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Wilson-Loop Characterization of Inversion-Symmetric Topological Insulators | | A. Alexandradinata
; Xi Dai
; B. Andrei Bernevig
; | | Date: |
21 Aug 2012 | | Abstract: | In the context of translationally-invariant insulators, Wilson loops describe
the adiabatic evolution of the ground state around a closed circuit in the
Brillouin zone. We propose that the Wilson-loop eigenspectrum provides a
complete characterization of the inversion-symmetric topological insulator.
Through the Wilson loop, we formulate a criterion for nontriviality that
indicates a Z classification of 1D inversion-symmetric insulators. If the
ground-state wavefunctions at momenta 0 and pi transform under different
representations of inversion, we find that a subset of the Wilson-loop
eigenvalues are robustly quantized to -1; we identify the number of -1
eigenvalues as a topological index N in Z. Physical interpretations of N are
provided in holonomy and in the geometric-phase theory of polarization. In
addition, we identify N with the number of protected boundary modes in the
entanglement spectrum. In 2D, we identify a relative winding number W which
provides a Z classification of 2D inversion-symmetric insulators. For
insulators with nonzero W, their Wilson-loop eigenspectra exhibit spectral flow
that is protected only by inversion symmetry. Hence, W is the inversion-analog
of the first Chern class C (for charge-conserving insulators) and the Z_2
invariant Xi (for time-reversal invariant insulators). Finally, we establish
relations between the topological invariants (W, C, Xi) and the Wilson-loop
eigenvalues at symmetric lines in the 2D Brillouin zone. | | Source: | arXiv, 1208.4234 | | Services: | Forum | Review | PDF | Favorites | |
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