Metal-insulator transition in a two-dimensional electron system: the orbital effect of in-plane magnetic field

TL;DR

This paper models how an in-plane magnetic field induces a metal-insulator transition in a 2D electron system by affecting transverse quantization modes, leading to conductance reduction and mode closure.

Contribution

It introduces a novel approach treating the magnetic field as a non-local scatterer affecting transverse modes in a 2D electron system.

Findings

Conductance decreases rapidly with increasing magnetic field.

Magnetic field reduces the number of transverse quantization modes.

Closing of the last current-carrying mode causes the metal-insulator transition.

Abstract

The conductance of an open quench-disordered two-dimensional (2D) electron system subject to an in-plane magnetic field is calculated within the framework of conventional Fermi liquid theory applied to actually a three-dimensional system of spinless electrons confined to a highly anisotropic (planar) near-surface potential well. Using the calculation method suggested in this paper, the magnetic field piercing a finite range of infinitely long system of carriers is treated as introducing the additional highly non-local scatterer which separates the circuit thus modelled into three parts -- the system as such and two perfect leads. The transverse quantization spectrum of the inner part of the electron waveguide thus constructed can be effectively tuned by means of the magnetic field, even though the least transverse dimension of the waveguide is small compared to the magnetic length. The initially finite (metallic) value of the conductance, which is attributed to the existence of extended modes of the transverse quantization, decreases rapidly as the magnetic field grows. This decrease is due to the mode number reduction effect produced by the magnetic field. The closing of the last current-carrying mode, which is slightly sensitive to the disorder level, is suggested as the origin of the magnetic-field-driven metal-to-insulator transition widely observed in 2D systems.