Two-dimensional Quantum Spin Hall Research Articles

Large-Gap Quantum Spin Hall Insulators in Two-Dimensional Hafnium Halides: Unraveling the Impact of Strain and Substrate.

Two-dimensional (2D) topological insulators (TIs) or quantum spin Hall (QSH) insulators, characterized by insulating 2D electronic band structures and metallic helical edge states protected by time-reversal symmetry, offer a platform for realizing the quantum spin Hall effect, making them promising candidates for future spintronic devices and quantum computing. However, observing a high-temperature quantum spin Hall effect requires large-gap 2D TIs, and only a few 2D systems have been experimentally confirmed to possess this property. In this study, we employ first-principles calculations, combined with a structural search based on an evolutionary algorithm, to predict a class of 2D QSH insulators in hafnium halides, namely, HfF, HfCl, and HfBr with sizable band gaps of 0.12, 0.19, and 0.38 eV. Their topological nontrivial nature is confirmed by a Z2 invariant which equals to 1 and the presence of gapless edge states. Furthermore, the QSH effect in these materials remains robust under biaxial tensile strain of up to 10%, and the use of h-BN as a substrate effectively preserves the QSH states in these materials. Our findings pave the way for future theoretical and experimental investigations of 2D hafnium halides and their potential for realizing the QSH effect.

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.

Non-trivial topological phases in transition metal rich half-Heusler oxides

Topological insulators with gapless surface states and insulating bulk in non-centrosymmetric cubic systems have been extensively explored following the discovery of two-dimensional quantum spin hall effect in zincblende HgTe. In such systems the negative band inversion strength E (= E E 0) governs the robustness of the non-trivial topological states at ambient conditions. Hence, realizing large negative values of E has been a guiding motivation of several investigations reported in literature. Here, we present a material design approach which can be employed to realize large negative values of E in cubic materials such as half-Heusler (HH) oxides with 18 valence electron configurations. We explore 27 HH oxides of the form ABO (A = Li, K, Rb; B = Cu, Ag, Au) in α-, β-, and γ-phase (by placing transition metal atom at different Wyckoff positions) for their non-trivial topological phase. Off these three phases, we found that, the α-phase of nine HH oxides (wherein the transition metal atoms occupy 4a Wyckoff positions in the crystal structure) is the most promising with non-trivial topological phase which is governed by the mass-Darwin fully-relativistic effects enhancing E. Whereas the other phases were found to be either trivial semiconductors or semimetals or metals and most of them being dynamically unstable. We focus on RbAuO in α-phase with E of −1.29 eV and the effect of strain fields on the topological surface states of this compound. We conclude that the α-phase of HH oxide presented here can be synthesized experimentally for diverse room temperature applications in spintronics and nanoelectronics.

MX6C2H monolayers: The novel two-dimensional tunable Dirac cone materials family and quantum spin Hall insulators

Two-dimensional (2D) Dirac cone materials have many interesting physical properties. Therefore, people have been trying to find 2D materials with Dirac cones. Here, based on first principle calculations, we studied a new 2D Dirac cone material family MX6C2H monolayers (M = N,P,As and Sb, X = C,Si,Ge and Sn). The calculation of the cohesive energy indicated that the MX6C2H sheets have excellent energy stability. And the phonon spectrum showed their excellent dynamical stability. The electronic calculation revealed that the 2D MX6C2H monolayers have graphene-like band structures and ultra-high Fermi velocities comparable to graphene. The spin–orbit–coupling effect can open a sizable topological band gap in SbSn6C2H monolayer so that it can be effectively classified as quantum spin Hall insulators. In addition, the Dirac cone of PC6C2H monolayer can be adjusted by applying in-plane uniaxial strain, which is much easier than that of graphene. These interesting properties indicate that the novel 2D MX6C2H system has potential application value in nanoelectronics.

A second wave of topological phenomena in photonics and acoustics.

Light and sound are the most ubiquitous forms of waves, associated with a variety of phenomena and physical effects such as rainbows and echoes. Light and sound, both categorized as classical waves, have lately been brought into unexpected connections with exotic topological phases of matter. We are currently witnessing the onset of a second wave of active research into this topic. The past decade has been marked by fundamental advances comprising two-dimensional quantum Hall insulators and quantum spin and valley Hall insulators, whose topological properties are characterized using linear band topology. Here, going beyond these conventional topological systems, we focus on the latest frontiers, including non-Hermitian, nonlinear and non-Abelian topology as well as topological defects, for which the characterization of the topological features goes beyond the standard band-topology language. In addition to an overview of the current state of the art, we also survey future research directions for valuable applications.

Ultrafast nonequilibrium dynamics and high-harmonic generation in two-dimensional quantum spin Hall materials

We develop the theoretical framework of nonequilibrium ultrafast photonics in monolayer quantum spin Hall insulators supporting a multitude of topological states. In these materials, ubiquitous strong light-matter interactions in the femtosecond scale lead to nonadiabatic quantum dynamics, resulting in topology-dependent nonlinear optoelectronic transport phenomena. We investigate the mechanism driving topological Dirac fermions interacting with strong ultrashort light pulses and uncover various experimentally accessible physical quantities that encode fingerprints of the quantum material's topological electronic state from the high-harmonic generated spectrum. Our work sets the theoretical cornerstones to realize the full potential of time-resolved harmonic spectroscopy for understanding nonequilibrium processes in quantum topological systems and identifying topological invariants in two-dimensional quantum spin Hall solid state systems.

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 band gap quantum spin Hall insulators in plumbene monolayer decorated with amidogen, hydroxyl and thiol functional groups.

Two-dimensional Quantum Spin Hall (QSH) insulators featuring edge states that are topologically protected against back-scattering are arising as a novel state of quantum matter. One of the major obstacles to finding QSH insulators operable at room temperature is the insufficiency of suitable materials demonstrating the QSH effect with a large bulk band gap. Plumbene, the latest group-IV graphene analogous material, shows a large SOC-induced band gap opening but the coupling between topological states at different momentum points makes it a topologically trivial insulator. Pristine plumbene can be chemically functionalized to transform it from a conventional insulator to a topologically non-trivial insulator with a considerable bulk band gap. In this work, three new QSH phases in plumbene have been theoretically predicted through functionalization with amidogen (-NH2), hydroxyl (-OH) and thiol (-SH) groups. The derived electronic properties show non-trivial topological states in plumbene with very high bulk band gaps ranging from 1.0911 eV to as high as 1.1515 eV. External strain can be used to further enhance and tune these bulk gaps, as demonstrated in this work. We also propose a H-terminated SiC (0001) surface as a suitable substrate for the practical implementation of these monolayers to minimize lattice mismatch and maintain their topological order. The robustness of these QSH insulators against strain and substrate effects and the large bulk gaps provide a promising platform for potential applications of future low dissipation nanoelectronic devices and spintronic devices at room temperature.

Thermal transport of helical Majorana edge modes in a superconducting antiferromagnetic quantum spin Hall insulator

In the system composed of a two-dimensional antiferromagnetic quantum spin Hall insulator (AFQSHI) nanoribbon covered by s -wave superconductors, possessing helical Majorana edge mode (HMEM), and preserving effective time-reversal symmetry. Based on such the AFQSHI-SC hybrid system, we investigate the band structure and thermal transport properties. The two-terminal thermal conductance κ e l and electric conductance G are calculated by using the Landauer-Büttiker formula and the nonequilibrium Green’s function method. When a pair of intersecting edge states exists in the bulk band gap, a helical topological superconductor with Z 2 invariant ν = ± 1 is formed, which has a pair of Majorana edge states with opposite chirality, that is Majorana Kramer pairs, leading to a integer quantized thermal conductance plateau. We find that the quantized thermal conductance plateau is well preserved in a certain range of temperature. The presence and number of Majorana Kramer pairs in helical topological superconductor can be confirmed with the help of the quantized thermal conduction plateau, which is promising for the experimental detection of helical Majorana fermions. • In this manuscript, based on the Landauer-Buttiker formula and the nonequilibrium Green’s function method, we investigate the properties of helical Majorana fermions edge states thermal transport in a hybrid AFQSHI-SC structure. • When a pair of Majorana edge states with opposite chirality residing at the edge of the central topological superconductor region, a integer quantized thermal conductance plateau is discovered. • This quantized plateau can be used as strong evidence for the experimental detection of helical topological superconductors.

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.

Intrinsic Ferroelectric Quantum Spin Hall Insulator in Monolayer Na3Bi with Surface Trimerization.

Two-dimensional (2D) ferroelectric quantum spin Hall (FEQSH) insulator, which features coexisting ferroelectric and topologically insulating orders in two-dimension, is generally considered available only in engineered 2D systems. This is detrimental to the synthesis and application of next generation nonvolatile functional candidates. Therefore, exploring the intrinsic 2D FEQSH insulator is crucial. Here, by means of first-principles, we report a long-thought intrinsic 2D FEQSH insulator in monolayer Na3Bi with surface trimerization. The material harbors merits including large ferroelectric polarization, sizable nontrivial band gap, and low switching barrier, which are particularly beneficial for the detection and observation of ferroelectric topologically insulating states. Also, it is capable of nonvolatile switching of nontrivial spin textures via inherent ferroelectricity. The fantastic combination of excellent ferroelectric and topological phases in intrinsic the Na3Bi monolayer serves as an alluring platform for accelerating both scientific discoveries and innovative applications.

Observation of room temperature excitons in an atomically thin topological insulator

Optical spectroscopy of ultimately thin materials has significantly enhanced our understanding of collective excitations in low-dimensional semiconductors. This is particularly reflected by the rich physics of excitons in atomically thin crystals which uniquely arises from the interplay of strong Coulomb correlation, spin-orbit coupling (SOC), and lattice geometry. Here we extend the field by reporting the observation of room temperature excitons in a material of non-trivial global topology. We study the fundamental optical excitation spectrum of a single layer of bismuth atoms epitaxially grown on a SiC substrate (hereafter bismuthene or Bi/SiC) which has been established as a large-gap, two-dimensional (2D) quantum spin Hall (QSH) insulator. Strongly developed optical resonances are observed to emerge around the direct gap at the K and K’ points of the Brillouin zone, indicating the formation of bound excitons with considerable oscillator strength. These experimental findings are corroborated, concerning both the character of the excitonic resonances as well as their energy scale, by ab-initio GW and Bethe-Salpeter equation calculations, confirming strong Coulomb interaction effects in these optical excitations. Our observations provide evidence of excitons in a 2D QSH insulator at room temperature, with excitonic and topological physics deriving from the very same electronic structure.

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.

Two-dimensional anisotropic Dirac materials PtN4C2 and Pt2N8C6 with quantum spin and valley Hall effects

We propose two different two-dimensional topological Dirac materials, planar ${\mathrm{PtN}}_{4}{\mathrm{C}}_{2}$ and ${\mathrm{Pt}}_{2}{\mathrm{N}}_{8}{\mathrm{C}}_{6}$, which exhibit graphenelike electronic structures with linearly dispersive Dirac-cone states exactly at the Fermi level. Moreover, the Dirac cone is anisotropic, resulting in anisotropic Fermi velocities and making it possible to realize orientation-dependent quantum devices. Using first-principles electronic structure calculations, we have systemically studied the structural, electronic, and topological properties. We find that spin-orbit coupling opens a sizable topological band gap so that the materials can be classified as quantum spin Hall insulators as well as quantum valley Hall insulators. Helical edge states that reside in the insulating band gap connecting the bulk conduction and valence bands are observed. Our work not only expands the Dirac-cone material family, but also provides another avenue to search for more two-dimensional topological quantum spin and valley Hall insulators.

Ultrafast Momentum-Resolved Hot Electron Dynamics in the Two-Dimensional Topological Insulator Bismuthene.

Two-dimensional quantum spin Hall (QSH) insulators are a promising material class for spintronic applications based on topologically protected spin currents in their edges. Yet, they have not lived up to their technological potential, as experimental realizations are scarce and limited to cryogenic temperatures. These constraints have also severely restricted characterization of their dynamical properties. Here, we report on the electron dynamics of the novel room-temperature QSH candidate bismuthene after photoexcitation using time- and angle-resolved photoemission spectroscopy. We map the transiently occupied conduction band and track the full relaxation pathway of hot photocarriers. Intriguingly, we observe photocarrier lifetimes much shorter than those in conventional semiconductors. This is ascribed to the presence of topological in-gap states already established by local probes. Indeed, we find spectral signatures consistent with these earlier findings. Demonstration of the large band gap and the view into photoelectron dynamics mark a critical step toward optical control of QSH functionalities.

Magnetic impurities along the edge of a quantum spin Hall insulator: Realizing a one-dimensional AIII insulator

In this paper we construct a one-dimensional insulator with an approximate chiral symmetry belonging to the AIII class and discuss its properties. The construction principle is the intentional pollution of the edge of a two-dimensional quantum spin Hall insulator with magnetic impurities. The resulting bound states hybridize and disperse along the edge. We discuss under which circumstances this chain possesses zero-dimensional boundary modes on the level of an effective low-energy theory. The main appeal of our construction is the independence on details of the impurity lattice: the zero modes are stable against disorder and random lattice configurations. We also show that in the presence of Rashba coupling, which changes the symmetry class to A, one can still expect localized half-integer boundary excess charges protected by mirror symmetry although there is no nontrivial topological index. All of the results are confirmed numerically in a microscopic model.

Prediction of Dirac semimetals and hourglass surface states in stacked hydrogenated Xenes ( X=Sn and Pb)

Based on density-functional theory calculations and symmetry analysis, topological Dirac semimetals (DSMs) and exotic hourglass surface states are predicted in stacked hydrogenated stanene and plumbene [Xenes ($X$ = Sn and Pb)]. Two types of topologically nontrivial DSMs are predicted in the hydrogenated Xene crystals, with the two most stable stacking patterns, respectively. The Dirac points in SnH are found occurring along the three- or sixfold (screw) rotation axes due to the inversion of the Sn $5s$ ($5{p}_{z}$) and Sn $5{p}_{x,y}$ bands. The unique Fermi arcs are observed on the surfaces parallel to the rotation axes in the crystals. Very specially, the nonsymmorphic symmetry of a glide-mirror plane in the hydrogenated Xene crystals gives rise to exotic hourglass surface states which can lead to a giant value of spin-Hall conductivity and make the crystals be ideal systems applied in prospective dissipationless spintronics. The topological nature of the both types of the DSMs is identified by the calculations of the ${\mathrm{Z}}_{2}$ indexes. Phase transitions from topologically nontrivial DSM states to normal insulators (NIs) or to other types of DSMs are also investigated. Our work provides an ideal material platform for carrying out DSMs and a comprehensive study for understanding how DSMs evolve from two-dimensional NIs or quantum spin Hall materials.

Two-dimensional MX Dirac materials and quantum spin Hall insulators with tunable electronic and topological properties

We propose a novel class of two-dimensional (2D) Dirac materials in the MX family (M = Be, Mg, Zn and Cd, X = Cl, Br and I), which exhibit graphene-like band structures with linearly-dispersing Dirac-cone states over large energy scales (0.8–1.8 eV) and ultra-high Fermi velocities comparable to graphene. Spin-orbit coupling opens sizable topological band gaps so that these compounds can be effectively classified as quantum spin Hall insulators. The electronic and topological properties are found to be highly tunable and amenable to modulation via anion-layer substitution and vertical electric field. Electronic structures of several members of the family are shown to host a Van-Hove singularity (VHS) close to the energy of the Dirac node. The enhanced density-of-states associated with these VHSs could provide a mechanism for inducing topological superconductivity. The presence of sizable band gaps, ultra-high carrier mobilities, and small effective masses makes the MX family promising for electronics and spintronics applications.

Quantum anomalous Hall insulator phases in Fe-doped GaBi honeycomb

We discuss electronic and magnetic properties of the Fe-doped GaBi honeycomb using first principles calculations. Our analysis shows that the pristine GaBi honeycomb transitions from being a two-dimensional quantum spin Hall (QSH) insulator to a quantum anomalous Hall (QAH) insulator when it is doped with one Fe atom in a 4 × 4 GaBi honeycomb. The QAH phase in Fe-doped GaBi is found to be robust in that it maintains its Chern number (C = 1) under fairly large strains ( ∼ 4%) and supports a gap as large as 112 meV at 2.21% strain. The QAH phase is also retained when the Fe-doped GaBi is placed on a CdTe substrate, suggesting that Fe-doped GaBi films could be useful for spintronics applications.

Prediction of tetragonal monolayer CuN with a quantum spin Hall state

Abstract Two-dimensional (2D) quantum spin Hall (QSH) insulator are promising candidates for miniaturized electronic and dissipationless transport devices. The bottleneck preventing applications from QSH phase, however, is lack of feasible 2D materials in experiments so far. By using first-principles calculations, here we propose a realistic 2D QSH phase in tetragonal CuN, which is dynamically and mechanically stable. Band structure analysis reveals that it is a nontrivial QSH phase robust against external strains. The origin of QSH effect can be identified by a px-pz band inversion, topological invariant Z2, and helical edge states within the bulk gap. Also, a heterostructure composed of CuN deposited on semiconducting AlAs substrate remains topologically nontrivial with a sizable gap. These findings provide a promising platform to design new QSH insulators in tetragonal lattices, which show potential applications in multifunctional spintronics devices.