title: Continuum theory of edge states of topological insulators: variational principle and boundary conditions.
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 to derive natural boundary conditions valid for such systems. Our formulation is particularly suited for developing 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 modelled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian, we show that the continuum theory with a natural boundary condition provides an appropriate description of the low energy physics.
authors: Centre for Condensed Matter Theory, Indian Institute of Science, Bangalore 560012, India. amedhi@physics.iisc.ernet.in
authors: Amal
authors: A
authors: Medhi
authors: Vijay B
authors: VB
authors: Shenoy