Quantum Spin Hall System Research Articles

Anomalous supercurrent and diode effect in locally perturbed topological Josephson junctions

The simultaneous breaking of time-reversal and inversion symmetry can lead to peculiar effects in Josephson junctions, such as the anomalous Josephson effect or supercurrent rectification, which is a dissipationless analog of the diode effect. Due to their impact in new quantum technologies, it is important to find robust platforms and external means to manipulate the above-mentioned effects in a controlled way. Here, we theoretically consider a Josephson junction based on a quantum spin Hall system as the normal channel, subjected to a magnetic field in the direction defined by spin-momentum locking, and in the presence of a local tip in close proximity to one of the metallic edges in the normal region. We consider different local perturbations, model normal and magnetic tips, and study how they affect the Josephson response of the device. In particular, we argue that magnetic tips are a useful tool that allows for tunability of both ϕ0 response and supercurrent rectification.

Spin-textured Volkov–Pankratov states and their tunnel magnetoresistance response

Volkov–Pankratov (VP) states are a family of sub-gap states that appear at the smooth interface/domain wall between topologically distinct gaped states. We carry out quantum transport simulations on one- and two-dimensional lattice models to demonstrate the emergence of such states in the edge spectrum of a quantum spin Hall system subjected to a smoothly varying exchange field that switches its sign at a given spatial point. We show the VP states possess non-trivial spin textures that can be characterized by a winding number in real space. It is further demonstrated that the application of an electric field along the edge provides control of this spin texture without altering the winding number. Finally, we illuminate how these spin textures can be read off via the local tunnel magnetoresistance (TMR) response of spin-polarized tunnel probes attached to the edge and the TMR can be controlled by purely electrical means akin to a Datta–Das type spin transistor.

Thermal dissipation of the quantum spin Hall edge states in HgTe/CdTe quantum well

Quantum spin Hall effect is characterized by topologically protected helical edge states. Here we study the thermal dissipation of helical edge states by considering two types of dissipation sources. The results show that the helical edge states are dissipationless for normal dissipation sources with or without Rashba spin–orbit coupling in the system, but they are dissipative for spin dissipation sources. Further studies on the energy distribution show that electrons with spin-up and spin-down are both in their own equilibrium without dissipation sources. Spin dissipation sources can couple the two subsystems together to induce voltage drop and non-equilibrium distribution, leading to thermal dissipation, while normal dissipation sources cannot. With the increase of thermal dissipation, the subsystems of electrons with spin-up and spin-down evolve from non-equilibrium finally to mutual equilibrium. In addition, the effects of disorder on thermal dissipation are also discussed. Our work provides clues to reduce thermal dissipation in the quantum spin Hall systems.

Topological phase transition in a disordered elastic quantum spin Hall system

Topological phase transition in a disordered elastic quantum spin Hall system

Spin-dependent gain and loss in photonic quantum spin Hall systems

Spin-dependent gain and loss in photonic quantum spin Hall systems

Quantum Spin Hall Effect in Two-Monolayer-Thick InN/InGaN Coupled Multiple Quantum Wells.

In this study, we present a theoretical study of the quantum spin Hall effect in InN/InGaN coupled multiple quantum wells with the individual well widths equal to two atomic monolayers. We consider triple and quadruple quantum wells in which the In content in the interwell barriers is greater than or equal to the In content in the external barriers. To calculate the electronic subbands in these nanostructures, we use the eight-band k∙p Hamiltonian, assuming that the effective spin-orbit interaction in InN is negative, which represents the worst-case scenario for achieving a two-dimensional topological insulator. For triple quantum wells, we find that when the In contents of the external and interwell barriers are the same and the widths of the internal barriers are equal to two monolayers, a topological insulator with a bulk energy gap of 0.25 meV can appear. Increasing the In content in the interwell barriers leads to a significant increase in the bulk energy gap of the topological insulator, reaching about 0.8 meV. In these structures, the topological insulator can be achieved when the In content in the external barriers is about 0.64, causing relatively low strain in quantum wells and making the epitaxial growth of these structures within the range of current technology. Using the effective 2D Hamiltonian, we study the edge states in strip structures containing topological triple quantum wells. We demonstrate that the opening of the gap in the spectrum of the edge states caused by decreasing the width of the strip has an oscillatory character regardless of whether the pseudospin-mixing elements of the effective Hamiltonian are omitted or taken into account. The strength of the finite size effect in these structures is several times smaller than that in HgTe/HgCdTe and InAs/GaSb/AlSb topological insulators. Therefore, its influence on the quantum spin Hall effect is negligible in strips with a width larger than 150 nm, unless the temperature at which electron transport is measured is less than 1 mK. In the case of quadruple quantum wells, we find the topological insulator phase only when the In content in the interwell barriers is larger than in the external barriers. We show that in these structures, a topological insulator with a bulk energy gap of 0.038 meV can be achieved when the In content in the external barriers is about 0.75. Since this value of the bulk energy gap is very small, quadruple quantum wells are less useful for realizing a measurable quantum spin Hall system, but they are still attractive for achieving a topological phase transition and a nonlocal topological semimetal phase.

Topology of three-dimensional Dirac semimetals and quantum spin Hall systems without gapless edge modes

A theoretical framework is outlined for calculating the spin-Chern number of topological Dirac semimetals and quantum spin Hall insulators lacking spin-conservation law and gapless edge modes. Spin-charge separation and quantized spin-pumping are probed by inserting a magnetic flux tube.

Breakdown of topological protection due to nonmagnetic edge disorder in two-dimensional materials in the quantum spin Hall phase

We study the suppression of the conductance quantization in quantum spin Hall systems by a combined effect of electronic interactions and edge disorder, that is ubiquitous in exfoliated and chemical vapor deposition grown two-dimensional (2D) materials. We show that the interplay between the electronic localized states due to edge defects and electron-electron interactions gives rise to local magnetic moments, that break time-reversal symmetry and the topological protection of the edge states in 2D topological systems. Our results suggest that edge disorder leads to small deviations of a perfect quantized conductance in short samples and to a strong conductance suppression in long ones. Our analysis is based on the Kane-Mele model, an unrestricted Hubbard mean-field Hamiltonian, and on a self-consistent recursive Green's function technique to calculate the transport quantities.

Light-induced phase crossovers in a quantum spin Hall system

In this work, we theoretically investigate the light-induced topological phases and finite-size crossovers in a paradigmatic quantum spin Hall (QSH) system with high-frequency pumping optics. Taking the HgTe quantum well for an example, our numerical results show that circularly polarized light can break time-reversal symmetry and induce the quantum anomalous Hall (QAH) phase. In particular, the coupling between the edge states is spin dependent and is related not only to the size of the system, but also to the strength of the polarized pumping optics. By tuning the two parameters (system width and optical pumping strength), we obtain four transport regimes, namely, QSH, QAH, edge conducting, and normal insulator. These four different transport regimes have contrasting edge conducting properties, which will feature prominently in transport experiments on various topological materials.

Band inversion induced large-gap quantum spin Hall states in III-Bi-monolayer/ SiO2

We extend the ${p}_{x}\ensuremath{-}{p}_{y}$ large-gap scenario to the band inversion systems and exemplify the mechanism with a family of III-Bi honeycomb monolayers on $\mathrm{Si}{\mathrm{O}}_{2}$, which can be the next generation of large-gap quantum spin Hall (QSH) systems. First, it suggests a topological gap of the same order as the current record kept of bismuthene/SiC(0001). Second, the band inversion mechanism in which these QSH insulators originate is qualitatively distinct from the Kane-Mele paradigm. Our work demonstrates that the ${p}_{x}\text{\ensuremath{-}}{p}_{y}$ scenario can be utilized to promote large-gap QSH states with both Kane-Mele and band inversion mechanisms, providing an efficient building principle for future topological device construction.

Simulating and studying the topological properties of the photon-phonon coupled modes in a one-dimensional superconducting circuit lattice

We theoretically study the topological properties in a one-dimensional superconducting circuit lattice, where each unit cell is composed of a superconducting microwave cavity, a nanomechanical resonator (NAMR) and a superconducting qubit. By using diagonalization and dimensional reduction methods, the quantum spin Hall system of the photon-phonon coupled modes can be achieved. We analyze the energy spectrum and edge states of different lattice sizes. It is found that the number of lattices affects the topological characteristics of the system, and the inversion of the edge state distribution can be realized. In addition, considering the effects of defects, dissipation and disorder on the system, we find that they will respectively expand the region of the edge state, change the maximum value of the energy spectrum and cause small fluctuation of the energy spectrum. But the edge state is still very stable, which is due to the topological protection of the edge state. This scheme opens up a new way to study the application of topological matter in quantum information processing, meanwhile, the research results can be used to design novel quantum devices.

Spin-polarized voltage probes for helical edge state: A model study

Theoretical models of a spin-polarized voltage probe (SPVP) tunnel-coupled to the helical edge states (HES) of a quantum spin Hall system (QSHS) are studied. Our first model of the SPVP comprises $N_{P}$ spin-polarized modes (subprobes), each of which is locally tunnel-coupled to the HES, while the SPVP, as a whole, is subjected to a self-consistency condition ensuring zero average current on the probe. We carry out a numerical analysis which shows that the optimal situation for reading off spin-resolved voltage from the HES depends on the interplay of the probe-edge tunnel-coupling and the number of modes in the probe ($N_P$). We further investigate the stability of our findings by introducing Gaussian fluctuations in {\it{(i)}} the tunnel-coupling between the subprobes and the HES about a chosen average value and {\it{(ii)}} spin-polarization of the subprobes about a chosen direction of the net polarization of SPVP. We also perform a numerical analysis corresponding to the situation where four such SPVPs are implemented in a self-consistent fashion across a ferromagnetic barrier on the HES and demonstrate that this model facilitates the measurements of spin-resolved four-probe voltage drops across the ferromagnetic barrier. As a second model, we employ the edge state of a quantum anomalous Hall state (QAHS) as the SPVP which is tunnel-coupled over an extended region with the HES. A two-dimensional lattice simulation for the quantum transport of the proposed device setup comprising a junction of QSHS and QAHS is considered and a feasibility study of using the edge of the QAHS as an efficient spin-polarized voltage probe is carried out in presence of an optimal strength of the disorder.

Crystalline Weyl semimetal phase in Quantum Spin Hall systems under magnetic fields

We investigate an unconventional topological phase transition that occurs in quantum spin Hall (QSH) systems when applying an external in-plane magnetic field. We show that this transition between QSH and trivial insulator phases is separated by a stable topological gapless phase, which is protected by the combination of particle-hole and reflection symmetries, and thus, we dub it as crystalline Weyl semimetal. We explore the stability of this new phase when particle-hole symmetry breaking terms are present. Especially, we predict a robust unconventional topological phase transition to be visible for materials described by the Kane and Mele model even if particle-hole symmetry is significantly broken.

Protection of edge transport in quantum spin Hall samples: spin-symmetry based general approach and examples

Understanding possible mechanisms, which can lead to suppression of helical edge transport in quantum spin Hall (QSH) systems, attracted huge attention right after the first experiments revealing the fragility of the ballistic conductance. Despite the very intensive research and the abundance of theoretical models, the fully consistent explanation of the experimental results is still lacking. We systematize various theories of helical transport with the help of the spin conservation analysis which allows one to single out setups with the ballistic conductance being robustly protected regardless of the electron backscattering. First, we briefly review different theories of edge transport in the QSH samples with and without the spin axial symmetry of the electrons including those theoretical predictions which are not consistent with the spin conservation analysis and, thus, call for a deeper study. Next, we illustrate the general approach by a detailed study of representative examples. One of them addresses the helical edge coupled to an array of Heisenberg-interacting magnetic impurities (MIs) and demonstrates that the conductance remains ballistic even if the time-reversal symmetry on the edge is (locally) broken but the total spin is conserved. Another example focuses on the effects of the space-fluctuating spin–orbit interaction on the QSH edge. It reveals weakness of the protection in several cases, including, e.g. the presence of either the U(1)-symmetric, though not fully isotropic, MIs or generic electron–electron interactions.

Research progress of integrated photonic quantum simulation

Quantum simulation is to use a controllable quantum system to simulate other complicated or hard-to-control quantum system, and to deal with some complex unknown quantum systems that cannot be simulated on classical computers due to the exponential explosion of the Hilbert space. Among different kinds of physical realizations of quantum simulation, integrated optical systems have emerged as an appropriate platform in recent years due to the advantages of flexible control, weak decoherence, and no interaction in optical systems. In this review, we attempt to introduce some of the basic models used for quantum simulation in integrated photonic systems. This review article is organized as follows. In Section 2, we introduce the commonly used material platforms for integrated quantum simulation, including the silicon-based, lithium niobate-based integrated circuits, and the femtosecond laser direct writing optical waveguides. Several integrated optical platforms such as the coupled waveguide arrays, photonic crystals, coupled resonator arrays, and multiport interferometers are also introduced. In Section 3, we focus on the analog quantum simulations in the integrated photonic platform, including Anderson localization of light in disordered systems, various kinds of topological insulators, nonlinear and non-Hermitian systems. More specifically, in Subsection 3.1, we present the integrated photonic realizations of disordered and quasi-periodic systems. In Subsection 3.2, we review the integrated photonic realizations of the topological insulators with and without time-reversal symmetry, including Floquet topological insulators, quantum spin hall system, anomalous quantum hall system, valley hall system, Su-Schrieffer-Heeger (SSH) model, and photonic topological Anderson insulators. Besides, topological insulator lasers and topologically protected quantum photon sources are briefly reviewed. In Subsection 3.3, we review the nonlinear and non-Hermitian integrated optical systems. In Section 4 we present the integrated digital quantum simulations based on the multiport interferometers, including the discrete-time quantum random walk, Boson sampling, and molecular simulation. In Section 5, we summarize the content of the article and present the outlook on the future perspectives of the integrated photonic quantum simulation. We believe that the integrated photonic platforms will continue to provide an excellent platform for quantum simulation. More practical applications will be found based on this system through combining the fields of topological photonics, laser technologies, quantum information, nonlinear and non-Hermitian physics.

Epitaxial Growth of Ultraflat Bismuthene with Large Topological Band Inversion Enabled by Substrate-Orbital-Filtering Effect.

Quantum spin Hall (QSH) systems hold promises of low-power-consuming spintronic devices, yet their practical applications are extremely impeded by the small energy gaps. Fabricating QSH materials with large gaps, especially under the guidance of design principles, is essential for both scientific research and practical applications. Here, we demonstrate that large on-site atomic spin-orbit coupling can be directly exploited via the intriguing substrate-orbital-filtering effect to generate large-gap QSH systems and experimentally realized on the epitaxially synthesized ultraflat bismuthene on Ag(111). Theoretical calculations reveal that the underlying substrate selectively filters Bi pz orbitals away from the Fermi level, leading pxy orbitals with nonzero magnetic quantum numbers, resulting in large topological gap of ∼1 eV at the K point. The corresponding topological edge states are identified through scanning tunneling spectroscopy combined with density functional theory calculations. Our findings provide general strategies to design large-gap QSH systems and further explore their topology-related physics.

Pressure-induced superconductivity and structure phase transition in Pt2HgSe3

Recently monolayer jacutingaite (Pt2HgSe3), a naturally occurring exfoliable mineral, discovered in Brazil in 2008, has been theoretically predicted as a candidate quantum spin Hall system with a 0.5 eV band gap, while the bulk form is one of only a few known dual-topological insulators that may host different surface states protected by symmetries. In this work, we systematically investigate both structure and electronic evolution of bulk Pt2HgSe3 under high pressure up to 96 GPa. The nontrivial topology is theoretically stable, and persists up to the structural phase transition observed in the high-pressure regime. Interestingly, we found that this phase transition is accompanied by the appearance of superconductivity at around 55 GPa and the critical transition temperature Tc increases with applied pressure. Our results demonstrate that Pt2HgSe3 with nontrivial topology of electronic states displays a ground state upon compression and raises potentials in application to the next-generation spintronic devices.

Topological Proximity-Induced Dirac Fermion in Two-Dimensional Antimonene.

Antimonene is a promising two-dimensional (2D) material that is calculated to have a significant fundamental bandgap usable for advanced applications such as field-effect transistors, photoelectric devices, and the quantum-spin Hall (QSH) state. Herein, we demonstrate a phenomenon termed topological proximity effect, which occurs between a 2D material and a three-dimensional (3D) topological insulator (TI). We provide strong evidence derived from hydrogen etching on Sb2Te3 that large-area and well-ordered antimonene presents a 2D topological state. Delicate analysis with a scanning tunneling microscope of the evolutionary intermediates reveals that hydrogen etching on Sb2Te3 resulted in the formation of a large area of antimonene with a buckled structure. A topological state formed in the antimonene/Sb2Te3 heterostructure was confirmed with angle-resolved photoemission spectra and density-functional theory calculations; in particular, the Dirac point was located almost at the Fermi level. The results reveal that Dirac fermions are indeed realized at the interface of a 2D normal insulator (NI) and a 3D TI as a result of strong hybridization between antimonene and Sb2Te3. Our work demonstrates that the position of the Dirac point and the shape of the Dirac surface state can be tuned by varying the energy position of the NI valence band, which modifies the direction of the spin texture of Sb-BL/Sb2Te3 via varying the Fermi level. This topological phase in 2D-material engineering has generated a paradigm in that the topological proximity effect at the NI/TI interface has been realized, which demonstrates a way to create QSH systems in 2D-material TI heterostructures.

Hall and Spin Hall Viscosity in 2d Topological Systems

We study responses to metric perturbation in topological insulator models. In this paper we introduce a novel quantity, Hall viscosity to particle density ratio, which is analogous to the viscosity to entropy ratio suggested by AdS/CFT correspondence. This quantity corresponds to the filling fraction which characterizes the quantum Hall states, and hence it could be discussed in Haldane's zero-field quantum Hall system. We also consider dissipationless viscosity in the time reversal invariant quantum spin Hall system, which is related to a spin current.

Formation and detection of Majorana modes in quantum spin Hall trenches

We propose a novel realization for a topologically superconducting phase hosting Majorana zero modes on the basis of quantum spin Hall systems. Remarkably, our proposal is completely free of ferromagnets. Instead, we confine helical edge states around a narrow defect line of finite length in a two-dimensional topological insulator. We demonstrate the formation of a new topological regime, hosting protected Majorana modes in the presence of $s$-wave superconductivity and Zeeman coupling. Interestingly, when the system is weakly tunnel coupled to helical edge state reservoirs, a particular transport signature is associated with the presence of a non-Abelian Majorana zero mode.