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arXiv · 1306.2520

Topological insulators, spin, and the tight-binding method

Warren J. Elder·Eng Soon Tok·Dimitri D. Vvedensky·Jing Zhang
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Abstract

As one of the first proposed topologically protected states, the quantum spin Hall effect in graphene relies critically on the existence of a spin-dependent gap at the K/K' points of the Brillouin zone. Using a tight-binding formulation based on the method of invariants, we identify the origin of such an intrinsic gap as the three-center interaction between the pi-orbitals caused by spin-orbit interactions. This methodology incorporates all symmetry compliant interactions previously neglected and has wider applications for comparisons between first-principle calculations and the tight-binding method. It also identifies a correction to the Haldane model and its generalization, which incorporates the spin degrees of freedom and reproduces all the salient features required for the quantum spin Hall effect in graphene.

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Warren J. Elder, Eng Soon Tok, Dimitri D. Vvedensky, Jing Zhang. 2013-07-09. Topological insulators, spin, and the tight-binding method. https://arxiv.org/abs/1306.2520

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