Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes

TL;DR

This paper numerically estimates the critical exponent of the Anderson transition in three and four dimensional unitary classes, relevant for topological materials, using transfer matrix techniques.

Contribution

It provides new numerical estimates of the critical exponent for the Anderson transition in 3D and 4D unitary classes, linking theory to topological materials.

Findings

Estimated critical exponents for 3D and 4D unitary classes.

Highlights the relevance to Weyl semi-metals and topological insulators.

Uses transfer matrix numerical method.

Abstract

Disordered non-interacting systems are classified into ten symmetry classes, with the unitary class being the most fundamental. The three and four dimensional unitary universality classes are attracting renewed interest because of their relation to three dimensional Weyl semi-metals and four dimensional topological insulators. Determining the critical exponent of the correlation/localistion length for the Anderson transition in these classes is important both theoretically and experimentally. Using the transfer matrix technique, we report numerical estimations of the critical exponent in a U(1) model in three and four dimensions.