Electrodynamics of the topological insulator (Bi$_{\mathrm{1-x}}$In$_{\mathrm{x}}$)$_{2}$Se$_{3}$ tuned to the brink of quantum criticality

We have utilized time-domain terahertz (THz) spectroscopy to investigate the low frequency optical conductivity in (Bi$_{\mathrm{1-x}}$In$_{\mathrm{x}}$)$_{2}$Se$_{3}$ through its topological phase transition from the pure compound (x$=$0) to the topologically trivial strongly insulating material (x$=$0.27). 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 $\sim$ 0.06 of a maximum in the mid-infrared absorption, which can be identified with the bulk band gap closing and change in topological class. The realization of a topological quantum critical point allows the possible realization of other novel phenomena including the Weyl semi-metal. I will discuss our results on the THz response of these systems in a new generation of materials with greatly suppressed bulk carrier density levels. Reference: Wu, \textit{et al}, \textbf{Nature Physics} 9, 410-414 (2013).