Direct observation of moir\'e flat-band breakdown at the edge of magic-angle twisted bilayer graphene

TL;DR

This study uses scanning tunneling microscopy to observe how moiré flat bands in magic-angle twisted bilayer graphene break down at sample edges, revealing that complete moiré supercells are essential for flat-band existence.

Contribution

It provides the first direct experimental evidence that moiré flat bands require a complete supercell structure, even at sample edges where symmetry is broken.

Findings

Flat bands exist in complete moiré supercells at edges.

Incomplete moiré patterns lack flat-band characteristics.

Complete supercells are necessary for flat-band formation.

Abstract

Low-energy moir\'e flat bands in magic-angle twisted bilayer graphene (tBG) have demonstrated incredible potentials to exhibit rich exotic quantum phenomena. Theoretically, the moir\'e flat bands of tBG are based on the extended structures, i.e., the moir\'e patterns with periodic boundary conditions. However, a fundamental question of whether the flat bands can exist in the graphene moir\'e patterns with a reduced structure symmetry, such as sample edges, remains unanswered. Here, via scanning tunneling microscopy and spectroscopy, we study the local electronic properties of a magic-angle tBG near the sample terminated edge and report a direct observation of breakdown of the moir\'e flat bands. We show that the moir\'e electronic structures, including the low-energy flat bands, can sufficiently exist in a complete moir\'e spot, i.e., a moir\'e supercell, right at the edge even the translational symmetry of the moir\'e patterns is broken in one direction. However, the flat-band characteristic is obviously absent in the incomplete moir\'e spots that are partly terminated by the edge. Our results indicate that a whole moir\'e spot is sufficient and indispensable for the generation of the effective moir\'e flat bands in tBG.