Robustness of the spin-Chern number

By E. Prodan. 2009

228 citations recorded by the source corpus.

The spin Chern $({C}_{s})$ was originally introduced on finite samples by imposing spin boundary conditions at the edges. This definition leads to confusing and contradictory statements. On one hand, the original paper by Sheng et al. revealed robust properties of ${C}_{s}$ against disorder and certain deformations of the model and, on the other hand, several people pointed out that ${C}_{s}$ can change sign under special deformations that keep the bulk Hamiltonian gap open. Because of the later findings, the spin-Chern number was dismissed as a true bulk topological invariant and now is viewed as something that describes the edge where the spin boundary conditions are imposed. In this paper, we define the spin-Chern number directly in the thermodynamic limit, without using any boundary conditions. We demonstrate its quantization in the presence of strong disorder and we argue that ${C}_{s}$ is a true bulk topological invariant whose robustness against disorder and smooth deformations of the Hamiltonian have important physical consequences. The properties of the spin-Chern number remain valid even when the time reversal invariance is broken.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/3b5114b841d404a1c69ade81cd4e0939271d1c62

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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, methodology): “While in the presence of additional symmetries [114,115] such a splitting is possible, it is preferable to have a numerical method for computing , which does not require an explicit splitting of the Hilbert space.”
Bulk-Edge Correspondence for Two-Dimensional Topological Insulators (2012, background): “Thus spin resolved Chern numbers can be defined by homotopy [24,29] and the duality inferred from that of the quantum Hall case [28].”
Topological insulators and superconductors (2010, background): “Several approaches have been explored in the literature including spin Chern numbers (Fukui and Hatsugai, 2007; Prodan, 2009; Shenget al., 2006), topological invariants constructed from Bloch wave functions (Fu and Kane, 2006; Kane and Mele, 2005; Moore and Balents, 2007; Roy, 2009), and discrete…”