Computing topological invariants without inversion symmetry

By Alexey A. Soluyanov, D. Vanderbilt. 2011

372 citations recorded by the source corpus.

We consider the problem of calculating the weak and strong topological indices in noncentrosymmetric time-reversal ($\mathcal{T}$) invariant insulators. In 2D we use a gauge corresponding to hybrid Wannier functions that are maximally localized in one dimension. Although this gauge is not smoothly defined on the two torus, it respects the $\mathcal{T}$ symmetry of the system and allows for a definition of the ${\mathbb{Z}}_{2}$ invariant in terms of time-reversal polarization. In 3D we apply the 2D approach to $\mathcal{T}$-invariant planes. We illustrate the method with first-principles calculations on GeTe and on HgTe under $[001]$ and $[111]$ strain. Our approach differs from ones used previously for noncentrosymmetric materials and should be easier to implement in ab initio code packages.

Subfields: Atomic and Molecular Physics, and Optics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/132de9cf693eb4920af327636cfef13aa0c75173

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Citations in the corpus

Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials (2016, methodology): “Under this constraint, the HWCCs need to come in pairs of TR-symmetric momenta [67,95], and the individual Chern numbers of the two bands must be opposite (c2 = −c1).”
Maximally-localized Wannier Functions: Theory and Applications (2011, background): “…electric fields along a specific spatial direction (Giustino and Pasquarello, 2005; Giustino et al., 2003; Murray and Vanderbilt, 2009; Stengel and Spaldin, 2006a; Wu et al., 2006) or for analyzing aspects of topological insulators (Coh and Vanderbilt, 2009; Soluyanov and Vanderbilt, 2011a,b).”
Triple Point Topological Metals (2016, background): “Appendix G also contains an additional topological characterization of TPs in terms of Wilson loops [32] and Wannier charge centers [33,34].”