Bulk-boundary correspondence in three dimensional topological insulators

Details Bulk-boundary correspondence in three dimensional topological insulators Bulk-boundary correspondence in three dimensional topological insulators

2011-02-28

arxiv.org/abs/1103.0025v2

Phys. Rev. B 84, 075444 (2011)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

TeXLive (Unix), revtex4-1, 7 pages, 3 figures

Scientific paper

We discuss the relation between bulk topological invariants and the spectrum of surface states in three dimensional non-interacting topological insulators. By studying particular models, and considering general boundary conditions for the electron wavefunction on the crystal surface, we demonstrate that using experimental techniques that probe surface states, only strong topological and trivial insulating phases can be distinguished; the latter state being equivalent to a weak topological insulator. In a strong topological insulator, only the {\it parity} of the number of surface states, but not the number itself, is robust against time-reversal invariant boundary perturbations. Our results suggest a $\z$ definition of the bulk-boundary correspondence, compatible with the $\z$ classification of topological insulators.

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