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arXiv · 1202.3863

Continuum Theory of Edge States of Topological Insulators: Variational Principle and Boundary Conditions

Amal Medhi·Vijay B. Shenoy
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Abstract

We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural boundary conditions valid for such systems. Our formulation is particularly suited to develop a continuum theory of the protected edge/surface excitations of topological insulators both in two and three dimensions. By a detailed comparison of our analytical formulation with tight binding calculations of ribbons of topological insulators modeled by the Bernevig-Hughes-Zhang (BHZ) hamiltonian, we show that the continuum theory with the natural boundary condition provides an appropriate description of the low energy physics. As a spin-off, we find that in a certain parameter regime, the gap that arises in topological insulator ribbons of finite width due to the hybridization of edges states from opposite edges, depends non-monotonically on the ribbon width and can nearly vanish at certain "magic widths".

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Amal Medhi, Vijay B. Shenoy. 2012-02-17. Continuum Theory of Edge States of Topological Insulators: Variational Principle and Boundary Conditions. https://doi.org/10.1088/0953-8984%2F24%2F35%2F355001

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