Two-dimensional electron systems beyond the diffusive regime

TL;DR

This paper investigates the size dependence of parameters characterizing electron transport in disordered 2D systems, confirming theoretical predictions and exploring critical behavior near the metal-insulator transition.

Contribution

It provides numerical analysis of new parameters $K_{11}$ and $\gamma$ in 2D disordered models, validating their behavior against single parameter transport theory.

Findings

$\gamma$ approaches zero in the localized regime regardless of symmetry.

In the diffusive regime, $\gamma$ equals the symmetry parameter $eta$.

Identifies a non-universal critical value $\gamma_c$ at the metal-insulator transition.

Abstract

Transport properties of disordered electron system can be characterized by the conductance, Lyapunov exponent, or level spacing. Two additional parameters, $K_{11}$ and $\gamma $ were introduced recently which measure the non-homogeneity of the spatial distribution of the electron inside the sample. % [Phys. Rev. Lett. {\bf 82}, 4272 (1999)]. For the orthogonal, unitary and symplectic two dimensional disordered models, we investigate numerically the system size dependence of these parameters in the diffusive and localized regime. Obtained size and disorder dependence of $K_{11}$ and $\gamma$ is in agreement with with single parameter transport theory. In the localized regime, $\gamma\to 0$ independently on the physical symmetry of the model. In the diffusive regime, $\gamma$ equals to the symmetry parameter $\beta$. For the symplectic model we analyze the size dependence of $\gamma$ in the critical region of the metal-insulator transition and found the non-universal critical value $\gamma_c$.