Electronic Structures and Surface States of Topological Insulator Bi$_{1-x}$Sb$_{x}$

TL;DR

This study uses first-principle calculations to analyze the electronic and surface states of Bi$_{1-x}$Sb$_x$, revealing how Sb doping and pressure induce topological phases and predicting spin-resolved Fermi surfaces.

Contribution

It demonstrates how Sb doping and uniaxial pressure can induce topological phases in Bi$_{1-x}$Sb$_x$ and provides detailed predictions of surface states and Fermi surfaces validated by calculations.

Findings

Pure Bi is topologically trivial.

Sb doping induces a topologically non-trivial phase.

Uniaxial pressure enhances the bulk band gap.

Abstract

We investigate the electronic structures of the alloyed Bi$_{1-x}$Sb$_x$ compounds based on first-principle calculations including spin-orbit coupling (SOC), and calculate the surface states of semi-infinite systems using maximally localized Wannier function (MLWF). From the calculated results, we analyze the topological nature of Bi$_{1-x}$Sb$_x$, and found the followings: (1) pure Bi crystal is topologically trivial; (2) topologically non-trivial phase can be realized by reducing the strength of SOC via Sb doping; (3) the indirect bulk band gap, which is crucial to realize the true bulk insulating phase, can be enhanced by uniaxial pressure along c axis. (4) The calculated surface states can be compared with experimental results, which confirms the topological nature; (5) We predict the spin-resolved Fermi surfaces and showed the vortex structures, which should be examined by future experiments.