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Register a new userMesoscopic transport in two-dimensional topological insulators
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Topological states of matter have attracted a lot of attention due to their many intriguing transport properties. In particular, two-dimensional topological insulators (2D TI) possess gapless counter propagating conducting edge channels, with opposite spin, that are topologically protected from backscattering. Two basic features are supposed to confirm the existence of the ballistic edge channels in the submicrometer limit: the 4-terminal conductance is expected to be quantized at the universal value $2e^{2}/h$, and a nonlocal signal should appear due to a net current along the sample edge, carried by the helical states. On the other hand for longer channels the conductance has been found to deviate from the quantized value. This article reviewer the experimental and theoretical work related to the transport in two-dimensional topological insulators (2D-TI), based on HgTe quantum wells in zero magnetic field. We provide an overview of the basic mechanisms predicting a deviation from the quantized transport due to backscattering (accompanied by spin-flips) between the helical channels. We discuss the details of the model, which takes into account the edge and bulk contribution to the total current and reproduces the experimental results.
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One of the unique features of Dirac Fermions is pseudo-diffusive transport by evanescent modes at low Fermi energies when the disorder is low. At higher Fermi energies i.e. carrier densities, the electrical transport is diffusive in nature and the propagation occurs via plane-waves. In this study, we report the detection of such evanescent modes in the surface states of topological insulator through 1/f noise. While signatures of pseudo-diffusive transport have been seen experimentally in graphene, such behavior is yet to be observed explicitly in any other system with a Dirac dispersion. To probe this, we have studied 1/f noise in topological insulators as a function of gate-voltage, and temperature. Our results show a non-monotonic behavior in 1=f noise as the Fermi energy is varied, suggesting a crossover from pseudo-diffusive to diffusive transport regime in mesoscopic topological insulators. The temperature dependence of noise points towards conductance fluctuations from quantum interference as the dominant source of the noise in these samples.
Excitation of a topological insulator by a high-frequency electric field of a laser radiation leads to a dc electric current in the helical edge channel whose direction and magnitude are sensitive to the radiation polarization and depend on the physical properties of the edge. We present an overview of theoretical and experimental studies of such edge photoelectric effects in two-dimensional topological insulators based on semiconductor quantum wells. First, we give a phenomenological description of edge photocurrents, which may originate from the photogalvanic effects or the photon drag effects, for edges of all possible symmetry. Then, we discuss microscopic mechanisms of photocurrent generation for different types of optical transitions involving helical edge states. They include direct and indirect optical transitions within the edge channel and edge-to-bulk optical transitions.
The particle wave duality sets a fundamental correspondence between optics and quantum mechanics. Within this framework, the propagation of quasiparticles can give rise to superposition phenomena which, like for electromagnetic waves, can be described by the Huygens principle. However, the utilization of this principle by means of propagation and manipulation of quantum information is limited by the required coherence in time and space. Here we show that in topological insulators, which in their pristine form are characterized by opposite propagation directions for the two quasiparticles spin channels, mesoscopic focusing of coherent charge density oscillations can be obtained at large nested segments of constant energy contours by magnetic surface doping. Our findings provide evidence of strongly anisotropic Dirac fermion-mediated interactions. Even more remarkably, the validity of our findings goes beyond topological insulators but applies for systems with spin orbit lifted degeneracy in general. It demonstrates how spin information can be transmitted over long distances, allowing the design of experiments and devices based on coherent quantum effects in this fascinating class of materials.
Two-dimensional topological insulators are characterized by gapped bulk states and gapless helical edge states, i.e. time-reversal symmetric edge states accommodating a pair of counter-propagating electrons. An external magnetic field breaks the time-reversal symmetry. What happens to the edge states in this case? In this paper we analyze the edge-state spectrum and longitudinal conductance in a two-dimensional topological insulator subject to a quantizing magnetic field. We show that the helical edge states exist also in this case. The strong magnetic field modifies the group velocities of the counter-propagating channels which are no longer identical. The helical edge states with different group velocities are particularly prone to get coupled via backscattering, which leads to the suppression of the longitudinal edge magnetoconductance.
We investigate the properties of a two-dimensional quasicrystal in the presence of a uniform magnetic field. In this configuration, the density of states (DOS) displays a Hofstadter butterfly-like structure when it is represented as a function of the magnetic flux per tile. We show that the low-DOS regions of the energy spectrum are associated with chiral edge states, in direct analogy with the Chern insulators realized with periodic lattices. We establish the topological nature of the edge states by computing the topological Chern number associated with the bulk of the quasicrystal. This topological characterization of the non-periodic lattice is achieved through a local (real-space) topological marker. This work opens a route for the exploration of topological insulating materials in a wide range of non-periodic lattice systems, including photonic crystals and cold atoms in optical lattices.
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