Exceptional topology in non-Hermitian twisted bilayer graphene

TL;DR

This paper explores non-Hermitian effects in twisted bilayer graphene, revealing exceptional rings, non-Hermitian flat bands, and topological features that differ from Hermitian systems, opening new avenues in moiré physics.

Contribution

It introduces a non-Hermitian generalization of the TBG model, discovering exceptional rings, an exceptional magic angle, and topological properties unique to non-Hermitian moiré systems.

Findings

Exceptional rings form at specific valleys in the moiré Brillouin zone.

Non-Hermitian flat bands with zero energy and finite lifetime are identified.

Topological charge conservation suggests potential for non-Hermitian fractional quantum Hall states.

Abstract

Twisted bilayer graphene (TBG) has extraordinary electronic properties at the magic angle along with an isolated flat band at the magic angle. However, the non-Hermitian phenomena in twisted bilayer graphene remain unexplored. In this work, we study a non-Hermitian TBG formed by one-layer graphene twisted relative to another layer with gain and loss. Using a non-Hermitian generalization of the Bistritzer-MacDonald model, we find Dirac cones centered at only the $K_M$ ($K'_M$) corner of the moir\'e Brillouin zone at the $K'$ ($K$) valley deform into rings of exceptional points in the presence of non-Hermiticity, which is different from single-layer graphene with gain and loss, where exceptional rings appear in both $K$ and $K'$ corners of the Brillouin zone. We show that the exceptional rings are protected by non-Hermitian chiral symmetry. More interestingly, at an ``exceptional magic angle" larger than the Hermitian magic angle, the exceptional rings coincide and form non-Hermitian flat bands with zero energy and a finite lifetime. These non-Hermitian flat bands in the moir\'e system, which are isolated from dispersive bands, are distinguished from those in non-Hermitian frustrated lattices. In addition, we find that the non-Hermitian flat band has topological charge conserved in the moir\'e Brillouin zone, which is allowed for analogs of non-Hermitian fractional quantum Hall states.