The metal-insulator transition in 2D systems at T = 0: one-particle approach

TL;DR

This paper models the metal-insulator transition in 2D electron systems at zero temperature by reducing the problem to one-dimensional modes, showing phase transitions linked to mode changes that explain experimental resistance anomalies.

Contribution

It introduces a one-particle mode approach to analyze the 2D metal-insulator transition, connecting mode changes to phase transitions and resistance behavior.

Findings

Metallic state results from multiple extended modes.

Transition occurs via discrete mode reduction.

Qualitative agreement with experimental resistance anomalies.

Abstract

The conductance of a disordered finite-size electron system is calculated by reducing the initial dynamic problem of arbitrary dimensionality to strictly one-dimensional problems for one-particle mode propagators. The metallic ground state of a two-dimensional conductor, which is considered as a limiting case of the actually three-dimensional quantum waveguide, is shown to result from its multi-modeness. On lowering the waveguide thickness, in practice, e.g., due to application of the ``pressing'' potential (depletion voltage), the electron system undergoes a set of continuous phase transitions connected with the discrete change in the number of extended modes. The closing of the last current-carrying mode is interpreted as the electron system transition from metallic to dielectric state. The results obtained agree qualitatively with the observed ``anomalies'' of the resistance of different electron and hole systems.