Conductivity in Two-Dimensional Disordered Model with Anisotropic Long-Range Hopping

TL;DR

This paper investigates electrical conductivity in a two-dimensional disordered system with anisotropic long-range hopping, analyzing how site distribution and particle density affect transport properties.

Contribution

It introduces a model with anisotropic transfer elements and computes conductivity by summing diffusion and cooperon ladder diagrams, providing new insights into disordered 2D systems.

Findings

Conductivity varies with site distribution and particle density.

Anisotropic long-range hopping significantly influences transport.

Theoretical calculations align with expected disordered system behaviors.

Abstract

We consider two-dimensional system of particles localized on randomly distributed sites of squared lattice with anisotropic transfer matrix elements between localized sites. By summing of "diffusion ladder" and "cooperon ladder" type vertices we calculated the conductivity for various sites and particles densities.