Wilson-Loop Characterization of Inversion-Symmetric Topological Insulators

By A. Alexandradinata, X. Dai, Bogdan Andrei Bernevig. 2012

255 citations recorded by the source corpus.

The ground state of translationally-invariant insulators comprise bands which can assume topologically distinct structures. There are few known examples where this distinction is enforced by a point-group symmetry alone. In this paper we show that 1D and 2D insulators with the simplest point-group symmetry - inversion - have a $Z^{\geq}$ classification. In 2D, we identify a relative winding number that is solely protected by inversion symmetry. By analysis of Berry phases, we show that this invariant has similarities with the first Chern class (of time-reversal breaking insulators), but is more closely analogous to the $Z_2$ invariant (of time-reversal invariant insulators). Implications of our work are discussed in holonomy, the geometric-phase theory of polarization, the theory of maximally-localized Wannier functions, and in the entanglement spectrum.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/87dbb9d3498c8712476caca1d59d5f6916919a03

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials (2016, background): “[70] A Alexandradinata, Xi Dai, and B Andrei Bernevig, “Wilson-loop characterization of inversion-symmetric topological insulators,” Phys.”
Triple Point Topological Metals (2016, background): “Note that the σv symmetry constrains the φi such that the Wilson loop spectrum is mirror symmetric φi 1⁄4 −φj [25].”
Symmetry-protected topological photonic crystal in three dimensions (2015, unknown): “This approach is also known as the Wilson loops [31, 32].”
Superconductivity, superfluidity and quantum geometry in twisted multilayer systems (2021, background): “The combined antiunitary operator (PC2zT ) 2 = −1 mimics the case of spinful time-reversal symmetry and protects Kramers doublets in the Wilson spectrum at k M1 =0 and kM1 = π [113, 118] (see Fig.”
Higher-order topological insulators (2017, methodology): “As we show in the Supplementary Materials, this domain wall either binds an R moving mode withMxymirror eigenvalue il = i sgn(vz) or an L moving mode with mirror eigenvalue − i sgn(vz).”
Topological bands for ultracold atoms (2018, unknown): “However in more complex situations, interferometry can also reveal nonAbelian features of the transport (see e.g. Alexandradinata et al. (2014)).”