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The optical properties of Sn-doped Bi$_{1.1}$Sb$_{0.9}$Te$_{2}$S, the most bulk-insulating topological insulator thus far, have been examined at different temperatures over a broad frequency range. No Drude response is detected in the low-frequency range down to 30~cm$^{-1}$, corroborating the excellent bulk-insulating property of this material. Intriguingly, we observe a sharp peak at about 2,200~cm$^{-1}$ in the optical conductivity at 5~K. Further quantitative analyses of the line shape and temperature dependence of this sharp peak, in combination with first-principles calculations, suggest that it corresponds to a van Hove singularity arising from Mexican-hat-shaped inverted bands. Such a van Hove singularity is a pivotal ingredient of various strongly correlated phases.
Topological surface states have been extensively observed via optics in thin films of topological insulators. However, in typical thick single crystals of these materials, bulk states are dominant and it is difficult for optics to verify the existenc
The ferromagnetic topological insulator V:(Bi,Sb)$_2$Te$_3$ has been recently reported as a quantum anomalous Hall (QAH) system. Yet the microscopic origins of the QAH effect and the ferromagnetism remain unclear. One key aspect is the contribution o
Rare earth ions typically exhibit larger magnetic moments than transition metal ions and thus promise the opening of a wider exchange gap in the Dirac surface states of topological insulators. Yet, in a recent photoemission study of Eu-doped Bi$_2$Te
To achieve and utilize the most exotic electronic phenomena predicted for the surface states of 3D topological insulators (TI),it is necessary to open a Dirac-mass gap in their spectrum by breaking time-reversal symmetry. Use of magnetic dopant atoms
In the context of the relaxation time approximation to Boltzmann transport theory, we examine the behavior of the Hall number, $n_H$, of a metal in the neighborhood of a Lifshitz transition from a closed Fermi surface to open sheets. We find a univer