Effective Hamiltonian for surface states of \ce{Bi2Te3} nanocylinders with hexagonal warping

TL;DR

This paper derives an effective Hamiltonian for the surface states of 2te32te3 nanocylinders that includes hexagonal warping effects, enabling better modeling of their electronic properties and potential applications in magnetic memory devices.

Contribution

The work extends the effective Hamiltonian to cylindrical geometries for 2te32te3, incorporating hexagonal warping terms, and validates it against full four-band models.

Findings

The effective Hamiltonian accurately reproduces the dispersion relation of surface states.

Hexagonal warping influences the transmission profile between magnetized cylinders.

Potential application in multi-state magnetic memory devices.

Abstract

The three-dimensional topological insulator \ce{Bi2Te3} differs from other topological insulators in the \ce{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 \ce{Bi2Te3} \textit{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 \ce{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.