A sudden collapse in the transport lifetime across the topological phase transition in $(Bi_{1-x}In_x)_2 Se_3$

TL;DR

This study investigates the topological phase transition in (Bi$_{1-x}$In$_x$)$_2$Se$_3$ using terahertz spectroscopy, revealing a sudden collapse in transport lifetime linked to surface state hybridization and bulk band gap closing.

Contribution

It demonstrates the thickness-dependent collapse of transport lifetime at the topological phase transition, highlighting finite size effects in the quantum phase transition of topological insulators.

Findings

Transport lifetime collapses at the transition point.

Threshold indium substitution level approaches 0.06.

Bulk band gap closing correlates with topological class change.

Abstract

Topological insulators (TIs) are newly discovered states of matter with robust metallic surface states protected by the topological properties of the bulk wavefunctions. A quantum phase transition (QPT) from a TI to a conventional insulator and a change in topological class can only occur when the bulk band gap closes. In this work, we have utilized time-domain terahertz spectroscopy (TDTS) to investigate the low frequency conductance in (Bi$_{1-x}$In$_x$)$_2$Se$_3$ as we tune through this transition by indium substitution. Above certain substitution levels we observe a collapse in the transport lifetime that indicates the destruction of the topological phase. We associate this effect with the threshold where states from opposite surfaces hybridize. The substitution level of the threshold is thickness dependent and only asymptotically approaches the bulk limit $x \approx 0.06$ where a maximum in the mid-infrared absorption is exhibited. This absorption can be identified with the bulk band gap closing and a change in topological class. The correlation length associated with the QPT appears as the evanescent length of the surface states. The observation of the thickness-dependent collapse of the transport lifetime shows the unusual role that finite size effects play in this topological QPT.