High-Resolution Faraday Rotation and Electron-Phonon Coupling in Surface States of the Bulk-Insulating Topological Insulator Cu$_{0.02}$Bi$_2$Se$_3$

We have utilized time-domain magneto-terahertz spectroscopy to investigate the low frequency optical response of topological insulator Cu$_{0.02}$Bi$_2$Se$_3$ and Bi$_2$Se$_3$ films. With both field and frequency dependence, such experiments give sufficient information to measure the mobility and carrier density of multiple conduction channels simultaneously. We observe sharp cyclotron resonances (CRs) in both materials. The small amount of Cu incorporated into the Cu$_{0.02}$Bi$_2$Se$_3$ induces a true bulk insulator with only a textit{single} type of conduction with total sheet carrier density $sim4.9times10^{12}/$cm$^{2}$ and mobility as high as 4000 cm$^{2}/$V$cdot$s. This is consistent with conduction from two virtually identical topological surface states (TSSs) on top and bottom of the film with a chemical potential $sim$145 meV above the Dirac point and in the bulk gap. The CR broadens at high fields, an effect that we attribute to an electron-phonon interaction. This assignment is supported by an extended Drude model analysis of the zero field Drude conductance. In contrast, in normal Bi$_2$Se$_3$ films two conduction channels were observed and we developed a self-consistent analysis method to distinguish the dominant TSSs and coexisting trivial bulk/2DEG states. Our high-resolution Faraday rotation spectroscopy on Cu$_{0.02}$Bi$_2$Se$_3$ paves the way for the observation of quantized Faraday rotation under experimentally achievable conditions to push chemical potential in the lowest Landau Level.

Time-resolved terahertz dynamics in thin films of the topological insulator Bi$_{2}$Se$_3$

We use optical pump--THz probe spectroscopy at low temperatures to study the hot carrier response in thin Bi$_2$Se$_3$ films of several thicknesses, allowing us to separate the bulk from the surface transient response. We find that for thinner films the photoexcitation changes the transport scattering rate and reduces the THz conductivity, which relaxes within 10 picoseconds (ps). For thicker films, the conductivity increases upon photoexcitation and scales with increasing both the film thickness and the optical fluence, with a decay time of approximately 5 ps as well as a much higher scattering rate. These different dynamics are attributed to the surface and bulk electrons, respectively, and demonstrate that long-lived mobile surface photo-carriers can be accessed independently below certain film thicknesses for possible optoelectronic applications.

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

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.