Numerical Study of Universal Conductance Fluctuation in Three-dimensional Topological Semimetals

TL;DR

This study investigates the universal conductance fluctuation in three-dimensional topological semimetals, combining theoretical predictions with numerical simulations to reveal behaviors in different semimetal types and their dependence on Fermi surface shape.

Contribution

It introduces a method to predict UCF in topological semimetals using energy level statistics and confirms predictions with numerical simulations, highlighting non-universal behavior in nodal line semimetals.

Findings

Theoretical predictions match numerical results for Dirac/Weyl semimetals.

Conductance fluctuation amplitude varies with SOC strength in nodal line semimetals.

Fermi surface shape influences conductance fluctuation behavior.

Abstract

We study the conductance fluctuation in topological semimetals. Through statistic distribution of energy levels of topological semimetals, we determine the dominant parameters of universal conductance fluctuation (UCF), i.e., the number of uncorrelated bands $k$, the level degeneracy $s$, and the symmetry parameter $\beta$. These parameters allow us to predict the zero-temperature intrinsic UCF of topological semimetals by the Altshuler-Lee-Stone theory. Then, we obtain numerically the conductance fluctuations for topological semimetals of quasi-1D geometry. We find that for Dirac/Weyl semimetals, the theoretical prediction coincides with the numerical results. However, a non-universal conductance fluctuation behavior is found for topological nodal line semimetals, i.e., the conductance fluctuation amplitude increases with the enlargement of SOC strength. We find that such unexpected parameter-dependent phenomena of conductance fluctuation are related to Fermi surface shape of 3D topological semimetals. These results will help us to understand the existing and future experimental results of UCF in 3D topological semimetals.