Disordered topological insulators via C*-algebras

By Terry A. Loring, M. B. Hastings. 2010

224 citations recorded by the source corpus.

The theory of almost commuting matrices can be used to quantify topological obstructions to the existence of localized Wannier functions with time-reversal symmetry in systems with time-reversal symmetry and strong spin-orbit coupling. We present a numerical procedure that calculates a Z2 invariant using these techniques, and apply it to a model of HgTe. This numerical procedure allows us to access sizes significantly larger than procedures based on studying twisted boundary conditions. Our numerical results indicate the existence of a metallic phase in the presence of scattering between up and down spin components, while there is a sharp transition when the system decouples into two copies of the quantum Hall effect. In addition to the Z2 invariant calculation in the case when up and down components are coupled, we also present a simple method of evaluating the integer invariant in the quantum Hall case where they are decoupled.

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

View Paper: https://www.semanticscholar.org/paper/01f0eeb0f58d1b7fd429f95e2bdd4525aaaa9cd3

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport (2016, methodology): “β is given by CBðβÞ 1⁄4 ImfTr1⁄2logðVUV†U†Þ g=2π [53].”
Z2Pack: Numerical Implementation of Hybrid Wannier Centers for Identifying Topological Materials (2016, background): “For the topological quantum spin Hall phase, C1,2 are odd, so that TR symmetry does not allow for the construction of smooth Bloch states spanning both these subspaces [66,113].”
Topological bands for ultracold atoms (2018, unknown): “Such systems can still be characterized by the Bott index (Loring and Hastings, 2010), which provides a real-space formulation of the Chern index applicable also to finite-sized systems.”
Topological insulators and superconductors (2010, background): “The disorerinduced TI state has been studied recently (Grothet al., 2009; Guo, 2010; Guoet al., 2010; Imuraet al., 2009; Jianget al., 2009; Liet al., 2009; Loring and Hastings, 2010; Obuseet al., 2008; Olshanetskyet al., 2010; Ostrovskyet al., 2009; Shindou and Murakami, 2009).”