"Unusual" metals in two dimensions: one-particle model of the metal-insulator transition at T=0

TL;DR

This paper models the metal-insulator transition at zero temperature in disordered nano-wires using a one-particle approach, revealing a continuous phase transition influenced by waveguide thinning.

Contribution

It introduces a one-particle model for the metal-insulator transition in two-dimensional systems, connecting multi-mode conductance to phase transition behavior.

Findings

Metallic ground state arises from multi-modeness.

Thinning the waveguide induces a continuous transition to an insulating state.

Model qualitatively explains resistance anomalies in planar electron systems.

Abstract

The conductance of disordered nano-wires at T=0 is calculated in one-particle approximation by reducing the original multi-dimensional problem for an open bounded system to a set of exactly one-dimensional non-Hermitian problems for mode propagators. Regarding two-dimensional conductor as a limiting case of three-dimensional disordered quantum waveguide, the metallic ground state is shown to result from its multi-modeness. On thinning the waveguide (in practice, e. g., by means of the ``pressing'' external electric field) the electron system undergoes a continuous phase transition from metallic to insulating state. The result predicted conform qualitatively to the observed anomalies of the resistance of different planar electron and hole systems.