# Condensed Matter seminar: "How to kill a topological insulator"

Topological insulators (TIs) are states of matter characterized by an inverted band structure driven by strong spin-orbit coupling (SOC). They have a variety of unusual properties including robust surface states (SS) that are protected by topological properties of the bulk wavefunctions. Of particular interest is the quantum phase transition that separates a TI from a conventional insulator. Such a transition between different topological classes 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 conductivity in (Bi1-xInx)2Se3 through this transition by tuning SOC through In substitution. Above a thickness dependent doping threshold we observe a sudden collapse in the transport lifetime that indicates the destruction of the topological phase. We associate this with the doping where the states from opposite surfaces hybridize. As a function of thickness this threshold asymptotically approaches the doping x ~ 0.06 of a maximum in the mid-infrared absorption, which can be identified with the band gap closing and change in topological class. Our work shows the fundamental role that finite size effects play in this transition though the `bulk-boundary correspondence' of topological systems.