Level Statistics Crossover of Chiral Surface States in a Three-Dimensional Quantum Hall System

Recent experiments have demonstrated the realization of the three-dimensional quantum Hall effect in highly anisotropic crystalline materials, such as ZrTe|_5 and BaMnSb_2. Such a system supports chiral surface states in the presence of a strong magnetic field, which exhibit a one-dimensional metal-insulator crossover due to suppression of surface diffusion by disorder potential. We study the nontrivial surface states in a lattice model and find a wide crossover of the level-spacing distribution through a semi-Poisson distribution. We also discover a nonmonotonic evolution of the level statistics due to the disorder-induced mixture of surface and bulk states.