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

Topological insulators (TIs) are promising for achieving dissipationless transport devices due to the robust gapless states inside the insulating bulk gap. However, currently realized two-dimensional (2D) TIs, quantum spin Hall (QSH) insulators, suffer from ultrahigh vacuum and extremely low temperature. Thus, seeking for desirable QSH insulators with high feasibility of experimental preparation and large nontrivial gap is of great importance for wide applications in spintronics. On the basis of the first-principles calculations, we predict a novel family of 2D QSH insulators in transition-metal halide MX (M = Zr, Hf; X = Cl, Br, and I) monolayers, especially, which is the first case based on transition-metal halide-based QSH insulators. MX family has the large nontrivial gaps of 0.12-0.4 eV, comparable with bismuth (111) bilayer (0.2 eV), stanene (0.3 eV), and larger than ZrTe5 (0.1 eV) monolayers and graphene-based sandwiched heterstructures (30-70 meV). Their corresponding 3D bulk materials are weak topological insulators from stacking QSH layers, and some of bulk compounds have already been synthesized in experiment. The mechanism for 2D QSH effect in this system originates from a novel d-d band inversion, significantly different from conventional band inversion between s-p, p-p, or d-p orbitals. The realization of pure layered MX monolayers may be prepared by exfoliation from their 3D bulk phases, thus holding great promise for nanoscale device applications and stimulating further efforts on transition metal-based QSH materials.

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.

Quantum Spin Hall (QSH) insulators with a large topologically nontrivial bulk gap are crucial for future applications of the QSH effect. Among these, group III-V monolayers and their halides with chair structure (regular hexagonal framework, RHF) were widely studied. Using first-principles calculations, we propose a new structure model for the functionalized group III-V monolayers, which consist of rectangular GaBi-X2 (X=I, Br, Cl) monolayers with a distorted hexagonal framework (DHF). These structures have a much lower energy than the GaBi-X2 monolayers with chair structure. Remarkably, the DHF GaBi-X2 monolayers are all QSH insulators, which exhibit sizeable nontrivial band gaps ranging from 0.17 eV to 0.39 eV. Those band gaps can be widely tuned by applying different spin-orbit coupling (SOC) strengths, resulting in a distorted Dirac cone.

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.

Spin‐polarized conducting edge currents counterpropagate in quantum spin Hall (QSH) insulators and are protected against disorder‐driven localizations by the time‐reversal symmetry. Using these spin‐currents for device applications requires materials with a large bandgap and fast switchable QSH states. By means of in‐depth first‐principles calculations, this study demonstrates the large bandgap and fast switchable QSH state in a newly introduced 2D material family with 1T′‐MGe2Z4 (M = Mo or W and Z = P or As). These Ge‐based compounds show superior properties with respect to other members of the same family. For the WGe2As4 monolayer it can stabilize the 1T′‐phase, while for the other members of the family, this study needs an appropriate strain. The dynamically stable 1T′‐MGe2Z4 monolayers have a large energy gap up to 237 meV for WGe2As4. These materials undergo a phase transition from a QSH insulator to a trivial insulator with a Rashba‐like spin splitting under the influence of an out‐of‐plane electric field, demonstrating a fast tunability of the bandgap and its band topology for the Ge‐based compounds. Fast topological phase switching in a large gap 1T′‐MGe2Z4 QSH insulators have potential applications in low‐power devices, quantum computation, and quantum communication.

Quantum spin Hall (QSH) insulator with large gap is highly desirable for potential spintronics application. Here we realize electrically tunable QSH insulator with large gap in van der Waals heterobilayer of monolayer transition metal dichalcogenide (TMD) and hexagonal boron arsenide (BAs), in particular the WSe2/BAs heterobilayer. When the type II band alignment gets inverted in an electric field, the hybridization by interlayer hopping between the spin-valley locked valence band edges in TMD and the BAs conduction band edges leads to a stacking-configuration dependent topological band inversion. In the non-interacting limit, the double spin degeneracy of BAs leaves an un-hybridized conduction band inside the gap, so the heterobilayer is a spin-valley locked metal instead of a QSH insulator. With the Coulomb interaction accounted in the double-layer geometry, the interaction with the hybridization induced electric dipole shifts this un-hybridized conduction band upwards in energy, giving rise to a sizable global QSH gap. Consequently, this heterobilayer provides a platform for engineering electrically tunable QSH insulator with sizable band gap. In the long-period moiré pattern with the spatial variation of local stacking-configurations, the competition between Coulomb interaction and interlayer hopping leads to superstructures of QSH insulators and excitonic insulators.

Achieving combination of spin and valley polarized states with topological insulating phase is pregnant to promote the fantastic integration of topological physics, spintronics and valleytronics. In this work, a spin-valley-coupled quantum spin Hall insulator (svc-QSHI) is predicted in Janus monolayer CSb1.5Bi1.5 with dynamic, mechanical and thermal stabilities. Calculated results show that the CSb1.5Bi1.5 is a direct band gap semiconductor with and without spin–orbit coupling, and the conduction-band minimum and valence-band maximum are at valley point. The inequivalent valleys have opposite Berry curvature and spin moment, which can produce a spin-valley Hall effect. In the center of Brillouin zone, a Rashba-type spin splitting can be observed due to missing horizontal mirror symmetry. The topological characteristic of CSb1.5Bi1.5 is confirmed by the Z 2 invariant and topological protected conducting helical edge states. Moreover, the CSb1.5Bi1.5 shows unique Rashba-splitting edge states. Both energy band gap and spin-splitting at the valley point are larger than the thermal energy of room temperature (25 meV) with generalized gradient approximation level, which is very important at room temperature for device applications. It is proved that the spin-valley-coupling and nontrivial quantum spin Hall state are robust again biaxial strain. Our work may provide a new platform to achieve integration of topological physics, spintronics and valleytronics.

Searching for realistic materials able to realize room-temperature quantum spin Hall (QSH) effects is currently a growing field, especially when compatibility with the current group-IV electronics industry is required. Here we predict, through first-principles calculations, a new class of QSH phases in flattened germanene and stanene functionalized with X atoms (f-GeX2 and f-SnX2; X = H, F, Cl, Br, I) with a bulk gap as large as 0.56 eV, that can be tuned efficiently under mechanical strain. More interestingly, different from the normal band order in buckled germanane and stanane, the structural flatness leads to an inverted band order without spin-orbit coupling (SOC), whereas the SOC only opens the band gap. We also find that the characteristics of edge states, such as the Fermi velocity, are enhanced greatly by edge modification. When these films are deposited on a BN substrate, a nontrivial QSH state is preserved with a Dirac cone lying within the nontrivial band gap. These findings provide a promising platform for future realistic applications of the QSH effect at room temperature in two-dimensional group-IV films.

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 study the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary. We calculate various edge properties in an N\to\inftyN→∞ limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as ``fractional’’ degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the quantum spin Hall state but with the full SU(2)SU(2) spin rotation symmetry, which cannot be realized if the bulk is gapped.

Layered transition-metal dinitrides are the recently proposed cousins of transition-metal dichalcogenides, which exhibit extraordinary electronic and magnetic properties. In this work, through first-principles calculations, we have identified the lowest energy geometry of the ReN2 nanosheet, which is a bilayer hexagonal structure (BHS) akin to the MoN2 system. Such a BHS-ReN2 nanosheet possesses robust dynamical, thermal, and mechanical stabilities at the free-standing state. Interestingly, without spin–orbit coupling (soc), this BHS-ReN2 system exhibits a semimetallic feature with a d-character Dirac cone, for which a band gap is opened at the Dirac point when the soc effect is taken into account. As a result, the BHS-ReN2 nanosheet becomes a quantum spin Hall (QSH) insulator in the presence of soc, whose bulk gap reaches up to 384 meV, sufficiently large for the room-temperature QSH effect. The nontrivial topological feature is characterized by a Z2 = 1 invariant and a pair of topologically protected ed...

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.

Chapter 5 - Quantum Spin Hall State in HgTe

Topologically protected edge states of 2D quantum spin Hall (QSH) insulators have paved the way for dissipationless transport. In this regard, one of the key challenges is to find suitable QSH insulators with large bandgaps. Group IV analogues of graphene such as silicene, germanene, stanene, plumbene etc. are promising materials for QSH insulators. This is because their high spin–orbit coupling (SOC) and large bandgap opening may be possible by chemically decorating these group IV graphene analogues. However, finding suitable chemical groups for such decoration has always been a demanding task. In this work, we investigate the performance of a plumbene monolayer with –CX3 (X = H, F, Cl) chemical decoration and report very large bandgaps in the range of 0.8414 eV to 0.9818 eV with spin–orbit coupling, which is much higher compared to most other topological insulators and realizable at room temperature. The topological invariants of the samples are calculated to confirm their topologically nontrivial properties. The existence of edge states and topological nontrivial property are illustrated by investigating PbCX3 nanoribbons with zigzag edges. Lastly, the structural and electronic stability of the topological materials against strain are demonstrated to extend the scope of using these materials. Our findings suggest that these derivatives are promising materials for spintronic and future high performance nanoelectronic devices.

The interplay between non-Hermiticity and topology opens an exciting avenue for engineering novel topological matter with unprecedented properties. While previous studies have mainly focused on one-dimensional systems or Chern insulators, here we investigate topological phase transitions to/from quantum spin Hall (QSH) insulators driven by non-Hermiticity. We show that a trivial to QSH insulator phase transition can be induced by solely varying non-Hermitian terms, and there exists exceptional edge arcs in QSH phases. We establish two topological invariants for characterizing the non-Hermitian phase transitions: i) with time-reversal symmetry, the biorthogonal $\mathbb{Z}_2$ invariant based on non-Hermitian Wilson loops, and ii) without time-reversal symmetry, a biorthogonal spin Chern number through biorthogonal decompositions of the Bloch bundle of the occupied bands. These topological invariants can be applied to a wide class of non-Hermitian topological phases beyond Chern classes, and provides a powerful tool for exploring novel non-Hermitian topological matter and their device applications.