• DOI:10.1103/PhysRevResearch.2.012009
• Corpus ID: 173990844

ZQ Berry phase for higher-order symmetry-protected topological phases

@article{Araki2019ZQB,
  title={ZQ
 Berry phase for higher-order symmetry-protected topological phases},
  author={Hiromu Araki and Tomonari Mizoguchi and Yasuhiro Hatsugai},
  journal={arXiv: Strongly Correlated Electrons},
  year={2019}
}

• Hiromu Araki, T. Mizoguchi, Y. Hatsugai
• Published 1 June 2019
• Physics
• arXiv: Strongly Correlated Electrons

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.