Non-Hermitian approach of edge states and quantum transport in a magnetic field

TL;DR

This paper introduces a non-Hermitian framework to analyze spectral and transport phenomena in two-dimensional mesoscopic systems under strong magnetic fields, focusing on edge states, quantum transport, and the effects of system openness.

Contribution

It presents a novel non-Hermitian approach to study edge states and quantum transport in open systems with magnetic fields, highlighting the impact of lead-system coupling on state lifetimes.

Findings

Identification of three regimes: resonant, quantum Hall, and superradiant.

Dependence of state lifetime on lead-system coupling.

Quantization of transmission coefficients and edge state behavior.

Abstract

We develop a manifest non-Hermitian approach of spectral and transport properties of two- dimensional mesoscopic systems in strong magnetic field. The finite system to which several ter- minals are attached constitutes an open system that can be described by an effective Hamiltonian. The life time of the quantum states expressed by the energy imaginary part depends specifically on the lead-system coupling and makes the difference among three regimes: resonant, integer quan- tum Hall effect and superradiant. The discussion is carried on in terms of edge state life time in different gaps, channel formation, role of hybridization, transmission coefficients quantization. A toy model helps in understanding non-Hermitian aspects in open systems.