Non-Abelian Stokes theorem and quantized Berry flux

Alexander C. Tyner; Shouvik Sur; Qunfei Zhou; Danilo Puggioni; Pierre Darancet; James M. Rondinelli; Pallab Goswami

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arXiv · 2102.06207

Non-Abelian Stokes theorem and quantized Berry flux

Alexander C. Tyner·Shouvik Sur·Qunfei Zhou·Danilo Puggioni·Pierre Darancet·James M. Rondinelli·Pallab Goswami

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Abstract

Band topology of anomalous quantum Hall insulators can be precisely addressed by computing Chern numbers of constituent non-degenerate bands that describe quantized, Abelian Berry flux through two-dimensional Brillouin zone. Can Chern numbers be defined for $SU(2)$ Berry connection of two-fold degenerate bands of materials preserving space-inversion ($\mathcal{P}$) and time-reversal ($\mathcal{T}$) symmetries or combined $\mathcal{PT}$ symmetry, without detailed knowledge of underlying basis? We affirmatively answer this question by employing a non-Abelian generalization of Stokes' theorem and describe a manifestly gauge-invariant method for computing magnitudes of quantized $SU(2)$ Berry flux (spin-Chern number) from eigenvalues of Wilson loops. The power of this method is elucidated by performing $\mathbb{N}$-classification of \emph{ab initio} band structures of three-dimensional, Dirac materials. Our work outlines a unified framework for addressing first-order and higher-order topology of insulators and semimetals, without relying on detailed symmetry data.

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cond-mat.mtrl-sci cond-mat.dis-nn cond-mat.mes-hall cond-mat.str-el hep-th

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Alexander C. Tyner, Shouvik Sur, Qunfei Zhou, Danilo Puggioni, Pierre Darancet, James M. Rondinelli, Pallab Goswami. 2021-02-11. Non-Abelian Stokes theorem and quantized Berry flux. https://arxiv.org/abs/2102.06207

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