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Register a new userTwo-dimensional topological insulators in quantizing magnetic fields
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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.
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The effect of quantizing magnetic field on the electron transport is investigated in a two dimensional topological insulator (2D TI) based on a 8 nm (013) HgTe quantum well (QW). The local resistance behavior is indicative of a metal-insulator transition at $Bapprox 6$ T. On the whole the experimental data agrees with the theory according to which the helical edge states transport in a 2D TI persists from zero up to a critical magnetic field $B_c$ after which a gap opens up in the 2D TI spectrum.
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.
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.
The edge states of a two-dimensional topological insulator are characterized by their helicity, a very remarkable property which is related to the time-reversal symmetry and the topology of the underlying system. We theoretically investigate a Hong-Ou-Mandel like setup as a tool to probe it. Collisions of two electrons with the same spin show a Pauli dip, analogous to the one obtained in the integer quantum Hall case. Moreover, the collisions between electrons of opposite spin also lead to a dip, known as $mathbb{Z}_{2}$ dip, which is a direct consequence of the constraints imposed by time-reversal symmetry. In contrast to the integer quantum Hall case, the visibility of these dips is reduced by the presence of the additional edge channels, and crucially depends on the properties of the quantum point contact. As a unique feature of this system, we show the possibility of three-electron interference, which leads to a total suppression of the noise independently of the point contact configuration. This is assured by the peculiar interplay between Fermi statistics and topology. This work intends to extend the domain of applicability of electron quantum optics.
We collect and review works which treat two-dimensional electron gases in quantum wells (mostly GaAs/GaAlAs heterostructures) in the presence of quantizing magnetic fields as open systems in contact with outside reservoirs. If a reservoir is sufficiently large, it pins the Fermi level to a certain energy. As a result, in a varying external magnetic field, the thermodynamic equilibrium will force oscillations of the electron density in and out of the quantum well (QW). This leads to a number of physical phenomena in magneto-transport, interband and intraband magneto-optics, magnetization, magneto-plasma dispersion, etc. In particular, as first proposed by Baraff and Tsui, the density oscillations in and out of QW lead to plateaus in the Integer Quantum Hall Effect (IQHE) at values observed in experiments. The gathered evidence, especially from magneto-optical investigations, allows us to conclude that, indeed, in most GaAs/GaAlAs hetrostructures one deals with open systems in which the electron density in QWs oscillates as the magnetic field varies. Relation of the density oscillations to other factors, such as electron localization, and their combined influence on the quantum transport in 2D electron gases, is discussed. In particular, a validity of the classical formula for the Hall resistivity {rho}xy = B/Nec is considered. It is concluded that the density oscillations are not sufficient to be regarded as the only source of plateaus in IQHE, although such claims have been sometimes made in the past and present. Still, our general conclusion is that the reservoir approach should be included in various descriptions of 2D electron gases in the present of a magnetic field. An attempt has been made to quote all the relevant literature on the subject.
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