Large-gap Quantum Spin Hall Insulators 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.

Nanoribbons of large-gap quantum spin Hall insulator: electronic structures and transport properties

Two-dimensional Bi grown on semiconductor substrate, a large-gap quantum spin Hall insulator characterized by a (p x , p y )-orbital hexagonal lattice, has been theoretically proposed and experimentally confirmed. Here, by combining tight-binding modeling with first-principles calculations, we investigate the electronic structures and quantum transport properties of Bi nanoribbons (NRs), focusing on the topological edge states for nanoelectronics. We reveal that band gap emerges due to the quantum confinement, and the gaps size depends crucially on the width and edge shape: for zigzag NRs, the gap decreases monotonically with the increase of width; while for armchair NRs, it can be categorized into three subgroups with band-gap hierarchies of Eg(3p−1)>Eg(3p)>Eg(3p+1) , so that the overall relation is an oscillating dependence dumped by 1/width decay. Quantum transport calculations demonstrate that the conductance is quantized to 2 e2/h , and an applied gate voltage can efficiently regulate the conductance plateau, originating from the interplay between gate voltage and topological gaps. Furthermore, the quantized conductance remains robust against strong disorder, suggesting the unique advantage of topological states for electronic transport. This work not only provides fundamental insights into the electronic properties of topological insulator nanostructures, but also sheds light on the potential applications of exotic states for quantum devices compatible with semiconductor technology.

Switching Rashba spin-splitting by reversing electric-field direction

The manipulation of the Rashba spin-splitting is crucial for the development of nanospintronic technology. Here, it is proposed that the Rashba spin-splitting can be turned on and off by reversing electric-field direction. By the first-principles calculations, our proposal is illustrated by a concrete example of Janus monolayer RbKNaBi. The designed RbKNaBi possesses dynamical, thermal, and mechanical stabilities, and is a large-gap quantum spin Hall insulator (QSHI) with Rashba spin-splitting near the Fermi level. A small built-in electric field is predicted due to very small electronegativity difference between the bottom and top atoms, which is very key to switch Rashba spin-splitting through the experimentally available electric field intensity. Due to out-of-plane structural asymmetry, the Janus monolayer has distinctive behaviors by applying external electric field $E$ with the same magnitude but different directions ($z$ or $\ensuremath{-}z$). Our results reveal that the Rashba energy (${E}_{R}$) and Rashba constant (${\ensuremath{\alpha}}_{R}$) are increased by the positive $E$, while a negative $E$ suppresses the Rashba splitting to disappear, and then appears again. In a certain $E$ region (0.15 $\mathrm{V}/\AA{}$ to 0.25 $\mathrm{V}/\AA{}$), switching Rashba spin-splitting can be achieved by only reversing electric-field direction. Besides, the piezoelectric strain coefficients ${d}_{11}$ and ${d}_{31}$ (5.52 pm/V and --0.41 pm/V) are predicted, which are higher than or compared with those of many 2D materials. By piezoelectric effect, the strain can also be used to tune Rashba spin-splitting of RbKNaBi. In Janus RbKNaBi monolayer, the combination of piezoelectricity and Rashba spin-splitting with topological insulating phase can promote the integration of various physical phenomena. Moreover, a possible spintronic device is proposed to realize the function of spintronic switch. Our proposed manipulation of the Rashba spin-splitting may make a special contribution to semiconductor spintronics.

Magnetic field effects and excitonic selection rules in monolayer palladium diselenide as a large-gap quantum spin Hall insulator

Quantum spin hall (QSH) effect, a class of quantum state, is promising for dissipationless transport with topologically protected helical edge state. Based on first-principles calculations, we theoretically demonstrate the topological physics of $1\mathrm{H}\text{\ensuremath{-}}\mathrm{Pd}{\mathrm{Se}}_{2}$ with a large gap up to 0.24 eV. The band inversion takes place either among the ${p}_{z}$ and ${p}_{x,y}$ orbitals of Se atom or due to spin-orbital coupling under compressive strains. The edge modes exist in the energy gap and can be characterized by an effective edge state Hamiltonian. Based on the derived two-band $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ model, we demonstrate the profound phenomena induced by the applied magnetic field effects and optical transitions for chiral fermions, which lead to complicated excitonic selection rules in this topologically nontrivial two-dimensional material. Our results will pave the way for future theoretical and experimental studies on $\mathrm{Pd}{X}_{2}$ $(X=\mathrm{S},\mathrm{Se},\mathrm{Te})$ monolayers.

Design and realization of topological Dirac fermions on a triangular lattice

Large-gap quantum spin Hall insulators are promising materials for room-temperature applications based on Dirac fermions. Key to engineer the topologically non-trivial band ordering and sizable band gaps is strong spin-orbit interaction. Following Kane and Mele’s original suggestion, one approach is to synthesize monolayers of heavy atoms with honeycomb coordination accommodated on templates with hexagonal symmetry. Yet, in the majority of cases, this recipe leads to triangular lattices, typically hosting metals or trivial insulators. Here, we conceive and realize “indenene”, a triangular monolayer of indium on SiC exhibiting non-trivial valley physics driven by local spin-orbit coupling, which prevails over inversion-symmetry breaking terms. By means of tunneling microscopy of the 2D bulk we identify the quantum spin Hall phase of this triangular lattice and unveil how a hidden honeycomb connectivity emerges from interference patterns in Bloch px ± ipy-derived wave functions.

Selective Substrate-Orbital-Filtering Effect to Realize the Large-Gap Quantum Spin Hall Effect.

Although Pb harbors a strong spin-orbit coupling effect, pristine plumbene (the last group-IV cousin of graphene) hosts topologically trivial states. Based on first-principles calculations, we demonstrate that epitaxial growth of plumbene on the BaTe(111) surface converts the trivial Pb lattice into a quantum spin Hall (QSH) phase with a large gap of ∼0.3 eV via a selective substrate-orbital-filtering effect. Tight-binding model analyses show the pz orbital in half of the Pb overlayer is selectively removed by the BaTe substrate, leaving behind a pz-px,y band inversion. Based on the same working principle, the gap can be further increased to ∼0.5-0.6 eV by surface adsorption of H or halogen atoms that filters out the other half of the Pb pz orbitals. The mechanism of selective substrate-orbital-filtering is general, opening an avenue to explore large-gap QSH insulators in heavy-metal-based materials. It is worth noting that plumbene has already been widely grown on various substrates experimentally.

Functionalization induced quantum spin Hall to quantum anomalous Hall phase transition in monolayer jacutingaite.

As novel states of quantum matter, quantum spin Hall (QSH) and quantum anomalous Hall (QAH) states have attracted considerable interest in condensed matter and materials science communities. Recently, a monolayer of the naturally occurring mineral jacutingaite (Pt2HgSe3), was theoretically proposed to be a large-gap QSH insulator and experimentally confirmed. Here, based on first-principles calculations and tight-binding modeling, we demonstrate QSH to QAH phase transition in jacutingaite by chemical functionalization with chalogen. We show that two-dimensional (2D) chalogenated jacutingaite, Pt2HgSe3-X (X = S, Se, Te), is ferromagnetic with Curie temperature up to 316 K, and it exhibits QAH effect with chiral edge states inside a sizeable topological gap. The physical mechanism lies in the adsorption induced transformation of the original Kane-Mele model into an effective four-band model involving (px, py) orbitals on a hexagonal lattice, so that the topological gap size can be controlled by spin-orbit coupling strength of the chalogen (0.28 eV for Pt2HgSe3-Te). These results not only show the promise of functionalization in orbital-engineering of 2D functional structures, but also provide an ideal and practical platform for achieving exotic topological phases for dissipationless transport and quantum computing.

Recent progress in two-dimensional transition metal<?A3B2 ACK?>dichalcogenides

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) have been emerged as a new class of van der Waals materials since the successful isolation of graphene. The strong spin-orbit coupling (SOC) and two-dimensionality give rise to plenty of novel physics including metal-insulator transition, charge density wave (CDW), valleytronics, quantum spin Hall effect, and unconventional superconductivity, which make TMDCs an ideal platform to study the fundamental physics and potential applications. In this review, we firstly introduce the crystal structure of 2D TMDCs materials. Then, we summarize the recent progress in the synthesis, novel physical properties, and applications of 2D TMDCs materials. Finally, a summary and an outlook on the topological superconductivity in this field are presented. 2D TMDCs have a chemical formula of MX2 (M=W, Mo and X=Te, Se, S) with a layered crystal structure. Depending on the coordination environments of M, TMDCs can crystallize in a variety of polytypic structures such as 2 H , 1 T , 1 T ′, and T d phases. In the monolayer 2 H -TMDCs, the breaking of an in-plane mirror symmetry and the presence of the out-of-plane mirror symmetry lead to an Ising spin–orbit coupling (SOC), which serves as an effective out-of-plane field acting on the copper pair and pins the electron spins to out-of-plane directions. This is called Ising superconductivity, which has been observed in gated MoS2, monolayer NbSe2 and TaS2. However, due to the inversion symmetry in monolayer 1 T ′-TMDCs, the introduction of SOC makes them a class of large-gap quantum spin Hall insulators such as monolayer 1 T ′-WTe2. Therefore, if we could consecutively tailor the TMDCs’ structure from 2 H to T d phase, the long-sought topological superconductivity may be realized in one substance by incorporating superconductivity and quantum spin Hall effect together. To explore the extraordinary physics and nanodevice applications, we develop a universal molten-salt-assisted chemical vapor deposition (CVD) method to prepare atomically thin TMDCs, including high-quality 2D superconductors such as monolayer MoTe2 and NbSe2. With the powerful sample growth technique , we demonstrate for the first time that a consecutive structural phase transition from T d to 1 T ′ to 2 H polytype can be realized by increasing the Se concentration in Se-substituted MoTe2. More importantly, the Se-substitution is found to dramatically enhance the superconductivity of the MoTe2 thin film, which is interpreted as the introduction of two-band superconductivity. Furthermore, in bilayer 1 T d-MoTe2, we find that the in-plane upper critical field goes beyond the Pauli paramagnetic limit and shows an emergent two-fold symmetry, which is different from the isotropic in-plane upper critical field in 2 H -TMDCs. We show that this is a result of a new type of asymmetric SOC in 1 T d-TMDCs, which has expanded the well-known Ising SOC. The polytypic structures and strong SOC in 2D TMDCs have led to a variety of novel physics and applications. Recent theoretical works have already shown that 2D TMDCs can be a platform to search for topological superconductivity. With the further development of sample preparation, 2D TMDCs will play an important role in realization of topological quantum computation.

Quantum Spin Hall Insulators in Tin Films: Beyond Stanene

Large-gap quantum spin Hall (QSH) insulators were previously predicted in stanene and its derivatives. Beyond stanene that is the thinnest [Formula: see text]-Sn(111) film, we propose to explore QSH insulators in [Formula: see text]-Sn films with different crystallographic orientations. Our first-principles calculations reveal that the thickness-dependent band gap of [Formula: see text]-Sn(100) and [Formula: see text]-Sn(110) films does not show a monotonic decrease as typically expected by quantum confinement, but displays an oscillating change behavior, an indicative of topological quantum phase transition. While these films are normal insulators in the ultrathin limit, the QSH phase emerges above a critical film thickness of around 10 layers. Remarkably, the QSH insulators are obtainable within a wide thickness range and their energy gaps are sizable (even [Formula: see text][Formula: see text]0.1[Formula: see text]eV), which facilitates experimental realization of the high-temperature QSH effect.

Flexible quantum spin Hall insulator in O-functionalized GaSe monolayer

The quantum spin Hall (QSH) insulators possess potential applications in dissipationless spintronics. With the rapid development of flexible electronics, it is highly desirable to search or design high-performance QSH insulators with excellent flexibility and large bandgap, which is still a huge challenge. Here, using first-principles calculations, we report that surface oxygen functionalization can transform two-dimensional (2D) GaSe monolayer from a trivial insulator to a nontrivial topological insulator with superior stretchability. The fully O-functionalized GaSe monolayer, GaSeO, exhibits a sizable QSH gap of 178 meV, in which the topological nature is characterized by the nontrivial Z2 topological invariant and the topological edge states. The nontrivial band topology originates from the s-p band inversion in the crystal field. Remarkably, the GaSeO monolayer shows isotropic mechanical flexibility and can sustain large strains of up to 26%, beyond graphene and 2D flexible Ti2C. Furthermore, the QSH state of GaSeO is robust against small elastic strains. The discovery of this 2D flexible and large-gap QSH insulator opens up new opportunities for developing stretchable and low-power electronic devices.

Topological Rashba-like edge states in large-gap quantum spin Hall insulators

The search for large-band-gap quantum spin Hall (QSH) insulators, in which the dissipationless gapless edge states lie inside the bulk gap, is critical for their practical applications at room temperature. Based on first-principles calculations, we propose a sort of QSH insulator in a rectangular structure, i.e., AuSb, AuAs, and CuAs monolayers, which exhibits sizable bulk gaps up to 258 meV. These compounds host unexpected topological Rashba-like edge states, which exhibit strong dispersion with a nearly-free-electron feature. Such nontrivial edge states originate from spin-orbital coupling and an abrupt discontinuous potential across the surface. Furthermore, we argue that the AuSb monolayer can be epitaxially grown on a rutile $\mathrm{Ti}{\mathrm{O}}_{2}(110)$ surface. Importantly, the thermodynamic stability of AuSb is enhanced while the topological features are perfectly preserved due to the weak van der Waals interaction at the interface. Our findings provide promising large-gap QSH candidates with exotic topological Rashba-like edge states that are in favor of experimental realization at room temperature.

Discovery of a new quantum spin Hall phase in bilayer plumbene

Two-dimensional (2D) large-gap quantum spin Hall (QSH) insulator are imperative for achieving dissipationless transport devices. The bottleneck preventing applications from QSH phase, however, is lack of feasible 2D films experimentally. By using first-principles calculations, here we propose a new 2D topological phase in the bilayer plumbene. Its geometric stability is confirmed by phonon spectrum simulation and ab initio molecular dynamics simulation. We find that it can turn into a nontrivial QSH phase under tensile strain and its nontrivial gap is highly tunable by external strains. The origin behind QSH effect can be identified by s–px,y band inversion, topological invariant Z2, and helical edge states within the bulk gap. Also, a heterostructure composed of bilayer plumbene deposited on semiconducting MoS2 substrate remains topologically nontrivial properties with a sizable gap. These findings provide a promising platform to design a large-gap QSH insulator in Pb film, which show potential applications in spintronics devices.

Quantum spin Hall insulator with a large bandgap, Dirac fermions, and bilayer graphene analog

The search for room temperature quantum spin Hall insulators (QSHIs) based on widely available materials and a controlled manufacturing process is one of the major challenges of today's topological physics. We propose a new class of semiconductor systems based on multilayer broken-gap quantum wells, in which the QSHI gap reaches 60 meV and remains insensitive to temperature. Depending on their layer thicknesses and geometry, these novel structures also host a graphene-like phase and a bilayer graphene analog. Our theoretical results significantly extend the application potential of topological materials based on III-V semiconductors.

Robust large-gap quantum spin Hall insulators in methyl-functionalized III-Bi buckled honeycombs

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.

Unconventional band inversion and intrinsic quantum spin Hall effect in functionalized group-V binary films

Adequately understanding band inversion mechanism, one of the significant representations of topological phase, has substantial implications for design and regulation of topological insulators (TIs). Here, by identifying an unconventional band inversion, we propose an intrinsic quantum spin Hall (QSH) effect in iodinated group-V binary (ABI2) monolayers with a bulk gap as large as 0.409 eV, guaranteeing its viable application at room temperature. The nontrivial topological characters, which can be established by explicit demonstration of Z2 invariant and gapless helical edge states, are derived from the band inversion of antibonding states of px,y orbitals at the K point. Furthermore, the topological properties are tunable under strain engineering and external electric field, which supplies a route to manipulate the spin/charge conductance of edge states. These findings not only provide a new platform to better understand the underlying origin of QSH effect in functionalized group-V films, but also are highly desirable to design large-gap QSH insulators for practical applications in spintronics.

Tunability of the Quantum Spin Hall Effect in Bi(110) Films: Effects of Electric Field and Strain Engineering

The quantum spin Hall (QSH) effect is promising for achieving dissipationless transport devices due to their robust gapless edge states inside insulating bulk gap. However, the currently discussed QSH insulators usually suffer from ultrahigh vacuum or low temperature due to the small bulk gap, which limits their practical applications. Searching for large-gap QSH insulators is highly desirable. Here, the tunable QSH state of a Bi(110) films with a black phosphorus (BP) structure, which is robust against structural deformation and electric field, is explored by first-principles calculations. It is found that the two-monolayer BP-Bi(110) film obtains a tunable large bulk gap by strain engineering and its QSH effect shows a favorable robustness within a wide range of combinations of in-plane and out-of-plane strains, although a single in-plane compression or out-of-plane extension may restrict the topological phase due to the self-doping effect. More interestingly, in view of biaxial strain, two competing physics on band topology induced by bonding-antibonding and px,y-pz band inversions are obtained. Meanwhile, the QSH effect can be persevered under an electric field of up to 0.9 V/Å. Moreover, with appropriate in-plane strain engineering, a nontrivial topological phase in a four-monolayer BP-Bi(110) film is identified. Our findings suggest that these two-dimensional BP-Bi(110) films are ideal platforms of the QSH effect for low-power dissipation devices.

Two-dimensional arsenene oxide: A realistic large-gap quantum spin Hall insulator

Searching for two-dimensional (2D) realistic materials that are able to realize room-temperature quantum spin Hall effects is currently a growing field. Here, through ab initio calculations, we identify arsenene oxide, AsO, as an excellent candidate, which demonstrates high stability, flexibility, and tunable spin-orbit coupling gaps. In contrast to known pristine or functionalized arsenene, the maximum nontrivial bandgap of AsO reaches 89 meV and can be further enhanced to 130 meV under biaxial strain. By sandwiching 2D AsO between boron nitride sheets, we propose a quantum well in which the band topology of AsO is preserved with a sizeable bandgap. Considering that AsO having fully oxidized surfaces are naturally stable against surface oxidization and degradation, this functionality provides a viable strategy for designing topological quantum devices operating at room temperature.

Searching for large-gap quantum spin hall insulators: boron-nitride/(Pb, Sn)/α-Al2O3 sandwich structures.

Topological insulators hold great potential for efficient information processing and storage. Using density functional theory calculations, we predict that a honeycomb lead monolayer can be stabilized on an Al2O3 (0001) substrate to become topologically non-trivial with a sizeable band gap (∼0.27 eV). Furthermore, we propose to use a hexagonal boron-nitride (h-BN) monolayer as a protection for the topological states of Pb/Al2O3 and Sn/Al2O3. Our findings suggest new possibilities for designing and protecting two-dimensional TIs for practical applications.

Films based on group IV–V–VI elements for the design of a large-gap quantum spin Hall insulator with tunable Rashba splitting

Rashba spin–orbit coupling (SOC) in topological insulators (TIs) has recently attracted significant interest due to its potential applications in spintronics.

Two-dimensional rectangular tantalum carbide halides TaCX (X = Cl, Br, I): novel large-gap quantum spin Hall insulators

Quantum spin Hall (QSH) insulates exist in special two-dimensional (2D) semiconductors, possessing the quantized spin-Hall conductance that are topologically protected from backscattering. Based on the first-principles calculations, we predict a novel family of QSH insulators in 2D tantalum carbide halides TaCX (X = Cl, Br, and I) with unique rectangular lattice and large direct energy gaps. The mechanism for 2D QSH effect originates from an intrinsic d−d band inversion in the process of chemical bonding. Further, stain and intrinsic electric field can be used to tune the electronic structure and enhance the energy gap. TaCX nanoribbon, which has the single-Dirac-cone edge states crossing the bulk band gap, exhibits a linear dispersion with a high Fermi velocity comparable to that of graphene. These 2D materials with considerable nontrivial gaps promise great application potential in the new generation of dissipationless electronics and spintronics.