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Register a new userTerahertz Faraday and Kerr rotation spectroscopy of Bi$_{1-x}$Sb$_x$ films in high magnetic fields up to 30 Tesla
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We report results of terahertz Faraday and Kerr rotation spectroscopy measurements on thin films of $text{Bi}_{1-x}text{Sb}_{x}$, an alloy system that exhibits a semimetal-to-topological-insulator transition as the Sb composition $x$ increases. By using a single-shot time-domain terahertz spectroscopy setup combined with a table-top pulsed mini-coil magnet, we conducted measurements in magnetic fields up to 30~T, observing distinctly different behaviors between semimetallic ($x < 0.07$) and topological insulator ($x > 0.07$) samples. Faraday and Kerr rotation spectra for the semimetallic films showed a pronounced dip that blue-shifted with the magnetic field, whereas spectra for the topological insulator films were positive and featureless, increasing in amplitude with increasing magnetic field and eventually saturating at high fields ($>$20~T). Ellipticity spectra for the semimetallic films showed resonances, whereas the topological insulator films showed no detectable ellipticity. To explain these observations, we developed a theoretical model based on realistic band parameters and the Kubo formula for calculating the optical conductivity of Landau-quantized charge carriers. Our calculations quantitatively reproduced all experimental features, establishing that the Faraday and Kerr signals in the semimetallic films predominantly arise from bulk hole cyclotron resonances while the signals in the topological insulator films represent combined effects of surface carriers originating from multiple electron and hole pockets. These results demonstrate that the use of high magnetic fields in terahertz magnetopolarimetry, combined with detailed electronic structure and conductivity calculations, allows us to unambiguously identify and quantitatively determine unique contributions from different species of carriers of topological and nontopological nature in Bi$_{1-x}$Sb$_x$.
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Using magneto-infrared spectroscopy, we have explored the charge dynamics of (Bi,Sb)$_2$Te$_3$ thin films on InP substrates. From the magneto-transmission data we extracted three distinct cyclotron resonance (CR) energies that are all apparent in the broad band Faraday rotation (FR) spectra. This comprehensive FR-CR data set has allowed us to isolate the response of the bulk states from the intrinsic surface states associated with both the top and bottom surfaces of the film. The FR data uncovered that electron- and hole-type Dirac fermions reside on opposite surfaces of our films, which paves the way for observing many exotic quantum phenomena in topological insulators.
Analytical solutions for the surface state (SS) of an extended Wolff Hamiltonian, which is a common Hamiltonian for strongly spin-orbit coupled systems, are obtained both for semi-infinite and finite-thickness boundary conditions. For the semi-infinite system, there are three types of SS solutions: (I-a) linearly crossing SSs in the direct bulk band gap, (I-b) SSs with linear dispersions entering the bulk conduction or valence bands away from the band edge, and (II) SSs with nearly flat dispersions entering the bulk state at the band edge. For the finite-thickness system, a gap opens in the SS of solution I-a. Numerical solutions for the SS are also obtained based on the tight-binding model of Liu and Allen [Phys. Rev. B, 52, 1566 (1995)] for Bi$_{1-x}$Sb$_x$ ($0le x le 0.1$). A perfect correspondence between the analytic and numerical solutions is obtained around the $bar{M}$ point including their thickness dependence. This is the first time that the character of the SS numerically obtained is identified with the help of analytical solutions. The size of the gap for I-a SS can be larger than that of bulk band gap even for a thick films ($lesssim 200$ bilayers $simeq 80$ nm) of pure bismuth. Consequently, in such a film of Bi$_{1-x}$Sb$_x$, there is no apparent change in the SSs through the band inversion at $xsimeq 0.04$, even though the nature of the SS is changed from solution I-a to I-b. Based on our theoretical results, the experimental results on the SS of Bi$_{1-x}$Sb$_x$ ($0le x lesssim 0.1$) are discussed.
We report magneto-transport studies of topological insulator Bi_{2}Te_{3} thin films grown by pulsed laser deposition. A non-saturating linear-like magneto-resistance (MR) is observed at low temperatures in the magnetic field range from a few Tesla up to 60 Tesla. We demonstrate that the strong linear-like MR at high field can be well understood as the weak antilocalization phenomena described by Hikami-Larkin-Nagaoka theory. Our analysis suggests that in our system, a topological insulator, the elastic scattering time can be longer than the spin-orbit scattering time. We briefly discuss our results in the context of Dirac Fermion physics and quantum linear magnetoresistance.
We show Shubnikov-de Haas oscillations in topological insulator (Bi$_{x}$Sb$_{1-x}$)$_{2}$Te$_{3}$ films whose carrier type is p-type (x = 0.29, 0.34) and n-type (x = 0.42). The physical properties such as the Berry phase, mobility, and the scattering time are significantly changed by tuning the Fermi-level position with the concentration x. The Landau-level fan diagram in the sample with x = 0.42 showed the $pi$ Berry phase and its mobility was as high as 17,000 cm$^{2}$/V/s, whereas the others had the 2$pi$ Berry phase and much lower mobility. This suggests that because the bulk band of the sample with x = 0.42 does not cross the Fermi level, it becomes bulk insulating, resulting in the topological surface-state dominating transport. Thus, we can switch sample properties from degenerate to bulk insulating by tuning the concentration x, which is consistent with results of angle-resolved photoemission spectroscopy.
Interfacing bulk conducting topological Bi$_2$Se$_3$ films with s-wave superconductors initiates strong superconducting order in the nontrivial surface states. However, bulk insulating topological (Bi$_{1-x}$Sb$_{x})_2$Te$_3$ films on bulk Nb instead exhibit a giant attenuation of surface superconductivity, even for films only two-layers thick. This massive suppression of proximity pairing is evidenced by ultrahigh-resolution band mappings and by contrasting quantified superconducting gaps with those of heavily n-doped topological Bi$_2$Se$_3$/Nb. The results underscore the limitations of using superconducting proximity effects to realize topological superconductivity in nearly intrinsic systems.
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