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arXiv · 1906.00218

$\mathbb{Z}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases

Hiromu Araki·Tomonari Mizoguchi·Yasuhiro Hatsugai
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Abstract

We propose the $\mathbb{Z}_Q$ Berry phase as a topological invariant for higher-order symmetry-protected topological (HOSPT) phases for two- and three-dimensional systems. It is topologically stable for electron-electron interactions assuming the gap remains open. As a concrete example, we show that the Berry phase is quantized in $\mathbb{Z}_4$ and characterizes the HOSPT phase of the extended Benalcazar-Bernevig-Hughes (BBH) model, which contains the next-nearest neighbor hopping and the intersite Coulomb interactions. In addition, we introduce the $\mathbb{Z}_4$ Berry phase for the spin-model-analog of the BBH model, whose topological invariant has not been found so far. Furthermore, we demonstrate the Berry phase is quantized in $\mathbb{Z}_4$ for the three-dimensional version of the BBH model. We also confirm the bulk-corner correspondence between the $\mathbb{Z}_4$ Berry phase and the corner states in the HOSPT phases.

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Hiromu Araki, Tomonari Mizoguchi, Yasuhiro Hatsugai. 2019-06-01. $\mathbb{Z}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases. https://doi.org/10.1103/physrevresearch.2.012009

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