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Register a new userCorrelation effects in two-dimensional topological insulators
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Topological insulators have become one of the most active research areas in condensed matter physics. This article reviews progress on the topic of electronic correlations effects in the two-dimensional case, with a focus on systems with intrinsic spin-orbit coupling and numerical results. Topics addressed include an introduction to the noninteracting case, an overview of theoretical models, correlated topological band insulators, interaction-driven phase transitions, topological Mott insulators and fractional topological states, correlation effects on helical edge states, and topological invariants of interacting systems.
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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.
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 study the surface of a three-dimensional spin chiral $mathrm{Z}_2$ topological insulator (class CII), demonstrating the possibility of its localization. This arises through an interplay of interaction and statistically-symmetric disorder, that confines the gapless fermionic degrees of freedom to a network of one-dimensional helical domain-walls that can be localized. We identify two distinct regimes of this gapless insulating phase, a `clogged regime wherein the network localization is induced by its junctions between otherwise metallic helical domain-walls, and a `fully localized regime of localized domain-walls. The experimental signatures of these regimes are also discussed.
With a combination of numerical methods, including quantum Monte Carlo, exact diagonalization, and a simplified dynamical mean-field model, we consider the attosecond charge dynamics of electrons induced by strong-field laser pulses in two-dimensional Mott insulators. The necessity to go beyond single-particle approaches in these strongly correlated systems has made the simulation of two-dimensional extended materials challenging, and we contrast their resulting high-harmonic emission with more widely studied one-dimensional analogues. As well as considering the photo-induced breakdown of the Mott insulating state and magnetic order, we also resolve the time and ultra-high frequency domains of emission, which are used to characterize both the photo-transition, and the sub-cycle structure of the electron dynamics. This extends simulation capabilities and understanding of the photo-melting of these Mott insulators in two-dimensions, at the frontier of attosecond non-equilibrium science of correlated 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.
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