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Thin layers of topological insulator materials are quasi-two-dimensional systems featuring a complex interplay between quantum confinement and topological band structure. To understand the role of the spatial distribution of carriers in electrical transport, we study the Josephson effect, magnetotransport, and weak anti-localization in bottom-gated thin Bi$_2$Te$_3$ topological insulator films.We compare the experimental carrier densities to a model based on the solutions of the self-consistent Schrodinger-Poisson equations and find excellent agreement. The modeling allows for a quantitative interpretation of the weak antilocalization correction to the conduction and of the critical current of Josephson junctions with weak links made from such films without any ad hoc assumptions.
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Topological surface states with intrinsic magnetic ordering in the MnBi$_2$Te$_4$(Bi$_2$Te$_3$)$_n$ compounds have been predicted to host rich topological phenomena including quantized anomalous Hall effect and axion insulator state. Here we use scanning tunneling microscopy to image the surface Dirac fermions in MnBi$_2$Te$_4$ and MnBi$_4$Te$_7$. We have determined the energy dispersion and helical spin texture of the surface states through quasiparticle interference patterns far above Dirac energy, which confirms its topological nature. Approaching the Dirac point, the native defects in the MnBi$_2$Te$_4$ septuple layer give rise to resonance states which extend spatially and potentially hinder the detection of a mass gap in the spectra. Our results demonstrate that regulating defects is essential to realize exotic topological states at higher temperatures in these compounds.
We used low-energy, momentum-resolved inelastic electron scattering to study surface collective modes of the three-dimensional topological insulators Bi$_2$Se$_3$ and Bi$_{0.5}$Sb$_{1.5}$Te$_{3-x}$Se$_{x}$. Our goal was to identify the spin plasmon predicted by Raghu and co-workers [S. Raghu, et al., Phys. Rev. Lett. 104, 116401 (2010)]. Instead, we found that the primary collective mode is a surface plasmon arising from the bulk, free carrers in these materials. This excitation dominates the spectral weight in the bosonic function of the surface, $chi (textbf{q},omega)$, at THz energy scales, and is the most likely origin of a quasiparticle dispersion kink observed in previous photoemission experiments. Our study suggests that the spin plasmon may mix with this other surface mode, calling for a more nuanced understanding of optical experiments in which the spin plasmon is reported to play a role.
Alloys of Bi$_2$Te$_3$ and Sb$_2$Te$_3$ ((Bi$_{1-x}$Sb$_x$)$_2$Te$_3$) have played an essential role in the exploration of topological surface states, allowing us to study phenomena that would otherwise be obscured by bulk contributions to conductivity. Thin films of these alloys have been particularly important for tuning the energy of the Fermi level, a key step in observing spin-polarized surface currents and the quantum anomalous Hall effect. Previous studies reported the chemical tuning of the Fermi level to the Dirac point by controlling the Sb:Bi composition ratio, but the optimum ratio varies widely across various studies with no consensus. In this work, we use scanning tunneling microscopy and Landau level spectroscopy, in combination with X-ray photoemission spectroscopy to isolate the effects of growth factors such as temperature and composition, and to provide a microscopic picture of the role that disorder and composition play in determining the carrier density of epitaxially grown (Bi,Sb)$_2$Te$_3$ thin films. Using Landau level spectroscopy, we determine that the ideal Sb concentration to place the Fermi energy to within a few meV of the Dirac point is $xsim 0.7$. However, we find that the post- growth annealing temperature can have a drastic impact on microscopic structure as well as carrier density. In particular, we find that when films are post-growth annealed at high temperature, better crystallinity and surface roughness are achieved; but this also produces a larger Te defect density, adding n-type carriers. This work provides key information necessary for optimizing thin film quality in this fundamentally and technologically important class of materials.
We have investigated the optical properties of thin films of topological insulators Bi$_{2}$Te$_{3}$, Bi$_{2}$Se$_{3}$ and their alloys Bi$_2$(Te$_{1-x}$Se$_x$)$_3$ on BaF$_{2}$ substrates by a combination of infrared ellipsometry and reflectivity in the energy range from 0.06 to 6.5 eV. For the onset of interband absorption in Bi$_2$Se$_3$, after the correction for the Burstein-Moss effect, we find the value of direct bandgap of $215pm10$ meV at 10 K. Our data supports the picture that Bi$_2$Se$_3$ has a direct band gap located at the $Gamma$ point in the Brillouin zone and that the valence band reaches up to the Dirac point and has the shape of a downward oriented paraboloid, i.e. without a camel-back structure. In Bi$_2$Te$_3$, the onset of strong direct interband absorption at 10 K is at a similar energy of about 200 meV, with a weaker additional feature at about 170 meV. Our data support the recent GW band structure calculations suggesting that the direct interband transition does not occur at the $Gamma$ point but near the Z-F line of the Brillouin zone. In the Bi$_2$(Te$_{1-x}$Se$_x$)$_3$ alloy, the energy of the onset of direct interband transitions exhibits a maximum near $x=0.3$ (i.e. the composition of Bi$_2$Te$_2$Se), suggesting that the crossover of the direct interband transitions between the two points in the Brillouin zone occurs close to this composition.
Doping Bi$_2$Se$_3$ by magnetic ions represents an interesting problem since it may break the time reversal symmetry needed to maintain the topological insulator character. Mn dopants in Bi$_2$Se$_3$ represent one of the most studied examples here. However, there is a lot of open questions regarding their magnetic ordering. In the experimental literature different Curie temperatures or no ferromagnetic order at all are reported for comparable Mn concentrations. This suggests that magnetic ordering phenomena are complex and highly susceptible to different growth parameters, which are known to affect material defect concentrations. So far theory focused on Mn dopants in one possible position, and neglected relaxation effects as well as native defects. We have used ab initio methods to calculate the Bi$_2$Se$_3$ electronic structure influenced by magnetic Mn dopants, and exchange interactions between them. We have considered two possible Mn positions, the substitutional and interstitial one, and also native defects. We have found a sizable relaxation of atoms around Mn, which affects significantly magnetic interactions. Surprisingly, very strong interactions correspond to a specific position of Mn atoms separated by van der Waals gap. Based on the calculated data we performed spin dynamics simulations to examine systematically the resulting magnetic order for various defect contents. We have found under which conditions the experimentally measured Curie temperatures ${T_{rm{C}}}$ can be reproduced, noticing that interstitial Mn atoms appear to be important here. Our theory predicts the change of ${T_{rm{C}}}$ with a shift of Fermi level, which opens the way to tune the system magnetic properties by selective doping.
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