Equivalent expression of Z 2 topological invariant for band insulators using the non-Abelian Berry connection

By R. Yu, Xiao-Liang Qi, A. Bernevig, Z. Fang, X. Dai. 2011

584 citations recorded by the source corpus.

We introduce an expression for the Z(2) topological invariant of band insulators using the non-Abelian Berry connection. Our expression can identify the topological nature of a general band insulator without any of the gauge-fixing problems that plague the concrete implementation of previous invariants. This expression can be derived from the "partner switching" of the Wannier function center during time-reversal pumping and is thus equivalent to the Z(2) topological invariant proposed by Kane and Mele. Using our expression, we have recalculated the Z(2) topological index for several topological insulator material systems and obtained consistent results with the previous studies.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/f7906fe20ccde0770be53780008d6a87a9f237a5

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials (2016, methodology): “[66, 69], for the special case of TR-symmetric systems.”
A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions (2015, unknown): “alculate. An altogether different approach, which is robust and calculatable, uses the scattering matrix instead of the Hamiltonian[13]. In this Chapter we review a deﬁnition of the bulk Z 2 invariant[37] based on the dimensional reduction to charge pumps. This is equivalent to the originally deﬁned”
Colloquium: Strong-field phenomena in periodic systems (2017, background): “…gauge symmetry U(1), the Berry connection and curvature have multiple components in a subspace of degenerate Bloch bands, so that they become matrices with a non-Abelian gauge structure (Alexandradinata and Bernevig, 2016; Li et al., 2016; Wilczek and Zee, 1984; Xiao et al., 2010; Yu et al., 2011).”
Topological Nematic States and Non-Abelian Lattice Dislocations (2011, background): “[39] Rui Yu, Xiao-Liang Qi, Andrei Bernevig, Zhong Fang, and Xi Dai, An Equivalent Expression of Z2 Topological Invariant for Band Insulators Using the Non-Abelian Berry Connection, Phys.”