Topological States in Restrictive Geometries

Topological Insulators (TIs) are a novel class of materials possessing symmetry-protected surface states that have promising applications in spintronics and quantum computing. The properties and robustness of TI surface states are well understood for macrosopic samples with flat boundaries, but it is not clearly established what features are retained for curved boundaries - especially when the radius of curvature and/or the sample size are decreased and become comparable to the decay length of the surface states. Consequently, here we investigate the nature of the topological surface states for finite samples with curved interfaces. In particular, we study a model of a 2-dimensional TI with circular boundary of radius R, described by a 4 × 4 Dirac-like Hamiltonian. We present exact solutions for the surface states of this system, derive the effective surface Hamiltonian, and discuss the deviations of the dispersion and spin texture from the flat surface case.