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Dirac quantum well engineering on the surface of topological insulator

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 Added by Xin Lu
 Publication date 2020
  fields Physics
and research's language is English




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We investigate a quantum well that consists of a thin topological insulator sandwiched between two trivial insulators. More specifically, we consider smooth interfaces between these different types of materials such that the interfaces host not only the chiral interface states, whose existence is dictated by the bulk-edge correspondence, but also massive Volkov-Pankratov states. We investigate possible hybridization between these interface states as a function of the width of the topological material and of the characteristic interface size. Most saliently, we find a strong qualitative difference between an extremely weak effect on the chiral interface states and a more common hybridization of the massive Volkov-Pankratov states that can be easily understood in terms of quantum tunneling in the framework of the model of a (Dirac) quantum well we introduce here.



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The concept of topological insulator (TI) has introduced a new point of view to condensed-matter physics, relating a priori unrelated subfields such as quantum (spin, anomalous) Hall effects, spin-orbit coupled materials, some classes of nodal superconductors and superfluid $^3$He, etc. From a technological point of view, topological insulator is expected to serve as a platform for realizing dissipationless transport in a non-superconducting context. The topological insulator exhibits a gapless surface state with a characteristic conic dispersion (a surface Dirac cone). Here, we review peculiar finite-size effects applicable to such surface states in TI nanostructures. We highlight the specific electronic properties of TI nanowires and nanoparticles, and in this context contrast the cases of weak and strong TIs. We study robustness of the surface and the bulk of TIs against disorder, addressing the physics of Dirac and Weyl semimetals as a new perspective of research in the field.
We study the quantum Hall effect of Dirac fermions on the surface of a Wilson-Dirac type topological insulator thin film in the strong topological insulating phase. Although a magnetic field breaks time reversal symmetry of the bulk, the surface states can survive even in a strong field regime. We examine how the Landau levels of the surface states are affected by symmetry breaking perturbations.
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.
Three dimensional topological insulators are bulk insulators with $mathbf{Z}_2$ topological electronic order that gives rise to conducting light-like surface states. These surface electrons are exceptionally resistant to localization by non-magnetic disorder, and have been adopted as the basis for a wide range of proposals to achieve new quasiparticle species and device functionality. Recent studies have yielded a surprise by showing that in spite of resisting localization, topological insulator surface electrons can be reshaped by defects into distinctive resonance states. Here we use numerical simulations and scanning tunneling microscopy data to show that these resonance states have significance well beyond the localized regime usually associated with impurity bands. At native densities in the model Bi$_2$X$_3$ (X=Bi, Te) compounds, defect resonance states are predicted to generate a new quantum basis for an emergent electron gas that supports diffusive electrical transport.
Aiming at the future spintronics device applications of the spin-polarized surface states in three-dimensional topological insulator, a highly insulating bulk state and a tunable Dirac cone surface state are required. Here we employ a slab model having hetero-structural Bi2Se3-related quintuple layers and perform first-principles simulations. Our computational results show that the Dirac-point energy can be optimally tuned by selecting an appropriate pair of materials so that the work function at the surface quintuple layer is slightly different from that at the inner quintuple layers. The ideal surface state is obtained in Bi2Te3/(Bi2Te2Se)4/Bi2Te3 slab, in which the Fermi lines show the significant warping effect and both the in-plane and the out-of-plane components of the spin polarization emerge.
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