Fermi energy sensitive universal conductance fluctuations in anisotropic materials

Abstract

Universal conductance fluctuations (UCF) are a hallmark of quantum interference in mesoscopic devices. According to the Altshuler-Lee-Stone theory, the amplitude of UCF remains independent of system parameters such as Fermi energy and disorder strength. However, recent experiments have demonstrated a significant variation in UCF with respect to Fermi energy in the anisotropic Dirac semimetal $\mathrm{Cd_3As_2}$, suggesting a dependence on band anisotropy. In this work, we reconcile the discrepancy between theoretical predictions and experimental observations through a detailed study of UCF versus Fermi energy using a tight-binding model with tunable anisotropy parameters. Near the band edge, the Hamiltonian is simplified to an anisotropic free electron gas model, recovering the generalized Altshuler-Lee-Stone theory. However, as the Fermi energy shifts toward the band center, where rotational symmetry breaks into $C_4$ (four-fold rotational) symmetry, the UCF amplitude deviates from the standard theory. Our findings reveal that UCF becomes increasingly sensitive to Fermi energy as the anisotropy grows stronger. Furthermore, using realistic parameters for $\mathrm{Cd_3As_2}$, our calculations demonstrate an increase in UCF away from the Dirac point, in qualitative agreement with experimental results. The enhancement of UCF occurs in two perpendicular transport directions that we have calculated, albeit with quantitative differences in magnitude, which can be tested in future experiments. Given the prevalence of anisotropic materials and technical advances in engineering anisotropy through strain or twist, our results offer a valuable reference for characterizing intrinsic electronic properties via UCF.