Coulomb interactions and delocalization in quantum Hall constrictions

TL;DR

This paper investigates how long-range Coulomb interactions affect quantum Hall tunneling in different geometries, revealing a transition from localization to delocalization and an insulator-metal transition depending on the constriction angle.

Contribution

It demonstrates that duality persists with long-range interactions and calculates tunneling exponents, revealing a geometry-dependent localization-delocalization transition in quantum Hall constrictions.

Findings

Duality between weak tunneling and backscattering is maintained with long-range interactions.

Coulomb interactions cause localization in wide channels and delocalization in narrow constrictions.

An insulator-metal transition occurs at a critical angle alpha_c depending on interaction strength and filling fraction.

Abstract

We study a geometry-dependent effect of long-range Coulomb interactions on quantum Hall (QH) tunneling junctions. In an X-shaped geometry, duality relates junctions with opening angles alpha and (pi - alpha). We prove that duality between weak tunneling and weak backscattering survives in the presence of long range interactions, and that their effects are precisely cancelled in the self dual geometry alpha=pi/2. Tunneling exponents as a function of alpha, the interaction strength chi, and the filling fraction nu are calculated. We find that Coulomb interaction induces localization in narrow channels (large alpha), and delocalization for sharply pinched constrictions (small alpha). Consequently, an insulator to metal transition happens at an angle alpha_c(chi,nu) <=pi/2. We discuss the implications of our results for tunneling experiments in QH-constriction and cleaved-edge geometries.