Bulk-Edge Correspondence for Two-Dimensional Topological Insulators

By G. M. Graf, M. Porta. 2012

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Topological insulators can be characterized alternatively in terms of bulk or edge properties. We prove the equivalence between the two descriptions for two-dimensional solids in the single-particle picture. We give a new formulation of the $${\mathbb{Z}_{2}}$$Z2-invariant, which allows for a bulk index not relying on a (two-dimensional) Brillouin zone. When available though, that index is shown to agree with known formulations. The method also applies to integer quantum Hall systems. We discuss a further variant of the correspondence, based on scattering theory.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/5987fbb921b47d9e021fb17c1b95a393d9df2a84