Quantum spin Hall effect in a three-orbital tight-binding Hamiltonian

Both quantum spin Hall and quantum anomalous Hall states are novel states of quantum matter with promising applications. We propose junction quantum wells comprising II-VI, III-V or IV semiconductors as a large class of new materials realizing the quantum spin Hall state. Especially, we find that the bulk band gap for the quantum spin Hall state can be as large as 0.1 eV. Further more, magnetic doping would induce the ferromagnetism in these junction quantum wells due to band edge singularities in the band-inversion regime and to realize the quantum anomalous Hall state.

Chapter 5 - Quantum Spin Hall State in HgTe

A large bulk band gap is critical for the applications of quantum spin hall (QSH) insulators in spintronics at room temperature. Based on first-principles calculations, we predict that the methyl-functionalized III-Bi monolayers, namely III-Bi-(CH3)2 (III=Ga, In, Tl) thin films, own QSH states with band gap as large as 0.260, 0.304 and 0.843 eV, respectively, making them suitable for room-temperature applications. The topological characteristics are confirmed by s-px,y band inversion, topological invariant Z2, and the topologically protected edge states. Noticeably, for GaBi/InBi-(CH3)2 films, the s-px,y band inversion occurred in the progress of spin-orbital coupling (SOC), while for TlBi(CH3)2 film, the s-px,y band inversion happened in the progress of chemical bonding. Significantly, the QSH states in III-Bi-(CH3)2 films are robust against the mechanical strains and various methyl coverages, making these films particularly flexible to substrate choice for device applications. Besides, the h-BN substrate is an ideal substrate for III-Bi-(CH3)2 films to realize large gap nontrivial topological states.. These findings demonstrate that the methyl-functionalized III-Bi films may be good QSH effect platforms for topological electronic devices design and fabrication in spintronics.

The quantum spin Hall (QSH) effect and the quantum anomalous Hall (QAH) effect in Lieb lattice are investigated in the presence of both Rashba spin-orbit coupling (SOC) and uniform exchange field. The Lieb lattice has a simple cubic symmetry, which is characterized by the single Dirac-cone per Brillouin zone and the middle flat band in the band structure. The intrinsic SOC is essentially needed to open the full energy gap in the bulk. The QSH effect could survive even in the presence of the exchange field. In terms of the first Chern number and the spin Chern number, we study the topological nature and the topological phase transition from the time-reversal symmetry broken QSH effect to the QAH effect. For Lieb lattice ribbons, the energy spectrum and the wave-function distributions are obtained numerically, where the helical edge states and the chiral edge states reveal the non-trivial topological QSH and QAH properties, respectively.

The quantum spin Hall (QSH) state, observed in a zero magnetic field in HgTe quantum wells, respects the time-reversal symmetry and is distinct from quantum Hall (QH) states. We show that the QSH state persists in strong quantizing fields and is identified by counterpropagating (helical) edge channels with nonlinear dispersion inside the band gap. If the Fermi level is shifted into the Landau-quantized conduction or valence band, we find a transition between the QSH and QH regimes. Near the transition the longitudinal conductance of the helical channels is strongly suppressed due to the combined effect of the spectrum nonlinearity and enhanced backscattering. It shows a power-law decay B(-2N) with magnetic field B, determined by the number of backscatterers on the edge N. This suggests a rather simple and practical way to probe the quality of quasiballistic QSH devices using magnetoresistance measurements.

The quantum spin Hall state is a topologically nontrivial insulator state protected by the time-reversal symmetry. We show that such a state always leads to spin-charge separation in the presence of a pi flux. Our result is generally valid for any interacting system. We present a proposal to experimentally observe the phenomenon of spin-charge separation in the recently discovered quantum spin Hall system.

As one type of important topological quantum states, the quantum spin Hall (QSH) effect realized in two-dimensional (2D) materials still maintains sufficient attractiveness due to its promising spintronic applications. By using the first-principles calculations, we theoretically investigate the structural, electronic and topological properties of a newly 2D honeycomb-Kagome WI3 monolayer (ML). The WI3 ML possesses the excellent dynamical, thermal and mechanical stabilities, as has been confirmed by phonon spectra, molecular dynamics simulations and elastic constants calculations, respectively. It is found that the WI3 ML behaves a type-II quadratic non-Dirac band dispersion around the Fermi level in the absence of spin–orbit coupling (SOC), while that may be adjusted to the type-I and/or type-III case based on the half-unilateral hydrogenation method. In the presence of SOC, the system may transform from the quadratic non-Dirac semimetal state into an intrinsic QSH state with nonzero topological invariant and Dirac-like edge states. The nontrivial topology of the system should originate from the strong SOC interaction of the degenerate W dx 2–y2/dxy states at Γ point, and a nearly 0.10 eV nontrivial global band gap has been obtained under the 4% compressive strain. The half/fully-substitutional Mo doping, hydrogenation modulation as well as substrate effect on the electronic structures and topological states of the WI3 ML have been explored. Intriguingly, the unilateral hydrogenated WI3 ML present a topological semimetal phase with robust nontrivial edge stets against SOC and in-plane biaxial strain, while the fully hydrogenated one exhibits a Dirac-type QSH state around the high-symmetry K/K′ points. Therefore, the honeycomb-Kagome WI3 ML should be the potential candidate platform for future low-power nanoelectronic and spintronic applications.

We theoretically study the helical edge states in the quantum spin Hall (QSH) effect based on an effective 4-band tight-binding model for HgTe/CdTe quantum wells. We microscopically describe the spatial dependence of the helical edge modes in the QSH state. It is found that the helical edge states are gapped when the width of sample narrows. This is because the edge states on the opposite boundary of the sample overlap each other, and then the backward scattering channel opens up.

We present the first experimental evidence of a topological phase transition in a monoelemental quantum spin Hall insulator. Particularly, we show that low-buckled epitaxial germanene is a quantum spin Hall insulator with a large bulk gap and robust metallic edges. Applying a critical perpendicular electric field closes the topological gap and makes germanene a Dirac semimetal. Increasing the electric field further results in the opening of a trivial gap and disappearance of the metallic edge states. This electric field-induced switching of the topological state and the sizable gap make germanene suitable for room-temperature topological field-effect transistors, which could revolutionize low-energy electronics.

We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluride-cadmium telluride semiconductor quantum wells. When the thickness of the quantum well is varied, the electronic state changes from a normal to an "inverted" type at a critical thickness d(c). We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss methods for experimental detection of the QSH effect.

Research on the quantum nature of matter and light has flourished in recent years, as the field has grown for theorists and experimentalists alike. New research directions, such as the study of novel phases in quantum materials, have laid the ground for new foundational theories and future quantum technologies. In particular, novel topological materials and superconducting hybrid systems are promising for the development of novel superconductors and quantum computers. This Focus Issue aims to highlight some of the latest achievements in the field of quantum matter. It includes 3 Reviews, 1 Perspective, and 3 Research Articles on a range of topics, including single-photon emitters for quantum technologies, topological quantum materials, and quantum sensing and metrology: Rare-Earth Doped Thin Films for Optical Quantum Technologies (Philippe Goldner et al., 10.1002/qute.202500026): A Review article on rare earth-doped thin films—materials that are highly promising for use in on-chip photonic circuits thanks to their excellent coherence properties. The integration of rare-earth thin films into photonic platforms could potentially enable photonic quantum technologies, such as optical quantum memories, which are relevant for communications and processing. Cuprate twistronics for quantum hardware (Nicola Poccia et al., 10.1002/qute.202500203): A topical Review on the emerging field of cuprate twistronics, which involves stacking and twisting ultrathin layers of cuprate superconductors. This technique creates Moiré patterns and new electronic states, uncovering new opportunities in both applied (e.g., quantum hardware) and fundamental physics. Quantum spin Hall effects in van der Waals materials (Qiong Ma et al., 10.1002/qute.202500327): A Review of the Quantum Spin Hall (QSH) effect in two-dimensional van der Waals (vdW) materials. The QSH effect is promising for the development of low-power electronics and topological quantum computing. The article explores the main developments in the field, emerging research directions, as well as experimental challenges. Beyond kagome: p-bands in kagome metals (Alexander Tsirlin et al., 10.1002/qute.202500336): A Perspective arguing that p-bands (electron bands from non-transition metals) play a critical, often overlooked, role in the electronic instabilities, such as charge-density waves and superconductivity, observed in kagome lattice metals. High-purity single-photon emission in the telecom O-band from droplet-epitaxy InAs quantum dots integrated into a GaAs/AlGaAs planar microcavity on vicinal GaAs(111) (Battulga Munkhbat et al., 10.1002/qute.202500159): A Research article on developing a reliable source of single photons in the telecom O-band (a critical wavelength for fibre communication) using InAs quantum dots grown via droplet epitaxy. Single-photon emission from such sources could potentially be useful for building global quantum communication networks. Can Janus monolayer transition-metal dihalides be bright excitonic insulators? (Yuanchang Li et al., 10.1002/qute.202500345): This Research article explores Janus monolayers (asymmetric 2D materials) as potential candidates for bright excitonic insulators (EIs). EIs are a state of matter where electrons and holes spontaneously form excitons that condense, and bright EIs could provide a unique platform for coherent quantum optical devices. Highly sensitive magnetometer with continuous excitation Ramsey protocol by utilizing long dephasing time of millimetre-scale spin ensembles in (111) diamond (Mutsuko Hatano et al., 10.1002/qute.202500056): This Research article presents a method to significantly enhance the sensitivity of magnetometers by utilizing the long dephasing time of nitrogen-vacancy (NV) centre spin ensembles in a specific orientation of diamond. NV-diamond magnetometers are key for high-precision quantum sensing. Through this Focus Issue, we aim to highlight the major advances in quantum matter research and to offer perspectives on key directions for future research. We hope that readers will find the content of this collection both inspiring and useful.

The continuous pursuit of novel two-dimensional (2D) materials with intriguing properties has been a driving force in advancing various scientific and technological frontiers. Here, based on a wide range of first-principles calculations, we predicted the existence of a novel family of 2D transition-metal oxides, the Ti3O MOenes (MXene-like 2D transition oxides), and determined its distinctive electronic and topological properties. A pair of 2D antiferromagnetic (AFM) Dirac points precisely located at the Fermi level in the absence of spin-orbit coupling (SOC) is observed in the 1T-Ti3O monolayer. Moreover, upon halogenation on a bare monolayer, 1T-Ti3OCl3 and 1T-Ti3OBr3 monolayers display the quantum spin Hall (QSH) effect with nontrivial helical edge states within the gapless bulk states. Specifically, single layer 1T-Ti3OF3 behaves as an indirect semiconductor with a gap of 0.81 eV, exhibiting a strong light-harvesting capability. The indirect-gap feature can be switched to a direct one by only exerting a small tensile strain of 1.5%. These findings broaden emerging phenomena in a rich family of MOenes, suggesting a novel platform for the development of next-generation nanodevices.

Quantum spin Hall (QSH) effect, a fundamentally new quantum state of matter and topological phase transitions are characteristics of a kind of electronic material, popularly referred to as topological insulators (TIs). TIs are similar to ordinary insulator in terms of their bulk bandgap, but have gapless conducting edge-states that are topologically protected. These edge-states are facilitated by the time-reversal symmetry and they are robust against nonmagnetic impurity scattering. Recently, the quest for new materials exhibiting non-trivial topological state of matter has been of great research interest, as TIs find applications in new electronics and spintronics and quantum-computing devices. Here, we propose and demonstrate as a proof-of-concept that QSH effect and topological phase transitions can be realized in /InSb semiconductor quantum wells (QWs). The simultaneous incorporation of nitrogen and bismuth in InSb is instrumental in lowering the bandgap, while inducing opposite kinds of strain to attain a near-lattice-matching conducive for lattice growth. Phase diagram for bandgap shows that as we increase the QW thickness, at a critical thickness, the electronic bandstructure switches from a normal to an inverted type. We confirm that such transition are topological phase transitions between a traditional insulator and a TI exhibiting QSH effect—by demonstrating the topologically protected edge-states using the bandstructure, edge-localized distribution of the wavefunctions and edge-state spin-momentum locking phenomenon, presence of non-zero conductance in spite of the Fermi energy lying in the bandgap window, crossover points of Landau levels in the zero-mode indicating topological band inversion in the absence of any magnetic field and presence of large Rashba spin-splitting, which is essential for spin-manipulation in TIs.

We show that the spin quantum Hall effect in the vortex state of\ntwo-dimensional rotating superfluid He3 can be described as an adiabatic spin\ntransport of Bloch quasiparticles. We show that the spin Hall conductivity is\nwritten by the Berry phase as well as the Chern number. The results have\nsimilarity to the adiabatic pumping of Bloch electrons and the spontaneous\npolarization in crystalline dielectrics.\n

Quantum spin Hall effects (QSHE) arising from electron band topology are usually limited to crystals. Here, the authors extend the concept of QSHE to nonperiodic systems. They derive a spin Bott index to characterize the electronic topology in aperiodic and amorphous systems, and confirm its applicability by realizing the QSHE in quasicrystals. As in crystals, the QSHE in quasicrystals manifests with robust metallic edge states and quantized conductance. Their findings not only provide a better understanding of electronic properties of nonperiodic systems, but also extend the search of the QSH phase to aperiodic and amorphous materials that are experimentally feasible.