Two-dimensional disordered electron systems: a network model approach

TL;DR

This paper uses network models to explore the physics of disordered two-dimensional electron systems, revealing localization behaviors and phase transitions with specific critical exponents.

Contribution

It introduces a network model approach to classify universality classes and determine phase diagrams and critical exponents for disordered 2D electron systems.

Findings

Identifies three universality classes with distinct localization properties.

Determines phase diagrams and localization lengths for each class.

Finds a localization-delocalization transition with specific critical exponents.

Abstract

We demonstrate that network models for wave mechanical systems with quenched disorder cover the physics of mesoscopic electrons. The models are constructed as a network of random scattering matrices connecting incoming to outgoing wave amplitudes. The corresponding wave dynamics is given by a discrete unitary time evolution operator. We report on three different universality classes: two-dimensional, spinless, non-chiral electrons with (O2NC) and without time reversal symmetry (U2NC), and two-dimensional, non-chiral electrons with time reversal symmetric spin-scattering (S2NC). We determine the phase diagram in the parameter space of scattering strengths. The O/U2NC models show strong localization. We find symmetry factors in localization lengths as well as multifractal exponents in agreement with theoretical predictions. The S2NC model displays a localization-delocalization transition. We determine the critical exponent of the localization length and the multifractal scaling exponent of the order parameter to be $\nu \approx 2.4$ and $\alpha_0\approx 2.18$, respectively.