Extra Current and Integer Quantum Hall Conductance in the Spin-Orbit Coupling System

TL;DR

This paper investigates the particle current and quantized Hall conductance in a 2D k-cubic Rashba spin-orbit system, revealing an extra current term that refines the theoretical understanding of the quantum Hall effect.

Contribution

It provides a correct formula for charge current considering extra contributions and extends Noether's theorem for this system, enhancing the theoretical framework of quantum Hall phenomena.

Findings

Extra current term arises from cubic momentum dependence.

The extra current does not affect Hall conductance quantization.

Two methods yield consistent results for the current and conductance.

Abstract

We study the extra term of particle current in a 2D k-cubic Rashba spin-orbit coupling system and the integer quantization of the Hall conductance in this system. We provide a correct formula of charge current in this system and the careful consideration of extra currents provides a stronger theoretical basis for the theory of the quantum Hall effect which has not been considered before. The non-trivial extra contribution to the particle current density and local conductivity, which originates from the cubic dependence on the momentum operator in the Hamiltonian, will have no effect on the integer quantization of the Hall conductance. The extension of Noether's theorem for the 2D k-cubic Rashba system is also addressed. The two methods reach to exactly the same results.