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

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Recent experiments have demonstrated the realization of the three-dimensional quantum Hall effect in highly anisotropic crystalline materials,such as ZrTe5 and BaMnSb2.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.
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