Journal
PHYSICAL REVIEW B
Volume 98, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.98.045125
Keywords
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Funding
- MEXT KAKENHI [JP15H05854, JP17K05490, JP18H03676]
- CREST, JST [JPMJCR16F1]
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A higher-order topological insulator (HOTI) is an extended notion of the conventional topological insulator. It belongs to a special class of topological insulators to which the conventional bulk-boundary correspondence is not applicable. Provided the mirror symmetries are present, the bulk topological number is described by the quantized Wannier center located at a high-symmetry point of the crystal. The emergence of corner states is a manifestation of nontrivial topology in the bulk. In this paper we propose minimal models for the Wannier-type second-order topological insulator in two dimensions and the third-order topological insulator in three dimensions. They are anisotropic chiral-symmetric two-band models. It is explicitly shown that the Wannier center is identical to the winding number in the present model, demonstrating that it is indeed a topological quantum number. Finally we point out that the essential physics of phosphorene near the Fermi energy is described by making a perturbation of the Wannier-type HOTI. We predict that these corner states will be observed in the rhombus structure of phosphorene near the Fermi energy around -0.16 eV.
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