Effective Hamiltonian for surface states of Bi2Te3 nanocylinders with hexagonal warping
Abstract
The three-dimensional topological insulator Bi2Te3 differs from other topological insulators in the Bi2Se3 family in that the effective Hamiltonian of its surface states on a flat semi-infinite slab requires the addition of a cubic momentum hexagonal warping term in order to reproduce the experimentally measured constant energy contours. In this work, we derive the appropriate effective Hamiltonian for the surface states of a Bi2Te3 cylinder incorporating the corresponding hexagonal warping terms in a cylindrical geometry. We show that at the energy range where the surface states dominate, the effective Hamiltonian adequately reproduces the dispersion relation obtained from a full four-band Hamiltonian, which describe both the bulk and surface states. As an example application of our effective Hamiltonian, we study the transmission between two collinear Bi2Te3 cylinders magnetized in different directions perpendicular to their axes. We show that the hexagonal warping term results in a transmission profile between the cylinders which may be of utility in a multiple state magnetic memory bit.
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