Two-dimensional Quantum Spin Hall Insulator Research Articles

Ideal two-dimensional quantum spin Hall insulators MgA2Te4 (A = Ga, In) with Rashba spin splitting and tunable properties.

For decades, topological insulators have played a pivotal role in fundamental condensed-matter physics owing to their distinctive edge states and electronic properties. Here, based on in-depth first-principles calculations, we investigate the MgA2Te4 (A = Ga, In) structures belonging to the MA2Z4 2D material family. Among them, the topological insulator MgGaInTe4 exhibits band inversion and a sizeable bandgap of up to 60.8 meV which satisfies the requirement for room-temperature realization. Under the spin-orbit coupling effect, MgGaInTe4 with inversion asymmetry undergoes Rashba spin splitting. The Rashba-like and Dirac-type edge states emerge from different terminals along (010) for MgGaInTe4. The external vertical electric field is verified to modulate the inverted bandgap and topological state of MgGaInTe4 by converting a nontrivial state to a trivial state and MgIn2Te4 with the original trivial state to a nontrivial one. Accordingly, MgGaInTe4 and MgIn2Te4 have significant potential for application in topological quantum field-effect transistors. Our research identifies that the MgA2Te4 (A = Ga, In) structures have huge potential to be candidate 2D materials for spintronics and topological quantum devices.

Single-point spin Chern number in a supercell framework

We present an approach for the calculation of the topological invariant in non-crystalline two-dimensional quantum spin Hall insulators. While topological invariants were originally mathematically introduced for crystalline periodic systems, and crucially hinge on tracking the evolution of occupied states through the Brillouin zone, the introduction of disorder or dynamical effects can break the translational symmetry and imply the use of larger simulation cells, where the k-point sampling is typically reduced to the single Γ-point. Here, we introduce a single-point formula for the spin Chern number that enables to adopt the supercell framework, where a single Hamiltonian diagonalisation is performed. Inspired by the work of Prodan (2009 Phys. Rev. B 80 125327), our single-point approach allows to calculate the spin Chern number even when the spin operator does not commute with the Hamiltonian, as in the presence of Rashba spin–orbit coupling. We validate our method on the Kane–Mele model, both pristine and in the presence of Anderson disorder. Finally, we investigate the disorder-driven transition from the trivial phase to the topological state known as topological Anderson insulator. Beyond disordered systems, our approach is particularly useful to investigate the role of defects, to study topological alloys and in the context of ab-initio molecular dynamics simulations at finite temperature.

Large inverted band gap in strained three-layer InAs/GaInSb quantum wells

InAs/GaInSb quantum wells with three strained layers are theoretically two-dimensional quantum spin Hall insulators. Magnetotransport measurements reveal that these structures have indeed inverted band gaps as large as 45 meV and, moreover, have an edge conduction of possible topological origin.

Proximity-magnetized quantum spin Hall insulator: monolayer 1 T’ WTe2/Cr2Ge2Te6

Van der Waals heterostructures offer great versatility to tailor unique interactions at the atomically flat interfaces between dissimilar layered materials and induce novel physical phenomena. By bringing monolayer 1 T’ WTe2, a two-dimensional quantum spin Hall insulator, and few-layer Cr2Ge2Te6, an insulating ferromagnet, into close proximity in an heterostructure, we introduce a ferromagnetic order in the former via the interfacial exchange interaction. The ferromagnetism in WTe2 manifests in the anomalous Nernst effect, anomalous Hall effect as well as anisotropic magnetoresistance effect. Using local electrodes, we identify separate transport contributions from the metallic edge and insulating bulk. When driven by an AC current, the second harmonic voltage responses closely resemble the anomalous Nernst responses to AC temperature gradient generated by nonlocal heater, which appear as nonreciprocal signals with respect to the induced magnetization orientation. Our results from different electrodes reveal spin-polarized edge states in the magnetized quantum spin Hall insulator.

Transport Properties of Zigzag Ribbons Composed of Two-Dimensional Quantum Spin Hall Insulators with a Single Magnetic Impurity

We investigate the transport properties of a ribbon with zigzag-shaped edges, which is composed of a two-dimensional quantum spin Hall insulator and contains a single magnetic impurity near the edg...

Recent Advances in Tin: From Two-Dimensional Quantum Spin Hall Insulator to Bulk Dirac Semimetal.

An atomic layer of tin in a buckled honeycomb lattice, termed stanene, is a promising large-gap two-dimensional topological insulator for realizing room-temperature quantum-spin-Hall effect and therefore has drawn tremendous interest in recent years. Because the electronic structures of Sn allotropes are sensitive to lattice strain, e.g. the semimetallic α-phase of Sn can transform into a three-dimensional topological Dirac semimetal under compressive strain, recent experimental advances have demonstrated that stanene layers on different substrates can also host various electronic properties relating to in-plane strain, interfacial charge transfer, layer thickness, and so on. Thus, comprehensive understanding of the growth mechanism at the atomic scale is highly desirable for precise control of such tunable properties. Herein, the fundamental properties of stanene and α-Sn films, recent achievements in epitaxial growth, challenges in high-quality synthesis, and possible applications of stanene are discussed.

Majorana Corner Modes with Solitons in an Attractive Hubbard-Hofstadter Model of Cold Atom Optical Lattices.

Higher-order topological superconductors hosting Majorana-Kramers pairs (MKPs) as corner modes have recently been proposed in a two-dimensional quantum spin Hall insulator proximity-coupled to unconventional cuprate or iron-based superconductors. Here, we show that such MKPs can be realized using a conventional s-wave superfluid with a soliton in cold atom systems governed by the Hubbard-Hofstadter model. The MKPs emerge in the presence of interaction at the "corners" defined by the intersections of line solitons and the one-dimensional edges of the system. Our scheme is based on the recently realized cold atom Hubbard-Hofstadter lattice and will pave the way for observing possible higher-order topological superfluidity with conventional s-wave superfluids or superconductors.

Proximity-induced surface superconductivity in Dirac semimetal Cd3As2

Cd3As2 is a three-dimensional Dirac semimetal with separated Dirac points in momentum space. In spite of extensive transport and spectroscopic studies on its exotic properties, the evidence of superconductivity in its surface states remains elusive. Here, we report the observation of proximity-induced surface superconductivity in Nb/Cd3As2 hybrid structures. Our four-terminal transport measurement identifies a pronounced proximity-induced pairing gap (gap size comparable to Nb) on the surfaces, which exhibits a flat conductance plateau in differential conductance spectra, consistent with our theoretical simulations. The surface supercurrent from Nb/Cd3As2/Nb junctions is also achieved with a Fraunhofer/SQUID-like pattern under out-of-plane/in-plane magnetic fields, respectively. The resultant mapping shows a predominant distribution on the top and bottom surfaces as the bulk carriers are depleted, which can be regarded as a higher dimensional analog of edge supercurrent in two-dimensional quantum spin Hall insulators. Our study provides the evidence of surface superconductivity in Dirac semimetals.

Crossed responses of spin and orbital magnetism in topological insulators

Crossed magnetic responses between spin and orbital angular momentum are studied in time-reversal symmetric topological insulators. Due to spin-orbit coupling in the quantum spin Hall systems and three-dimensional topological insulators, the magnetic susceptibility has crossed (intersectional) components between spin and orbital part of magnetism. In this study, the crossed susceptibility for the orbital magnetization is studied in two- and three-dimensional topological insulator models, in which an external magnetic field interacts with the electron spin by Zeeman coupling via distinct g-factors for conduction and valence energy bands. The crossed susceptibility in two-dimensional quantum spin Hall insulators shows a quantized signature of the $\mathbb{Z}_2$ topological phase in response to Zeeman coupling via an averaged g-factor, and the quantization persists even when $\sigma^z$-conservation of electrons is broken by a tilted magnetic field. The bulk orbital magnetization is interpreted by the persistent edge current attributed to the chiral anomaly at the (1+1)-dimensional boundary. In three-dimensional topological insulators, we found that the crossed susceptibility is proportional to the difference of g-factors of conduction and valence electrons, which is qualitatively different from the two-dimensional case. Steep changes of the crossed susceptibility in three dimensions at the phase transition points are explained by the surface Dirac fermion theory. Finally, dependence of the crossed susceptibility on g-factors in two- and three-dimensional cases is discussed from the viewpoint of time-reversal and particle-hole symmetries.

Emission of time-bin entangled particles into helical edge states

We propose a single-particle source which emits into the helical edge states of a two-dimensional quantum spin Hall insulator. Without breaking time-reversal symmetry, this source acts like a pair of noiseless single-electron emitters which each inject separately into a chiral edge state. By locally breaking time-reversal symmetry, the source becomes a proper single-particle emitter which exhibits shot noise. Due to its intrinsic helicity, this system can be used to produce time-bin entangled pairs of electrons in a controlled manner. The shot noise created by the source is related to the concurrence of the emitted state.

Interference of topologically protected edge states in silicene nanoribbons

Silicene is a two-dimensional quantum spin-Hall insulator. We study the edge channels of silicene nanoribbons from the viewpoint of the topological protection and the interference between the two edges. It is found that the behaviors of the helical edge channels (HECs) are completely different between the armchair and zigzag edges. The penetration depths $\xi$ of the HEC is antiproportional to the spin-orbit gap for the armchair edge $\xi_{\rm arm} \sim \hbar v_\text{F}/ \Delta$ ($v_\text{F}$: the Fermi velocity, $\Delta$: the gap due to the spin-orbit interaction), while it remains as short as the lattice constant for the zigzag edge. Zero-energy states disappear in armchair nanoribbons due to an interference of two edge states, while they remains in zigzag nanoribbons even if the width $W$ is quite narrow. The gap $\delta$ of HECs behaves as $\delta \sim \hbar v_\text{F}/W$ for $\Delta=0$, and as $\delta \sim \Delta \exp[- W/\xi_{\rm arm}]$ for $\Delta\not=0$ for armchair nanoribbons, while it remains essentially zero irrespectively of $\Delta$ for zigzag nanoribbons.

Quantum percolation in quantum spin Hall antidot systems

We study the influences of antidot-induced bound states on transport properties of two-dimensional quantum spin Hall insulators. The bound states are found able to induce quantum percolation in the originally insulating bulk. At some critical antidot densities, the quantum spin Hall phase can be completely destroyed due to the maximum quantum percolation. For systems with periodic boundaries, the maximum quantum percolation between the bound states creates intermediate extended states in the bulk which is originally gapped and insulating. The antidot-induced bound states plays the same role as the magnetic field in the quantum Hall effect, both makes electrons go into cyclotron motions. We also draw an analogy between the quantum percolation phenomena in this system and that in the network models of quantum Hall effect.

Spin-filtered edge states in graphene

Spin–orbit coupling changes graphene, in principle, into a two-dimensional topological insulator, also known as quantum spin Hall insulator. One of the expected consequences is the existence of spin-filtered edge states that carry dissipationless spin currents and undergo no backscattering in the presence of non-magnetic disorder, leading to quantization of conductance. Whereas, due to the small size of spin–orbit coupling in graphene, the experimental observation of these remarkable predictions is unlikely, the theoretical understanding of these spin-filtered states is shedding light on the electronic properties of edge states in other two-dimensional quantum spin Hall insulators. Here we review the effect of a variety of perturbations, like curvature, disorder, edge reconstruction, edge crystallographic orientation, and Coulomb interactions on the electronic properties of these spin filtered states.

Photoinduced spin Chern number change in a two-dimensional quantum spin Hall insulator with broken spin rotational symmetry

We propose a scheme by which the spin Chern number of two-dimensional insulators with generic spin-orbit interaction can be externally controlled by optical methods. When submitting the system to a circularly polarized laser field, and then adiabatically sweeping the amplitude of the latter, the various hopping integrals associated with an electron system effectively turn into tunable variables. This in turn transforms the spin Chern number, which governs the topological properties of the system into a function of the laser amplitude. This scheme can steer a conventional insulator into the quantum spin Hall state, and vice versa. We anticipate that our findings, which provide a firmly grounded connection between optical techniques and spin transport, will open up the possibility of developing spintronics devices that build on the physics of the photosteering of spin currents.

Half quantum spin Hall effect on the surface of weak topological insulators

We investigate interaction effects in three dimensional weak topological insulators (TI) with an even number of Dirac cones on the surface. We find that the surface states can be gapped by a surface charge density wave (CDW) order without breaking the time-reversal symmetry. In this sense, time-reversal symmetry alone cannot robustly protect the weak TI state in the presence of interactions. If the translational symmetry is additionally imposed in the bulk, a topologically non-trivial weak TI state can be obtained with helical edge states on the CDW domain walls. In other words, a CDW domain wall on the surface is topologically equivalent to the edge of a two-dimensional quantum spin Hall insulator. Therefore, the surface state of a weak topological insulator with translation symmetry breaking on the surface has a “half quantum spin Hall effect”, in the same way that the surface state of a strong topological insulator with time-reversal symmetry breaking on the surface has a “half quantum Hall effect”. The on-site and nearest neighbor interactions are investigated in the mean field level and the phase diagram for the surface states of weak topological insulators is obtained.

Dorokhov-Mello-Pereyra-Kumar equation for the edge transport of a quantum spin Hall insulator

Using the random matrix theory, we investigate the ensemble statistics of edge transport of a quantum spin Hall insulator with multiple edge states in the presence of quenched disorder. Dorokhov-Mello-Pereyra-Kumar equation applicable for such a system is established. It is found that a two-dimensional quantum spin Hall insulator is effectively a new type of one-dimensional (1D) quantum conductor with the different ensemble statistics from that of the ordinary 1D quantum conductor or the insulator with an even number of Kramers edge pairs. The ensemble statistics provides a physical manifestation of the ${Z}_{2}$ classification for the time-reversal invariant insulators.

One-dimensional topologically protected modes in topological insulators with lattice dislocations

Topological defects, such as domain walls and vortices, have long fascinated physicists. A novel twist is added in quantum systems such as the B-phase of superfluid helium He3, where vortices are associated with low-energy excitations in the cores. Similarly, cosmic strings may be tied to propagating fermion modes. Can analogous phenomena occur in crystalline solids that host a plethora of topological defects? Here, we show that indeed dislocation lines are associated with one-dimensional fermionic excitations in a ‘topological insulator’, a novel phase of matter believed to be realized in the material Bi0.9Sb0.1. In contrast to fermionic excitations in a regular quantum wire, these modes are topologically protected and not scattered by disorder. As dislocations are ubiquitous in real materials, these excitations could dominate spin and charge transport in topological insulators. Our results provide a novel route to creating a potentially ideal quantum wire in a bulk solid. Topological insulators are band insulators in which spin–orbit coupling takes the role of the applied magnetic field in the integer quantum Hall effect. Theory now predicts that dislocations in such systems can give rise to one-dimensional topologically protected states, resembling helical modes at the edge of a two-dimensional quantum spin Hall insulator.