One-dimensional $\mathbb{Z}$-classified topological crystalline insulator under space-time inversion symmetry

• URL: http://arxiv.org/abs/2411.00327v1
• Date: Fri, 01 Nov 2024 02:52:50 GMT
• Title: One-dimensional $\mathbb{Z}$-classified topological crystalline insulator under space-time inversion symmetry
• Authors: Ling Lin, Yongguan Ke, Chaohong Lee,
• Abstract summary: We classify one-dimensional (1D) topological crystalline insulators by $mathbbZ$ invariants under space-time inversion symmetry. This finding stands in marked contrast to the conventional classification of 1D band topology protected by inversion symmetry. We propose to experimentally discern band topology through relative polarization of edge states or bulk states.
• Score: 0.6144680854063939
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• Abstract: We explore a large family of one-dimensional (1D) topological crystalline insulators (TCIs) classified by $\mathbb{Z}$ invariants under space-time inversion symmetry. This finding stands in marked contrast to the conventional classification of 1D band topology protected by inversion symmetry and characterized by $\mathbb{Z}_2$-quantized polarization (Berry-Zak phase). By considering the nontrivial relative polarization among sublattices (orbitals), we introduce the inversion winding number as a topological invariant for characterizing and categorizing band topology. The inversion winding number reliably captures a novel bulk-edge correspondence, where gapped edge states are related to the inversion winding number of the sandwiching bands. Leveraging real-space analysis, we discover disorder-induced topological Anderson insulators and propose to experimentally discern band topology through relative polarization of edge states or bulk states. Our comprehensive findings present a paradigmatic illustration for the ongoing investigation and classification of band topology in TCIs.

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