Low-energy electrodynamics of the surface states of three-dimensional topological insulators by time-domain terahertz spectroscopy

Three-dimensional (3D) topological insulators are newly discovered states of matter with robust metallic surface states protected by the topological properties of their bulk wavefunctions. The helical Dirac surface states have a number of special properties, which can not be realized in a pure two-dimensional system. Spin is locked to the crystal momentum on the Dirac surface states, which leads to the suppression of back scattering. The topological surface states of 3D topological insulators have many other interesting properties including a half-integer quantum Hall effect and a topological magneto-electric effect. Majorana fermions may exist in a vortex core due to a proximity effect between a TI and an $s$-wave superconductor with the interface hosting spinless $p$-wave superconductivity. We use time-domain terahertz spectroscopy to probe the electrodynamics of the topological surface states. We developed a self-consistent analysis to distinguish the bulk/two-dimensional electron gas and topological surface state contributions by using time-domain magneto-terahertz spectroscopy and established the signature for topological surface states. Definitive evidence for cyclotron resonances from topological surface states is obtained in bulk-insulating topological insulators. Coupling to a Raman-active phonon is demonstrated through cyclotron resonances experiments and is supported by an extended-Drude-model analysis of the zero-field Drude conductance. A quantum phase transition between a 3D topological insulator and a 3D normal insulator is also investigated by time-domain terahertz spectroscopy. We demonstrate the signatures for the topological phase transition in AC transport measurements and a novel finite-size effect associated with topological surface states hybridization before the bulk gap closes. We also use a variety of methods including charge-transfer doping and charged polymers to lower the chemical potential of topological surface state to $\sim$ 35 meV above the Dirac point. The topological insulators with low Fermi energy enable us to realize the half-integer quantum Hall effect and probe the topological magneto-electric effect manifesting as a quantized Faraday rotation in terahertz measurements