Non-Hermitian topology of transport in the quantum Hall phases in graphene

TL;DR

This paper explores non-Hermitian topological phase transitions in multi-terminal quantum Hall devices in graphene, revealing new phenomena beyond chiral edge states and highlighting graphene's potential for topologically protected transport.

Contribution

It demonstrates that non-Hermitian topological phases can occur independently of chiral edge states in graphene quantum Hall devices, expanding understanding of topological transport phenomena.

Findings

Multi-terminal conductance matrices exhibit non-Hermitian topological phase transitions.

Device imperfections induce additional non-Hermitian phases during Landau level crossing.

Graphene serves as an ideal platform for studying non-Hermitian topological phenomena.

Abstract

It has recently been shown that signatures of non-Hermitian topology can be realized in a conventional quantum Hall device connected to multiple current sources. These signatures manifest as robust current-voltage characteristics, dictated by the presence of a nontrivial, non-Hermitian topological invariant of the conductance matrix. Chiral edge states are believed to be responsible for this non-Hermitian response, similar to how they lead to a quantized Hall conductivity in the presence of a single current source. Here, we go beyond this paradigm, showing that multi-terminal conductance matrices can exhibit non-Hermitian topological phase transitions that cannot be traced back to the presence and directionality of a boundary-localized chiral mode. By performing quantum transport simulations in the quantum Hall regime of monolayer graphene, we find that when the chemical potential is swept across the zeroth Landau level, unavoidable device imperfections cause the appearance of an additional non-Hermitian phase of the conductance matrix. This highlights graphene as an ideal platform for the study of non-Hermitian topological phase transitions, and is a first step towards exploring how the geometry of quantum devices can be harnessed to produce robust, topologically-protected transport characteristics.