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Register a new userSurface states in a 3D topological insulator: The role of hexagonal warping and curvature
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We explore a combined effect of hexagonal warping and of finite effective mass on both the tunneling density of electronic states (TDOS) and structure of Landau levels (LLs) of 3D topological insulators. We find the increasing warping to transform the square-root van Hove singularity into a logarithmic one. For moderate warping an additional logarithmic singularity and a jump in the TDOS appear. This phenomenon is experimentally verified by direct measurements of the local TDOS in Bi$_2$Te$_3$. By combining the perturbation theory and the WKB approximation we calculate the LLs in the presence of hexagonal warping. We predict that due to the degeneracy removal the evolution of LLs in the magnetic field is drastically modified.
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Hexagonal warping provides an anisotropy to the dispersion curves of the helical Dirac fermions that exist at the surface of a topological insulator. A sub-dominant quadratic in momentum term leads to an asymmetry between conduction and valence band. A gap can also be opened through magnetic doping. We show how these various modifications to the Dirac spectrum change the polarization function of the surface states and employ our results to discuss their effect on the plasmons. In the long wavelength limit, the plasmon dispersion retains its square root dependence on its momentum, $boldsymbol{q}$, but its slope is modified and it can acquire a weak dependence on the direction of $boldsymbol{q}$. Further, we find the existence of several plasmon branches, one which is damped for all values of $boldsymbol{q}$, and extract the plasmon scattering rate for a representative case.
The transport properties of the surface charge carriers of a three dimensional topological insulator under a terahertz (THz) field along with a resonant double barrier structure is theoretically analyzed within the framework of Floquet theory to explore the possibility of using such a device for photodetection purpose. We show that due to the contribution of elastic and inelastic scattering processes in the resulting transmission sidebands are formed in the conductance spectrum in somewhat similar way as in an optical cavity and this information can be used to detect the frequency of an unknown THz radiation. The dependence of the conductance on the bias voltage, the effect of THz radiation on resonances and the influence of zero energy points on the transmission spectrum are also discussed.
We have performed scanning tunneling microscopy and differential tunneling conductance ($dI/dV$) mapping for the surface of the three dimensional topological insulator Bi$_{2}$Se$_{3}$. The fast Fourier transformation applied to the $dI/dV$ image shows an electron interference pattern near Dirac node despite the general belief that the backscattering is well suppressed in the bulk energy gap region. The comparison of the present experimental result with theoretical surface and bulk band structures shows that the electron interference occurs through the scattering between the surface states near the Dirac node and the bulk continuum states.
The non-trivial topology of the three-dimensional (3D) topological insulator (TI) dictates the appearance of gapless Dirac surface states. Intriguingly, when a 3D TI is made into a nanowire, a gap opens at the Dirac point due to the quantum confinement, leading to a peculiar Dirac sub-band structure. This gap is useful for, e.g., future Majorana qubits based on TIs. Furthermore, these Dirac sub-bands can be manipulated by a magnetic flux and are an ideal platform for generating stable Majorana zero modes (MZMs), which play a key role in topological quantum computing. However, direct evidence for the Dirac sub-bands in TI nanowires has not been reported so far. Here we show that by growing very thin ($sim$40-nm diameter) nanowires of the bulk-insulating topological insulator (Bi$_{1-x}$Sb$_x$)$_2$Te$_3$ and by tuning its chemical potential across the Dirac point with gating, one can unambiguously identify the Dirac sub-band structure. Specifically, the resistance measured on gate-tunable four-terminal devices was found to present non-equidistant peaks as a function of the gate voltage, which we theoretically show to be the unique signature of the quantum-confined Dirac surface states. These TI nanowires open the way to address the topological mesoscopic physics, and eventually the Majorana physics when proximitised by an $s$-wave superconductor.
We propose theoretically a new effect, i.e. nonlinear planar Nernst effect (NPNE), in nonmagnetic topological insulator (TI) Bi2Te3 in the presence of an in-plane magnetic field. We find that the Nernst current scales quadratically with temperature gradient but linearly with magnetic field and exhibits a cosine dependence of the orientation of the magnetic field with respect to the direction of the temperature gradient. The NPNE has a quantum origin arising from the conversion of a nonlinear transverse spin current to a charge current due to a joint result of hexagonal warping effect, spin-momentum locking, and the time-reversal symmetry breaking induced by the magnetic field.
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