Metal - Insulator Transition in 3D Quantum Percolation

TL;DR

This study investigates the metal-insulator transition in a 3D quantum percolation model using transfer matrix methods, revealing critical properties and universality class similarities with the 3D Anderson model.

Contribution

It provides detailed analysis of the mobility edge, critical disorder, and critical exponent in 3D quantum percolation, highlighting universality and potential deviations at the band center.

Findings

Critical exponent matches 3D Anderson model

Mobility edge close to classical percolation threshold

Geometric mean of conductance predicts zero critical disorder at band center

Abstract

We present the metal - insulator transition study of a quantum site percolation model on simple cubic lattice. Transfer matrix method is used to calculate transport properties - Landauer conductance - for the binary distribution of energies. We calculate the mobility edge in disorder (ratio of insulating sites) - energy plane in detail and we find the extremal critical disorder somewhat closer to the classical percolation threshold, than formerly reported. We calculate the critical exponent $\nu$ along the mobility edge and find it constant and equal to the one of 3D Anderson model, confirming common universality class. Possible exception is the center of the conduction band, where either the single parameter scaling is not valid anymore, or finite size effects are immense. One of the reasons for such statement is the difference between results from arithmetic and geometric averaging of conductance at special energies. Only the geometric mean yields zero critical disorder in band center, which was theoretically predicted.