A new approach to the quantized electrical conductance

TL;DR

This paper derives and extends the theory of quantized electrical conductance in various low-dimensional electron systems using quasi-classical and quantum principles.

Contribution

It introduces a new derivation method for quantized conductance applicable to different geometries and conditions, including magnetic fields and two-dimensional systems.

Findings

Quantization of conductance derived for 1D electron gas

Extension to nanowires with finite cross-section

Application to 2D electron gas

Abstract

The quanta of electrical conductance is derived for a one-dimensional electron gas both by making use of the quasi-classical motion of a quantum fluid and by using arguments related to the uncertainty principle. The result is extended to a nanowire of finite cross-section area and to electrons in magnetic field, and the quantization of the electrical conductance is shown. An additional application is made to the two-dimensional electron gas.