Nonlinear edge transport in a quantum Hall system

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.