Low-velocity anisotropic Dirac fermions on the side surface of topological insulators

TL;DR

This paper reveals anisotropic Dirac-cone surface bands on the side surface of topological insulator Bi$_2$Se$_3$, showing direction-dependent electron velocities and spin textures, with implications for surface transport phenomena.

Contribution

It introduces the first-principles calculation of anisotropic Dirac cones on side surfaces and proposes an effective Hamiltonian for these Dirac fermions, highlighting their unique properties.

Findings

Electron velocity in side-surface Dirac cone is anisotropically reduced.

Electron spin depends on the wave vector direction due to anisotropic noncollinearity.

Implications for refractive transport at edges where different surfaces meet.

Abstract

We report anisotropic Dirac-cone surface bands on a side-surface geometry of the topological insulator Bi$_2$Se$_3$ revealed by first-principles density-functional calculations. We find that the electron velocity in the side-surface Dirac cone is anisotropically reduced from that in the (111)-surface Dirac cone, and the velocity is not in parallel with the wave vector {\bf k} except for {\bf k} in high-symmetry directions. The size of the electron spin depends on the direction of {\bf k} due to anisotropic variation of the noncollinearity of the electron state. Low-energy effective Hamiltonian is proposed for side-surface Dirac fermions, and its implications are presented including refractive transport phenomena occurring at the edges of tological insulators where different surfaces meet.