Hybridization and Field Driven Phase Transitions in Hexagonally Warped Topological Insulators

TL;DR

This paper investigates how material parameters and external fields induce quantum phase transitions in thin film topological insulators, highlighting the roles of hybridization, hexagonal warping, and electric fields in symmetry breaking and phase change.

Contribution

It reveals the conditions under which hybridization and hexagonal warping cause phase transitions, and how electric fields can be used to control these transitions in topological insulators.

Findings

Hybridization or hexagonal warping induces semi-metal to insulator transition.

Electric fields alone do not cause QPT but can facilitate it with tunneling.

Hexagonal warping leads to immediate PT symmetry breaking QPT.

Abstract

In this paper we discuss the role of material parameters and external field effects on a thin film topological insulator(TI) in the context of quantum phase transition(QPT). First, we consider an in-plane tilted magnetic field and determine the band structure of the surface states as a function of the tilt angle. We show that the presence of either a hybridization term or hexagonal warping or a combination of both leads to a semi-metal to insulator phase transition which is facilitated by their ${\cal PT}$ symmetry breaking character. We then note that while the introduction of an electric field does not allow for this QPT since it doesn't break ${\cal PT}$ symmetry, it can be used in conjunction with a tunneling element to reach a phase transition efficiently. The corresponding critical point is then non-trivially depend on the electric field, which is pointed out here. Then, we demonstrate that including a hexagonal warping term leads to an immediate ${\cal PT}$ symmetry violating QPT.