Year: 2014
Type: article
Abstract: The ground state of translationally invariant insulators comprises 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 ${\mathbb{Z}}^{\ensuremath{\ge}}$ 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 ${\mathbb{Z}}_{2}$ 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.
Source: Physical Review B
Authors: A. Alexandradinata, Xi Dai, B. Andrei Bernevig
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, Princeton University, National Natural Science Foundation of China, Defense Advanced Research Projects Agency, Materials Research Science and Engineering Center, Harvard University, National Key Research and Development Program of China, Office of Naval Research, Division of Materials Research
OpenAlex ID: W2964320881