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Register a new userMeasurement of the topological surface state optical conductance in bulk-insulating Sn-doped Bi$_{1.1}$Sb$_{0.9}$Te$_2$S single crystals
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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 existence of topological surface states definitively. In this work, we studied the charge dynamics of the newly formulated bulk-insulating Sn-doped Bi$_{1.1}$Sb$_{0.9}$Te$_2$S crystal by using time-domain terahertz spectroscopy. This compound shows much better insulating behavior than any other bulk-insulating topological insulators reported previously. The transmission can be enhanced an amount which is 5$%$ of the zero-field transmission by applying magnetic field to 7 T, an effect which we believe is due to the suppression of topological surface states. This suppression is essentially independent of the thicknesses of the samples, showing the two-dimensional nature of the transport. The suppression of surface states in field allows us to use the crystal slab itself as a reference sample to extract the surface conductance, mobility, charge density and scattering rate. Our measurements set the stage for the investigation of phenomena out of the semi-classical regime, such as the topological magneto-electric effect.
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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.
Three-dimensional topological insulators (TIs) host helical Dirac surface states at the interface with a trivial insulator. In quasi-one-dimensional TI nanoribbon structures the wave function of surface charges extends phase-coherently along the perimeter of the nanoribbon, resulting in a quantization of transverse surface modes. Furthermore, as the inherent spin-momentum locking results in a Berry phase offset of $pi$ of self-interfering charge carriers an energy gap within the surface state dispersion appears and all states become spin-degenerate. We investigate and compare the magnetic field dependent surface state dispersion in selectively deposited Bi$_2$Te$_3$ TI micro- and nanoribbon structures by analysing the gate voltage dependent magnetoconductance at cryogenic temperatures. Hall measurements on microribbon field effect devices show a high bulk charge carrier concentration and electrostatic simulations show an inhomogeneous gate potential profile on the perimeter of the TI ribbon. In nanoribbon devices we identify a magnetic field dependency of the surface state dispersion as it changes the occupation of transverse subbands close to the Fermi energy. We quantify the energetic spacing in between these subbands by measuring the conductance as a function of the applied gate potential and use an electrostatic model that treats the inhomogeneous gate profile and the initial charge carrier densities on the top and bottom surface. In the gate voltage dependent transconductance we find oscillations that change their relative phase by $pi$ at half-integer values of the magnetic flux quantum applied coaxial to the nanoribbon providing evidence for a magnetic flux dependent topological phase transition in narrow, selectively deposited TI nanoribbon devices.
We study disorder induced topological phase transitions in magnetically doped (Bi, Sb)$_2$Te$_3$ thin films, by using large scale transport simulations of the conductance through a disordered region coupled to reservoirs in the quantum spin Hall regime. Besides the disorder strength, the rich phase diagram also strongly depends on the magnetic exchange field, the Fermi level, and the initial topological state in the undoped and clean limit of the films. In an initially trivial system at non-zero exchange field, varying the disorder strength can induce a sequence of transitions from a normal insulating, to a quantum anomalous Hall, then a spin-Chern insulating, and finally an Anderson insulating state. While for a system with topology initially, a similar sequence, but only starting from the quantum anomalous Hall state, can be induced. Varying the Fermi level we find a similarly rich phase diagram, including transitions from the quantum anomalous Hall to the spin-Chern insulating state via a state that behaves as a mixture of a quantum anomalous Hall and a metallic state, akin to recent experimental reports.
V-doped (Bi,Sb)$_2$Te$_3$ has a ten times higher magnetic coercivity than its Cr-doped counterpart and therefore is believed to be a superior system for the quantum anomalous Hall effect (QAHE). The QAHE requires the opening of a magnetic band gap at the Dirac point. We do not find this gap by angle-resolved photoelectron spectroscopy down to 1 K. By x-ray magnetic circular dichroism (XMCD) we directly probe the magnetism at the V site and in zerofield. Hysteresis curves of the XMCD signal show a strong dependence of the coercivity on the ramping velocity of the magnetic field. The XMCD signal decays on a time scale of minutes which we conclude contributes to the absence of a detectable magnetic gap at the Dirac point.
We study the fate of the surface states of Bi$_2$Se$_3$ under disorder with strength larger than the bulk gap, caused by neon sputtering and nonmagnetic adsorbates. We find that neon sputtering introduces strong but dilute defects, which can be modeled by a unitary impurity distribution, whereas adsorbates, such as water vapor or carbon monoxide, are best described by Gaussian disorder. Remarkably, these two disorder types have a dramatically different effect on the surface states. Our soft x-ray ARPES measurements combined with numerical simulations show that unitary surface disorder pushes the Dirac state to inward quintuplet layers, burying it below an insulating surface layer. As a consequence, the surface spectral function becomes weaker, but retains its quasiparticle peak. This is in contrast to Gaussian disorder, which smears out the quasiparticle peak completely. At the surface of Bi$_2$Se$_3$, the effects of Gaussian disorder can be reduced by removing surface adsorbates using neon sputtering, which, however, introduces unitary scatterers. Since unitary disorder has a weaker effect than Gaussian disorder, the ARPES signal of the Dirac surface state becomes sharper upon sputtering.
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