\u003eTo eliminate the tunneling matrix contrast for different layers, we then focus on the Fe layer and collect detailed low-energy tunneling spectra at each Fe site. The normalized tunneling spectra along the three [100]-running cuts marked in Fig. 3(a) are plotted in Fig. 3(c) (with the corresponding raw spectra and normalization process summarized in Fig. S2). These tunneling spectra along each cut are almost homogeneous, exhibiting the sharp \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003ecoherence peaks around \u0026plusmn;10 meV and widened \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003ecoherence peaks wiggled within an energy range \u0026plusmn;(15-17) meV. The outer gap variation is likely from the local electronic modulation owing to the SrTiO\u003csub\u003e3\u003c/sub\u003e substrate\u003csup\u003e29\u003c/sup\u003e. In contrast, the inner coherence peaks are close to the \u003cem\u003eE\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e, resulting in a relatively small gap variation. One special point is that the tunneling spectra are particle-hole asymmetric. The spectra for the \u0026alpha;-Fe along the yellow dashed-line cut-1 (left panel) consistently exhibit much higher inner gap coherence peaks on the hole sides +\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e. The tunneling spectra of the \u0026alpha;-Fe along the yellow dashed-line cut-2, as plotted in the middle panel, show similar behaviors: the hole side of the inner coherence peak +\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e is still higher than the electron side -\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e. Surprisingly, a new feature emerges from the asymmetric tunneling spectra at \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e for \u0026beta;-Fe. As identified from the spectra taken along the green dashed-line cut-3 plotted in the right panel, the electron sideof the inner coherence peak -\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e becomes higher than the hole side +\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e. Hence, the tunneling spectra for the \u0026alpha;-Fe and \u0026beta;-Fe are completely different, resulting in a sublattice dichotomy for the tunneling spectra.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo further demonstrate this sublattice dichotomy feature, we take a complete scan of the area in Fig. 3(a) for the statistics. We define a ratio of inner-gap coherence peak intensity \u003cem\u003eZ\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e) = \u003cem\u003eg\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e)/\u003cem\u003eg\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, -\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e), where \u003cem\u003eg\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e) \u0026equiv; d\u003cem\u003eI\u003c/em\u003e/d\u003cem\u003eV\u0026nbsp;\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e), and plot the ratios \u003cem\u003eZ\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e) at \u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e= 10 meV in Fig. 3(b). The \u003cem\u003eZ\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e) is always larger than 1 for \u0026alpha;-Fe but smaller than1 for \u0026beta;-Fe. This particle-hole intensity switching behavior at \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003eis the sublattice dichotomy defined in Fig. 1(c). On the other hand, the widening \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003ecoherence peaks within \u0026plusmn; (15-17) meV resulting in large errors in \u003cem\u003eZ\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e). Hence, we try another strategy using \u003cem\u003eg\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e) mapping to show the sublattice dichotomy further and plot the \u003cem\u003eg\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e) with V\u003csub\u003eo\u003c/sub\u003e = 15 meV in Fig. 3(d). Compared with the \u0026beta;-Fe sites, the \u0026alpha;-Fe sites consistently show decreased intensities at the hole side +\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e and increased intensities at the electron side -\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e, which is exactly opposite to the electron-hole intensity contrast at \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e summarized in Fig. 3(b). Therefore, the results shown in Fig. 3 completely present the Fe-sublattice dichotomy illustrated in Fig. 1(c). In the SM, we plot a series of \u003cem\u003eg\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e) mapping images at \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e and \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e obtained simultaneously and the corresponding phase-referenced FFT on another sample (Fig. S3), which shows the reproducibility and robustness of the sublattice dichotomy effect. In contrast, there are no sublattice dichotomy features above \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e at liquid nitrogen temperature (Fig. S4).\u003c/p\u003e\n\u003cp\u003eWe briefly summarize our findings here. The distinct dual tunneling spectra corresponding to the two sublattices are presented by the two typical tunneling spectra of \u0026alpha;-Fe and \u0026beta;-Fe plotted in Fig. 4(a). For the inner-gap coherence peaks, the \u0026alpha;-Fe has a more pronounced hole peak at +\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e while the \u0026beta;-Fe has a more pronounced electron peak at -\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e. On the other hand, the outer-gap coherence peaks at \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e show a reverse behavior to the inner-gap coherence peaks at \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003e. \u0026nbsp;More precisely, the +\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003etunneling weight at \u0026alpha;-Fe is almost equal to the -\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003etunneling weight at \u0026beta;-Fe and vice versa. Notably, we check the d\u003cem\u003eI\u003c/em\u003e/d\u003cem\u003eV\u003c/em\u003e tunneling spectra and \u003cem\u003eg\u003c/em\u003e(\u003cem\u003er\u003c/em\u003e, \u003cem\u003eV\u003c/em\u003e) mapping images of the common FeSe-(2 \u0026times; 1) surface (Fig. S5) and observe the sublattice dichotomy features as well, though weakened due to the electronic modulation\u003csup\u003e30,31\u003c/sup\u003e. Furthermore, associated with the occurrence of checkerboard order under reduced in-plane anisotropy, this dichotomy feature is indiscernible\u003csup\u003e32\u003c/sup\u003e. This unexpected intrinsic phenomenon points to a highly unusual pairing function inside the monolayer FeSe.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eIt is clear that the space inversion symmetry is broken if there is a sublattice dichotomy. As we have mentioned in the introduction, for the monolayer FeSe on SrTiO\u003csub\u003e3\u003c/sub\u003e(001), the space inversion symmetry is broken at the coherent interface. However, the effect of the symmetry breaking on the electronic physics is largely unclear and has been ignored in both theoretical modeling and experimental studies. The absence of the inversion symmetry allows the normal pairing and interband pairings to coexist. This odd parity interband pairing is\u0026nbsp;known to produce the two-gap feature\u003csup\u003e28\u003c/sup\u003e. Therefore, it is natural to ask whether the combined action of interbandpairing and normal pairing can produce the dichotomy effect\u003csup\u003e33\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eTo capture the above physics and monolayer FeSe electronic structure, we follow the \u003cstrong\u003e\u003cem\u003ek\u003c/em\u003e\u003c/strong\u003e\u0026middot; \u003cstrong\u003e\u003cem\u003ep\u003c/em\u003e\u003c/strong\u003emodel around the \u003cem\u003eM\u0026nbsp;\u003c/em\u003epoint based on the symmetry of FeSe\u003csup\u003e34\u003c/sup\u003e, and then, add bothinterband pairing and normal pairing into the \u003cstrong\u003e\u003cem\u003ek\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u0026middot; \u003cstrong\u003e\u003cem\u003ep\u003c/em\u003e\u003c/strong\u003emodel. The local density of states (DOSs) at two sublattice sites are further calculated respectively (See the model details in SM). The tunneling DOSs for \u0026alpha;-Fe and \u0026beta;-Fe are plotted in Fig. 4(b). Our theoretical simulation captures the sublattice dichotomy effect nicely. Furthermore, in Fig. 4(b), the tunneling spectrum around zero bias at \u0026alpha;-Fe slightly shifts towards the negative voltage while the tunneling spectrum at \u0026beta;-Fe shifts opposite towards the positive voltage. This is the local particle-hole symmetry feature of interband pairing\u003csup\u003e33\u003c/sup\u003e. This feature is also visible in the experimental findings shown in Fig. 4(a). It is important to note that neither the normal pairing nor the interbandpairing individually can produce the dichotomy effect (Figs. S6(c, d)). It is also possible that the normal state already contains the symmetry-breaking effects. However, this normal state with normal pairing can only lead to sublattice difference without particle-hole asymmetry (Fig. S6(e)) rather than the sublattice dichotomy found here. Hence, the interbandpairing is an essential component of the sublattice dichotomy that we observed.\u003c/p\u003e\n\u003cp\u003eIn summary, we perform a systematic investigation on the sublattice degree of freedom of the monolayer FeSe. We successfully grow monolayer FeSe with an exclusive (1 \u0026times; 1) surface on the SrTiO\u003csub\u003e3\u003c/sub\u003e(001) substrate by MBE and then analyze the electronic structure by STS in combination with ARPES. We successfully identify dual-gap superconducting coherence peaks at \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u0026nbsp;\u003c/sub\u003eand \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e. By comparing the tunneling spectra at \u0026alpha;-Fe and \u0026beta;-Fe, we find sublattice dichotomy effects. More precisely, the coherence peak of \u0026alpha;-Fe at +\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003eis higher than \u0026beta;-Fe while the coherence peak of \u0026beta;-Fe at -\u003cem\u003eV\u003c/em\u003e\u003csub\u003ei\u003c/sub\u003eis also higher than \u0026alpha;-Fe with a similar difference. We also observe a reversed contrast at \u0026plusmn;\u003cem\u003eV\u003c/em\u003e\u003csub\u003eo\u003c/sub\u003e. We have shown that the coexistence of the normal pairing between \u003cstrong\u003e\u003cem\u003ek\u003c/em\u003e\u003c/strong\u003eand -\u003cstrong\u003e\u003cem\u003ek\u003c/em\u003e\u003c/strong\u003e and the interbandpairing between \u003cstrong\u003e\u003cem\u003ek\u003c/em\u003e\u003c/strong\u003eand -\u003cstrong\u003e\u003cem\u003ek\u003c/em\u003e\u003c/strong\u003e+ \u003cstrong\u003e\u003cem\u003eQ\u003c/em\u003e\u003c/strong\u003eis the key mechanism for this sublattice dichotomy. This interband pairing is also the extension of the \u003cem\u003e\u0026eta;-\u003c/em\u003epairing classified in Refs. [\u003cem\u003e28, 35, 36\u003c/em\u003e].\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe exceptionally high\u0026nbsp;superconducting transition temperature in the monolayer FeSe remains a central unresolved question in the field of iron-based superconductors. Deciphering the pairing structure in monolayer FeSe is key to addressing this mystery. Our research discovers a novel superconducting state in the monolayer FeSe on SrTiO₃, placing significant constraints on possible pairing configurations, as well as pairing mechanisms. Specifically, our findings suggest that the \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e enhancement arises from the activation of a new pairing channel, namely, the interband pairing. Traditionally, the interband pairing is not expected to dominate over the intraband pairing as the primary instability; however, our observation of sublattice dichotomy requires a strong interband pairing, which cannot be simply understood as a conventional Fermi surface instability. The \u003cem\u003eT\u003c/em\u003e\u003csub\u003ec\u003c/sub\u003e enhancement in the monolayer FeSe has generated intriguing conjectures on the pairing mechanisms including interfacial electron-phonon enhancement\u003csup\u003e13,23,24\u003c/sup\u003e and incipient pairing mechanism\u003csup\u003e37-40\u003c/sup\u003e. However, all of these proposals have not specified such a large interband pairing component. Therefore, our results offer fresh insights to examine the pairing mechanisms in monolayer FeSe and underscore the complex and rich physics associated with sublattice degrees of freedom.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSample preparation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eOur experiments were carried out in a Createc ultrahigh vacuum (1.0 \u0026times; 10\u003csup\u003e-10\u003c/sup\u003e mbar) low-temperature (4.8 K) STM system equipped with an MBE chamber. The Nb-doped SrTiO\u003csub\u003e3\u003c/sub\u003e(001) (0.05 wt.%) substrates were annealed above 1000 \u003csup\u003e◦\u003c/sup\u003eCto obtain dual-TiO\u003csub\u003e2-\u0026delta;\u003c/sub\u003e-termination. Monolayer FeSe films were prepared by standard co-evaporating and post-annealing, with a deposition rate of\u0026nbsp;\u0026sim;0.02 monolayer per minute at a substrate temperature of 470 \u003csup\u003e◦\u003c/sup\u003eC.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSTM experiments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll STM measurements were performed in a constant current mode (tunneling current set point \u003cem\u003eI\u003csub\u003et\u003c/sub\u003e\u0026nbsp;\u003c/em\u003e= 500 pA) with the bias voltage applied to the sample (\u003cem\u003eV\u003csub\u003es\u003c/sub\u003e\u003c/em\u003e), using a polycrystalline PtIr tip. The differential conductance d\u003cem\u003eI\u003c/em\u003e/d\u003cem\u003eV\u003c/em\u003e spectra, characterizing the local density of states around the \u003cem\u003eE\u003c/em\u003e\u003csub\u003eF\u003c/sub\u003e, are measured by disabling the feedback circuit, sweeping the sample voltage \u003cem\u003eV\u003csub\u003es\u003c/sub\u003e\u003c/em\u003e, and then extracting the differential tunneling current d\u003cem\u003eI\u003c/em\u003e/d\u003cem\u003eV\u003c/em\u003e using a standard lock-in technique with a small bias modulation (\u0026sim;1% of the sweeping range) at 937 Hz.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eARPES experiments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe FeSe/SrTiO\u003csub\u003e3\u003c/sub\u003e sample was \u003cem\u003ein-situ\u003c/em\u003e transferred to the ARPES chamber and measured under an ultrahigh vacuum below 1.5 \u0026times; 10\u003csup\u003e-10\u003c/sup\u003e mbar. Data were collected using a DA30 analyzer and a Scienta VUV 5050 helium lamp at 80 K. The energy and angular resolutions were set to 10 meV and 0.2\u003csup\u003e◦\u003c/sup\u003e, respectively. The Fermi surfaces, deduced from our ARPES measurements, consist of two overlapped ellipse-like electron pockets around each Brillouin zone (BZ) corner (\u003cem\u003eM\u003c/em\u003e\u003csub\u003ex\u003c/sub\u003e and \u003cem\u003eM\u003c/em\u003e\u003csub\u003ey\u003c/sub\u003e), consistent with the previous ARPES results\u003csup\u003e2,4,11-14\u003c/sup\u003e.\u0026nbsp;\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting Interests\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contributions\u003c/h2\u003e \u003cp\u003eC. D. and X. J. carried out the STM experiments; Q. H., W. Z. and L. Y. performed the ARPES experiments; L. W., J-F. J. and Q-K. X. designed and coordinated the experiments; Z-P. X, K. J. and J-P. H. performed the theoretical analysis. K. J., L. W. and J-P. H. wrote the manuscript with comments from all authors.\u003c/p\u003e\u003ch2\u003eAcknowledgment\u003c/h2\u003e \u003cp\u003eThe work is supported by the National Natural Science Foundation of China (Grant No. 92477204, No. 52388201, No. 1888101, No. 12174428, No. 11920101005), the National Key Research and Development Program of China (Grant No. 2022YFA1403100 and No. 2022YFA1403900), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB28000000 and No. XDB33000000), the New Cornerstone Investigator Program, the Chinese Academy of Sciences Project for Young Scientists in Basic Research (2022YSBR-048).\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eWang, Q.-Y. \u003cem\u003eet al.\u003c/em\u003e Interface-induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO\u003csub\u003e3\u003c/sub\u003e. Chin. Phys. 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Symmetry 12, 1402 (2020).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-4705720/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4705720/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA unit cell represents the smallest repeating structure in solid-state physics and serves as the fundamental building block of a material. In iron-based superconductors, each unit cell contains two iron atoms, which form two distinct sublattices in the two-dimensional iron layers. Under normal circumstances, these sublattices are expected to have identical physical properties due to space inversion symmetry. However, we discover that this sublattice structure can introduce a novel degree of freedom for probing unconventional pairing mechanisms in iron-based superconductors. Through molecular-beam epitaxy, we have successfully grown monolayer FeSe films with atomically homogeneous (1 × 1) structures on SrTiO₃(001) substrates. In these films, we observe distinct dual tunneling spectra within pairing gap energy corresponding to the two sublattices, a phenomenon we term \u003cem\u003esublattice dichotomy\u003c/em\u003e. This dichotomy can be quantitatively explained by a parity-breaking superconducting state, characterized by the coexistence of conventional pairing and interband parity pairing. The interband singlet pairing arises due to the lacking of inversion symmetry, which is naturally broken from the interface coupling between FeSe and the SrTiO₃ surface.\u003c/p\u003e","manuscriptTitle":"Parity Breaking and Sublattice Dichotomy in Monolayer FeSe Superconductor","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-02-15 15:52:18","doi":"10.21203/rs.3.rs-4705720/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"e3a3d784-5a46-44cb-ba18-f571ef32c4fd","owner":[],"postedDate":"February 15th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":44163463,"name":"Physical sciences/Physics/Condensed-matter physics/Superconducting properties and materials"},{"id":44163464,"name":"Physical sciences/Physics/Condensed-matter physics/Surfaces, interfaces and thin films"}],"tags":[],"updatedAt":"2025-08-12T10:36:29+00:00","versionOfRecord":[],"versionCreatedAt":"2025-02-15 15:52:18","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4705720","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4705720","identity":"rs-4705720","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}