1D Electronic Flat Bands in Untwisted Moiré Superlattices

Abstract

After the preparation of 2D electronic flat band (EFB) in van der Waals (vdW) superlattices, recent measurements suggest the existence of 1D electronic flat bands (1D‐EFBs) in twisted vdW bilayers. However, the realization of 1D‐EFBs is experimentally elusive in untwisted 2D layers, which is desired considering their fabrication and scalability. Herein, the discovery of 1D‐EFBs is reported in an untwisted in situ‐grown two atomic‐layer Bi(110) superlattice self‐aligned on an SnSe(001) substrate using scanning probe microscopy measurements and density functional theory calculations. While the Bi–Bi dimers of Bi zigzag (ZZ) chains are buckled, the epitaxial lattice mismatch between the Bi and SnSe layers induces two 1D buckling reversal regions (BRRs) extending along the ZZ direction in each Bi(110)‐11 × 11 supercell. A series of 1D‐EFBs arises spatially following BRRs that isolate electronic states along the armchair (AC) direction and localize electrons in 1D extended states along ZZ due to quantum interference at a topological node. This work provides a generalized strategy for engineering 1D‐EFBs in utilizing lattice mismatch between untwisted rectangular vdW layers.

Fubini–Study metric and topological properties of flat band electronic states: the case of an atomic chain with s − p orbitals

“…The FS metric of the model allows for the construction of a mapping f that can accurately distinguish between topological and nontopological systems, as well as between topological systems with and without FBs. This model is inspired by recent experimental evidence of one-dimensional FBs along established directions in two-dimensional van der Waals structures [40], as well as research that suggests that chains of elements such as boron [41], gallium [42] and tellurium [43,44] could be used to realize the proposed model experimentally.…”

Carbon Kagome nanotubes—quasi-one-dimensional nanostructures with flat bands

“…ref. 6 and 42–44) on quasi-two-dimensional systems and heterostructures, featuring one-dimensional flat bands, or flat bands along specific directions of a two-dimensional Brillouin zone. In contrast, the systems studied here are all elemental quasi-one-dimensional (1D) nanostructures that feature flat bands throughout the entirety of their (one-dimensional) Brillouin zone.…”

One-Dimensional Moiré Physics and Chemistry in Heterostrained Bilayer Graphene

“…Furthermore, it is possible to achieve one-dimensional (1D) moiré patterns between 2D materials by enforcing a periodic modulation selectively in one direction, as illustrated in Figure a. Different approaches for achieving these moiré patterns have been proposed, including vertical and lateral heterostructures of lattice-mismatch heterostrained materials, − nanotubes, , substrate-driven moiré patterns, or chemically functionalized surfaces. − However, earlier theoretical − and experimental − works restrict their focus mainly to the coexistence of the twist angle and accompanying strain in moiré materials, with a detailed understanding of the individual effect and properties of heterostrain currently lacking. In this Letter, we expand the class of moiré materials beyond twisted systems by introducing heterostrained bilayer graphene (hBLG), in which uniaxial strain is exerted in only one of the two layers.…”