Abstract
A two-dimensional (2D) topological band is characterized by the (first) Chern number. The zero and nonzero Chern numbers usually represent the trivial and nontrivial band topologies, respectively. In this paper, we study an extended Qi-Wu-Zhang model that hosts the topological band with a zero Chern number. We show that the zero Chern number band is topologically nontrivial, characterized by the half-integer wave polarization. The nontrivial topology is manifested by the anisotropic in-gap edge states, which are verified to be robust against 2D particle-hole symmetric disorders.
Highlights
Topological insulators and superconductors have many potential applications because of their topologically nontrivial bands [1,2]
The Chern number associated with the energy band is a topological invariant, which is a quantized Berry flux because the integration of Berry curvature over the whole Brillouin zone (BZ) indicates the band topology of 2D topological phases [50]
To elucidate the nontrivial topology and the presence of topological in-gap edge states in the region with a zero Chern number, we employ another topological characterization: The wave polarization, which is related to the integral of the Berry connection in the whole BZ and is equal to the 2D Zak phase divided by 2π [54]
Summary
Topological insulators and superconductors have many potential applications because of their topologically nontrivial bands [1,2]. The nonzero Chern number yields the topologically nontrivial phase; the difference between the Chern numbers of bands indicates the number of topologically protected edge states in the band gap [51,52]. The topologically protected edge states are absent [53]. Beyond the traditional understanding that the topological phase with a nonzero Chern number supports a pair of chiral edge states, we find that the anisotropic 2D lattice has a topologically nontrivial phase with a zero Chern number but nonzero Berry curvature. A pair of topologically protected in-gap edge states is present in the topological phase with a zero Chern number.
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