Numerical study of universal conductance fluctuations in three-dimensional topological semimetals

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