Nonlinear edge transport in a quantum Hall system

TL;DR

This paper theoretically investigates the nonlinear current-voltage relationship in quantum Hall edge transport, revealing how electron interactions induce nonlinearity and suggesting experimental ways to observe these effects.

Contribution

It introduces a theoretical framework for understanding third-order nonlinearities in quantum Hall edge transport due to electron-electron interactions.

Findings

Nonlinear Hall response arises from electron-electron interactions.

Nonlinearity appears up to third order in the Hall voltage.

Potential experimental observations are discussed.

Abstract

Nonlinear transport phenomena in condensed matter reflect the geometric nature, quantum coherence, and many-body correlation of electronic states. Electric currents in solids are classified into (i) Ohmic current, (ii) supercurrent, and (iii) geometric or topological current. While the nonlinear current-voltage $(I$-$V)$ characteristics of the former two categories have been extensive research topics recently, those of the last category remains unexplored. Among them, the quantum Hall current is a representative example. Realized in two-dimensional electronic systems under a strong magnetic field, the topological protection quantizes the Hall conductance in the unit of $e^2/h$ ($e$: elementary charge, $h$: Planck constant), of which the edge transport picture gives a good account. Here, we theoretically study the nonlinear $I$-$V_\text{H}$ characteristic of the edge transport up to third order in $V_\text{H}$. We find that nonlinearity arises in the Hall response from electron-electron interaction between the counterpropagating edge channels with the nonlinear energy dispersions. We also discuss possible experimental observations.