Moir\'e Band Topology in Twisted Bilayer Graphene

TL;DR

This paper provides evidence that twisted bilayer graphene hosts nontrivial band topology, revealed through nonlocal transport measurements, and discusses its implications for strongly correlated phenomena and topological engineering.

Contribution

It demonstrates the topological nature of moiré Dirac bands in twisted bilayer graphene using nonlocal transport and $K$-theory analysis, highlighting the role of $Z_2$ invariants.

Findings

Nonlocal responses in electron and hole superlattice gaps indicate nontrivial band topology.

Robustness of nonlocal responses to electric field, twist angle, and edge termination.

Identification of two $Z_2$ invariants characterizing the moiré Dirac bands.

Abstract

Recently twisted bilayer graphene (t-BLG) emerges as a new strongly correlated physical platform near a magic twist angle, which hosts many exciting phenomena such as the Mott-like insulating phases, unconventional superconducting behavior and emergent ferromagnetism. Besides the apparent significance of band flatness, band topology may be another critical element in determining strongly correlated twistronics yet receives much less attention. Here we report compelling evidence for nontrivial noninteracting band topology of t-BLG moir\'e Dirac bands through a systematic nonlocal transport study, in conjunction with an examination rooted in $K$-theory. The moir\'e band topology of t-BLG manifests itself as two pronounced nonlocal responses in the electron and hole superlattice gaps. We further show that the nonlocal responses are robust to the interlayer electric field, twist angle, and edge termination, exhibiting a universal scaling law. While an unusual symmetry of t-BLG trivializes Berry curvature, we elucidate that two $Z_2$ invariants characterize the topology of the moir\'e Dirac bands, validating the topological edge origin of the observed nonlocal responses. Our findings not only provide a new perspective for understanding the emerging strongly correlated phenomena in twisted van der Waals heterostructures, but also suggest a potential strategy to achieve topologically nontrivial metamaterials from topologically trivial quantum materials based on twist engineering.