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Local formula for the $Z_2$ invariant of topological insulators

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arxiv 1905.12649 v3 pith:ODXZHIYT submitted 2019-05-29 cond-mat.mes-hall math-phmath.MP

Zhi Li , Roger S.K. Mong This is my paper · ORCID
classification cond-mat.mes-hallmath-phmath.MP
keywords formulainvariantlocalinsulatorsmethodproposedtopologicalalmost
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abstract

We proposed a formula for the $Z_2$ invariant for topological insulators, which remains valid without translational invariance. Our formula is a local expression, in the sense that the contributions mainly come from quantities near a point. Using almost commute matrices, we proposed a method to approximate this invariant with local information. The validity of the formula and the approximation method is proved.

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  1. Two-Dimensional Time-Reversal-Invariant Topological Insulators via Fredholm Theory

    math-ph 2019-08 accept novelty 7.0 of 10

    For spectrally gapped, time-reversal-invariant, exponentially local 2D Hamiltonians, the Z2 bulk index equals the mod-2 index of an edge Fredholm operator.

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