Specific Plateaus of the Quantum Hall Effect Induced by an Applied Bias

TL;DR

This paper investigates how an applied bias in a finite 2D quantum system induces additional plateaus in the quantum Hall effect, explained through eigenstate equipotential properties and confirmed by numerical simulations.

Contribution

It introduces a novel mechanism for additional quantum Hall plateaus caused by an external bias, supported by numerical calculations using the Landauer-Büttiker approach.

Findings

Additional IQHE plateaus appear due to equipotential channels.

Eigenstates show equipotential and crossing behaviors under bias.

Numerical simulations confirm the formation of new plateaus.

Abstract

The spectrum and the eigenstates of a finite 2D tight-binding electronic system, with Dirichlet boundary conditions, in magnetic field and external linear potential are studied. The eigenstates show an equipotential character and may cross the plaquette in the direction perpendicular to the electric field. When leads are added to the plaquette, the channels carrying the current may be shortcut by equipotentials, resulting in additional plateaus situated inbetween the usual IQHE plateaus. This idea is confirmed by a numerical calculation within the four-terminal Landauer-B\"{u}ttiker approach.