Abstract
We investigate the transport and energy spectrum properties of a three-dimensional high-order topological structure formed by stacking two-dimensional square diatomic Chern insulator lattices. Electron-hole symmetry and the energy spectrum degeneracy at individual points in the semimetallic phase are proven to be due to chiral and antiunitary symmetries in the periodic system. Additionally, we explore the influence of boundary conditions in a slab system with varying surface atom connectivity, and we demonstrate analytically the presence of zero-energy surface states in specific configurations. Moreover, we describe the emergence of two chiral hinge states driven by a perpendicular phase in the nanowire geometry. Next, the quantum Hall resistance is computed in the cross-configuration of a four-lead device. In this paper, we demonstrate that the trajectories of hinge states, determined by the number of layers in parallelepiped finite structure, give rise to fractional Hall plateaus. Published by the American Physical Society 2024
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