The impact of dimensionality on universality of quantum Hall transitions

Abstract

Regardless of model and platform details, the critical phenomena exhibit universal behaviors that are remarkably consistent across various experiments and theories, resulting in a significant scientific success of condensed matter physics. One widely known and commonly used example is the 2D quantum Hall transition; yet, its universal exponents still somewhat conflict between experiments, theoretical models, and numerical ansatzes. We study critical behaviors of quasi-2D Weyl semimetal systems with a finite thickness $L_z>1$, disorder, and external magnetic field $B_z$. By analyzing the scaling behaviors of the localization lengths and local density of states using recursive methods, we find that the finite thickness yields a deviation from the 2D quantum Hall universality ($L_z=1$ case) and a crossover toward the 3D Gaussian Unitary Ensemble ($L_z\rightarrow \infty$ limit), potentially offering another cause of the discrepancy. Our work demonstrates the often-overlooked importance of auxiliary degrees of freedom, such as thickness, and that 3D quantum Hall physics is not merely a trivial finite-thickness extension of its 2D counterpart.