Chiral boundary conditions for Quantum Hall systems

TL;DR

This paper explores alternative boundary conditions for quantum billiards, introducing chiral boundary conditions that unify bulk and edge properties in Quantum Hall systems, potentially capturing complex physical effects.

Contribution

It proposes and analyzes chiral boundary conditions for quantum billiards, offering a new approach to model Quantum Hall systems with unified bulk and edge descriptions.

Findings

Chiral boundary conditions effectively describe Quantum Hall regimes.

Bulk and edge properties can be unified under these boundary conditions.

The approach captures effects of strong magnetic fields and interactions.

Abstract

A quantum mesoscopic billiard can be viewed as a bounded electronic system due to some external confining potential. Since, in general, we do not have access to the exact expression of this potential, it is usually replaced by a set of boundary conditions. We discuss, in addition to the standard Dirichlet choice, the other possibilities of boundary conditions which might correspond to more complicated physical situations including the effects of many body interactions or of a strong magnetic field. The latter case is examined more in details using a new kind of chiral boundary conditions for which it is shown that in the Quantum Hall regime, bulk and edge characteristics can be described in a unified way.