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Mott insulators with strong spin-orbit coupling have been proposed to host unconventional magnetic states, including the Kitaev quantum spin liquid. The $4d$ system $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ has recently come into view as a candidate Kitaev system, with evidence for unusual spin excitations in magnetic scattering experiments. We apply a combination of optical spectroscopy and Raman scattering to study the electronic structure of this material. Our measurements reveal a series of orbital excitations involving localized total angular momentum states of the Ru ion, implying that strong spin-orbit coupling and electron-electron interactions coexist in this material. Analysis of these features allows us to estimate the spin-orbit coupling strength, as well as other parameters describing the local electronic structure, revealing a well-defined hierarchy of energy scales within the Ru $d$ states. By comparing our experimental results with density functional theory calculations, we also clarify the overall features of the optical response. Our results demonstrate that $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$ is an ideal material system to study spin-orbit coupled magnetism on the honeycomb lattice.

We report the Drude oscillator strength D and the magnitude of the bulk band gap E_{g} of the epitaxially grown, topological insulator (Bi,Sb)_{2}Te_{3}. The magnitude of E_{g}, in conjunction with the model independent f-sum rule, allows us to establish an upper bound for the magnitude of D expected in a typical Dirac-like system composed of linear bands. The experimentally observed D is found to be at or below this theoretical upper bound, demonstrating the effectiveness of alloying in eliminating bulk charge carriers. Moreover, direct comparison of the measured D to magnetoresistance measurements of the same sample supports assignment of the observed low-energy conduction to topological surface states.

${\mathrm{Pb}}_{0.77}{\mathrm{Sn}}_{0.23}\mathrm{Se}$ is a promising thermoelectric alloy that exhibits a temperature dependent band inversion below 300 K. Recent work has shown that this band inversion also coincides with a trivial to nontrivial topological phase transition. To understand how the properties critical to thermoelectric efficiency are affected by the band inversion, we measured the broadband optical response of ${\mathrm{Pb}}_{0.77}{\mathrm{Sn}}_{0.23}\mathrm{Se}$ as a function of temperature. We find clear optical signatures suggesting the band inversion occurs at $160\ifmmode\pm\else\textpm\fi{}15$ K, and use the extended Drude model to accurately determine a ${T}^{3/2}$ dependence of the bulk carrier lifetime, associated with electron-acoustic phonon scattering. Due to the high bulk carrier doping level, no discriminating signatures of the topological surface states are found, although their presence cannot be excluded from our data.

High-temperature superconductors exhibit a wide variety of novel excitations. If contacted with a topological insulator, the lifting of spin rotation symmetry in the surface states can lead to the emergence of unconventional superconductivity and novel particles. In pursuit of this possibility, we fabricated high critical-temperature $({T}_{c}\ensuremath{\sim}85\phantom{\rule{0.28em}{0ex}}\mathrm{K})$ superconductor/topological insulator (${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}/{\mathrm{Bi}}_{2}{\mathrm{Te}}_{2}\mathrm{Se}$) junctions. Below 75 K, a zero-bias conductance peak (ZBCP) emerges in the differential conductance spectra of this junction. The magnitude of the ZBCP is suppressed at the same rate for magnetic fields applied parallel or perpendicular to the junction. Furthermore, it can still be observed and does not split up to at least 8.5 T. The temperature and magnetic field dependence of the excitation we observe appears to fall outside the known paradigms for a ZBCP.

Superconducting ${\mathrm{Cu}}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ has attracted significant attention as a candidate topological superconductor. Besides inducing superconductivity, the introduction of Cu atoms to this material has also been observed to produce a number of unusual features in DC transport and magnetic susceptibility measurements. To clarify the effect of Cu doping, we have performed a systematic optical spectroscopic study of the electronic structure of ${\mathrm{Cu}}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ as a function of Cu doping. Our measurements reveal an increase in the conduction band effective mass, while both the free carrier density and lifetime remain relatively constant for Cu content greater than $x=0.15$. The increased mass naturally explains trends in the superfluid density and residual resistivity as well as hints at the complex nature of Cu doping in ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$.

An optical spectroscopic study of exfoliated two-dimensional atomic crystals of Bi${}_{2}$Sr${}_{2}$CaCu${}_{2}$O${}_{8+\ensuremath{\delta}}$ reveals a pronounced suppression of optical conductivity with thickness. Through detailed analysis, the authors interpret this finding as the formation of an insulating surface layer.

In bismuth ferrite (BiFeO3), antiferromagnetic and ferroelectric order coexist at room temperature, making it of particular interest for studying magnetoelectric coupling. The mutual control of magnetic and electric properties is very useful for a wide variety of applications. This has led to an enormous amount of research into the properties of BiFeO$_3$. Nonetheless, one of the most fundamental aspects of this material, namely the symmetries of the lattice vibrations, remains controversial.We present a comprehensive Raman study of BiFeO$_3$ single crystals with the approach of monitoring the Raman spectra while rotating the polarization direction of the excitation laser. Our method results in unambiguous assignment of the phonon symmetries and explains the origin of the controversy in the literature. Furthermore, it provides access to the Raman tensor elements enabling direct comparison with theoretical calculations. Hence, this allows the study of symmetry breaking and coupling mechanisms in a wide range of complex materials and may lead to a noninvasive, all-optical method to determine the orientation and magnitude of the ferroelectric polarization., 5 pages, 4 figures, 1 table