Edge State Tunneling in a Split Hall Bar Model

TL;DR

This paper introduces an analytical model for edge state tunneling in split Hall bars, revealing how interaction strengths influence tunneling relevance and providing insights into experimental observations.

Contribution

It presents a solvable chiral electron model with adjustable interactions, highlighting the impact on tunneling processes and differentiating even and odd Fourier component dynamics.

Findings

Scaling dimensions depend on interaction strengths.

Repulsive interactions across the Hall bar suppress tunneling relevance.

Analytical solution distinguishes even and odd Fourier modes.

Abstract

In this paper we introduce and study the correlation functions of a chiral one-dimensional electron model intended to qualitatively represent narrow Hall bars separated into left and right sections by a penetrable barrier. The model has two parameters representing respectively interactions between top and bottom edges of the Hall bar and interactions between the edges on opposite sides of the barrier. We show that the scaling dimensions of tunneling processes depend on the relative strengths of the interactions, with repulsive interactions across the Hall bar tending to make breaks in the barrier irrelevant. The model can be solved analytically and is characterized by a difference between the dynamics of even and odd Fourier components. We address its experimental relevance by comparing its predictions with those of a more geometrically realistic model that must be solved numerically.