Effective Hamiltonian for surface states of Bi₂Te₃ nanocylinders with hexagonal warping

The three-dimensional topological insulator $\text{B}{\text{i}}_2\text{T}{\text{e}}_3$ differs from other topological insulators in the $\text{B}{\text{i}}_2\text{S}{\text{e}}_3$ 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 $\text{B}{\text{i}}_2\text{T}{\text{e}}_3$ 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 describes both the bulk and surface states. As an example application of our effective Hamiltonian, we study the transmission between two collinear $\text{B}{\text{i}}_2\text{T}{\text{e}}_3$ 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. (paper)