Spectral evidence of Wigner crystallisation over a one-dimensional moiré superlattice under magnetic fields

Abstract The advantages of moiré superlattice1,2 in engineering strongly correlated electronic properties have triggered a rising tide on exploration of the fascinating Wigner crystals3 in two-dimensional van der Waals heterostructures4-8. However, it remains a challenge to investigate one-dimensional (1D) Wigner crystals by constructing quasi-1D moiré superlattice. 1D Wigner crystals were only observed in carbon nanotubes9-12, but the insulating state that strikes at the heart of the strongly-correlated nature is still inaccessible. Here, we demonstrate the robust 1D Wigner crystallisation of dilute electrons over a quasi-1D moiré superlattice with a measured period of 75 nm in the bending Bi(111) film surface, using scanning tunnelling microscopy under magnetic fields in combination with calculations based on the extended Hubbard model13. Our results reveal spectral evidence for the strongly-correlated insulating states of the 1D Wigner crystal and charge density wave (CDW), with distinguishable field-dependent characteristics in the splitting Landau levels. A fairly sharp transition of the CDW into the Wigner crystal appears at the critical magnetic field of about 10.7 T that corresponds to the onset of the non-overlapped cyclotron orbits. Our findings shed light on insightful understanding of the mysterious correlated phenomena in 1D Wigner crystals based on emerging moiré materials.