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Topological insulators (TIs) are newly discovered states of matter withrobust metallic surface states protected by the topological properties of thebulk wavefunctions. A quantum phase transition (QPT) from a TI to aconventional insulator and a change in topological class can only occur whenthe bulk band gap closes. In this work, we have utilized time-domain terahertzspectroscopy (TDTS) to investigate the low frequency conductance in(Bi$_{1-x}$In$_x$)$_2$Se$_3$ as we tune through this transition by indiumsubstitution. Above certain substitution levels we observe a collapse in thetransport lifetime that indicates the destruction of the topological phase. Weassociate this effect with the threshold where states from opposite surfaceshybridize. The substitution level of the threshold is thickness dependent andonly asymptotically approaches the bulk limit $x \approx 0.06$ where a maximumin the mid-infrared absorption is exhibited. This absorption can be identifiedwith the bulk band gap closing and a change in topological class. Thecorrelation length associated with the QPT appears as the evanescent length ofthe surface states. The observation of the thickness-dependent collapse of thetransport lifetime shows the unusual role that finite size effects play in thistopological QPT.

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