A sudden collapse in the transport lifetime across the topological phase transition in (Bi1−xInx)2Se3

The quantum phase transition from a topological to a conventional insulator in In-doped Bi2Se3 occurs when the topological phase is destroyed by the hybridization of states on opposite surfaces. This is characterized by a sudden change in the transport lifetime, measured by means of optical spectroscopy. Topological insulators are newly discovered states of matter with robust metallic surface states protected by the topological properties of the bulk wavefunctions1,2,3,4,5,6. A quantum phase transition from a topological insulator to a conventional insulator and a change in topological class can occur only when the bulk bandgap closes3. In this work, we have used time-domain terahertz spectroscopy to investigate the low-frequency conductance in (Bi1−xInx)2Se3 as we tune through this transition by In 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≈0.06 where a maximum in the mid-infrared absorption is exhibited. This absorption can be identified with the bulk bandgap closing and change in topological class. The correlation length associated with the quantum phase transition 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 quantum phase transition.