Spin-valley Hall Research Articles

Valley selections and control of topological phases by bicircular laser field in transition-metal dichalcogenides

The energy spectra of transition metal dichalcogenides are influenced by three orbitals, forming a three-band model with strong spin-orbit interaction. Analyzing these bands through a two-band projection suffices for exploring electronic and optical properties. We examine topological phases and the spin-valley Hall effect, derived from spin-valley Chern numbers. Spin-orbit interaction breaks inversion symmetry but preserves time-reversal symmetry, resulting in non-zero spin-valley-dependent Hall conductivities, crucial for both spin and valley Hall effects. Interestingly, direct optical manipulation of the valley degree of freedom can be achieved using a trefoil field generated by a bicircular field. Selectable valley conductivity occurs when the field orientation matches the lattice symmetry, leading to a quantum anomalous Hall effect without magnetization. This approach suggests the potential for valley selection via field orientation, with applications in valleytronics and spintronics devices, enabling qubit encoding.

Optical control of berry curvature in gated WSe2 bilayers

Abstract Unlike single layers of 2H transition metal dichalcogenides (TMDCs), bilayers of 2H TMDCs maintain inversion and time reversal (TR) symmetries, resulting in a vanishing Berry curvature ( Ω ( k ) ∼ 0 ) that inhibits various potential transport phenomena. A nonzero Berry curvature ( Ω ( k ) ≠ 0 ) is imperative for the occurrence of several unconventional transport phenomena, including the anomalous Hall effect and the anomalous Nernst effect. To overcome this limitation, we break these symmetries in bilayer TMDCs using electrostatic gating and circularly polarized light as external means. For non-gated WSe2 bilayers, circularly polarized light breaks TR symmetry, creating a finite Berry curvature signal in both conduction and valence bands, controllable by light intensity and its polarity. In gated WSe2 bilayers, where inversion symmetry is also broken, we observe a sign reversal in Berry curvature within the conduction bands, the extent of which depends on the relative strengths of the electric gating and light intensity. Overall, under finite bias and light intensity, the 2H bilayers of WSe2 exhibits finite spin Hall, valley Hall, and anomalous Hall conductivities, which depend on the strengths of the applied perturbations.

Transport properties of Hall-type quantum states in disordered bismuthene

Bismuthene, an inherently hexagonal structure characterized by a huge bulk gap, offers a versatile platform for investigating the electronic transport of various topological quantum states. Using nonequilibrium Green’s function method and Landauer–Büttiker formula, we thoroughly investigate the transport properties of various Hall-type quantum states, including quantum spin Hall (QSH) edge states, quantum valley Hall kink (QVHK) states, and quantum spin–valley Hall kink (QSVHK) states, in the presence of various disorders. Based on the exotic transport features, a spin–valley filter, capable of generating a highly spin- and valley-polarized current, is proposed. The valley index and the spin index of the filtered QSVHK state are determined by the staggered potential and the intrinsic spin–orbit coupling, respectively. The efficiency of the spin–valley filter is supported by the spacial current distribution, the valley-resolved conductance, and the spin-resolved conductance. Compared with a sandwich structure for QSVHK, our proposed spin–valley filter can work with a much smaller size and is more accessible in the experiment.

Emergence of topological and spin valley hallmarks in buckled Xene bilayers

A subclass of two-dimensional materials with honeycomb structure, namely buckled Xene monolayers, are efficient for topological applications due to varying degrees of buckling in their lattice structure and have received a significant revival of interest in the last few years. However, to-date, less attention, as compared to, planer Xene bilayers has been assigned to the buckled Xene bilayers. The buckled Xene bilayers can offer a unique platform to study transport properties in bilayer systems. In this study, we explore the unknown topological behaviour of buckled Xene bilayers by exploiting the space inversion and time-reversal (TR) symmetries in these solids. In order to exploit the underline symmetries, we use light irradiation, layered antiferromagnetic exchange magnetization and vertical electric field as an external means. By mixing these three ingredients in a proper way, we achieve various topological phases in bilayers of buckled Xene solids, including TR-broken quantum spin Hall insulator, photo-induced quantum Hall insulator, photo-induced spin-polarized quantum Hall insulator, and quantum spin-valley Hall insulator. Furthermore, we establish a topological phase diagram and identify a topological domain wall in buckled Xene bilayers when subjected to circularly polarized light and gated voltage, which opens up possibilities for the propagation of perfectly valley-polarized channels.

Coexistence of Rashba effect and spin–valley coupling in TiX2 (X = Te, S, and Se) based heterostructures

Spin–orbit coupling (SOC) combined with broken inversion symmetry plays a key role in inducing Rashba effect. The combined spontaneous polarization and Rashba effect enables controlling a material's spin degrees of freedom electrically. In this work, we investigated an electronic band structure for several combinations of TiX2 monolayers (X = Te, S, and Se): TiTe2/TiSe2, TiTe2/TiS2, and TiSe2/TiS2. Based on the observed orbital hybridization between the different monolayers in these heterostructures (HSs), we conclude that the most significant Rashba splitting occurs in TiSe2/TiS2. Subsequently, we used fluorine (F) as an adatom over the surface of TiSe2/TiS2 at hollow and top sites of the surface to enhance the Rashba intensity, as the F adatom induces polarization due to the difference in charge distribution. Furthermore, by increasing the number of F atoms on the surface, we reinforced the band splitting, i.e., we observe Rashba splitting accompanied by Zeeman splitting at the valence-band edge states. Berry curvatures at K and K′ with equal and opposite nature confirm the existence of valley polarization. The computationally observed properties suggest that these HSs are promising candidates for spin–valley Hall effect devices and other spintronic applications.

Semiconductor and topological phases in lateral heterostructures constructed from germanene and AsSb monolayers.

Two-dimensional (2D) heterostructures have attracted a lot of attention due to their novel properties induced by the synergistic effects of the constituent building blocks. In this work, new lateral heterostructures (LHSs) formed by stitching germanene and AsSb monolayers are investigated. First-principles calculations assert the semimetal and semiconductor characters of 2D germanene and AsSb, respectively. The non-magnetic nature is preserved by forming LHSs along the armchair direction, where the band gap of the germanene monolayer can be increased to 0.87 eV. Meanwhile, magnetism may emerge in the zigzag-interline LHSs depending on the chemical composition. Such that, total magnetic moments up to 0.49 μB can be obtained, being produced mainly at the interfaces. The calculated band structures show either topological gap or gapless protected interface states, with quantum spin-valley Hall effects and Weyl semimetal characters. The results introduce new lateral heterostructures with novel electronic and magnetic properties, which can be controlled by the interline formation.

Robust Subthermionic Topological Transistor Action via Antiferromagnetic Exchange

The topological quantum field-effect transition in buckled two-dimensional-Xenes can potentially enable subthermionic transistor operation coupled with a dissipationless on-state conduction. We investigate realistic device structures that exploit the quantum field-effect transition between the dissipationless topological phase and the band-insulator phase. We find that the previously considered dual-gate structure is disadvantageous, leading to a near doubling of the subthreshold swing. However, we identify a single-gate strategy capable of overcoming the thermionic limit at the cost of sacrificing the dissipationless on-state conduction. By introducing an out-of-plane antiferromagnetic exchange in the material via proximity coupling, we exploit transitions between the quantum spin-valley Hall and the spin quantum anomalous Hall phase, which restore the topological robustness of the on state while simultaneously surpassing the thermionic limit. Our work thus outlines a realistic pathway to topological transistors that can overcome Boltzmann's tyranny while preserving topological robustness.

Valley-polarized hyperbolic exciton polaritons in few-layer two-dimensional semiconductors at visible frequencies

Polaritons are quasiparticles describing the coupling between light and matter. In two-dimensional materials, polaritonic phenomena are abundant and unique, owing to their low dimensionality and the extraordinary properties of the supported quasiparticles. In this work, we predict the existence of hyperbolic exciton polaritons (HEPs) in few-layer transition-metal dichalcogenides (TMDs) at visible frequencies. We show that hyperbolicity can be induced in the TMD under certain conditions owing to the resonant behavior of the supported excitons, leading to the existence of HEPs. We derive the HEPs' dispersion relation under these conditions and analyze their confinement and loss properties, incorporating nonlocal corrections stemming from the high momentum of the modes. In addition, we show that owing to the valley properties of TMDs, the HEPs are coupled to the valley degree of freedom, leading to a hyperbolic spin-valley Hall effect. Such highly confined and valley-polarized HEPs provide opportunities to control strong light-matter interaction at the atomic scale.

Extrinsic spin-valley Hall effect and spin-relaxation anisotropy in magnetized and strained graphene

The implementation of the quantum spin-valley Hall effect is a critical challenge for the spintronics and valleytronic experimentalists because it requires breaking both time-reversal symmetry ($\mathcal{T}$) and spatial inversion symmetry ($\mathcal{P}$) while preserving the joint symmetry $\mathcal{O}=\mathcal{T}\mathcal{P}$. Here, we demonstrate an extrinsic spin-valley Hall effect by the magnetic field and temperature modulation of the nonlocal resistance in a Hall bar device consisting of magnetized and strained graphene. Besides, we achieve a striking crossover from positive to negative nonlocal magnetoresistance owing to the magnetic field dependence of spin-valley relaxation instead of the usual Hanle spin precession. Moreover, we microscopically derive a large and tunable spin-relaxation anisotropy of the magnetized graphene within the Born-Markov and the Weiss-field approximations. Our findings offer fascinating opportunities to manipulate the spin and valley degrees of freedom and design novel electronic devices.

Rashba Splitting and Electronic Valley Characteristics of Janus Sb and Bi Topological Monolayers.

Janus Sb and Bi monolayers as a new class of 2D topological insulator materials, which could be fulfilled by asymmetrical functionalizations with methyl or hydroxyl, are demonstrated by first-principles spin–orbit coupling (SOC) electronic structure calculations to conflate nontrivial topology, Rashba splitting and valley-contrast circular dichroism. Cohesive energies and phonon frequency dispersion spectra indicate that all Janus Sb and Bi monolayers possess a structural stability in energetic statics but represent virtual acoustic phonon vibrations of the hydrogen atoms passivating on monolayer surfaces. Band structures of Janus Sb and Bi monolayers and their nanoribbons demonstrate they are nontrivial topological insulators. Rashba spin splitting at G point in Brillouin zone of Janus Bi monolayers arises from the strong SOC px and py orbitals of Bi bonding atoms together with the internal out-of-plane electric field caused by asymmetrical functionalization. Janus Sb and Bi monolayers render direct and indirect giant bandgaps, respectively, which are derived from the strong SOC px and py orbitals at band-valley Brillouin points K and K′ where valley-selective circular dichroism of spin valley Hall insulators is also exhibited.

Jacutingaite family: An efficient platform for coexistence of spin valley Hall effects, valley spin-valve realization, and layer spin crossover

Jacutingaite family, a family of naturally occurring exfoliable minerals (${\mathrm{Pt}}_{2}{\mathrm{HgSe}}_{3}$ and ${\mathrm{Pd}}_{2}{\mathrm{HgSe}}_{3}$) discovered in Brazil, is recently predicted to be the very first large-gap Kane-Mele quantum spin Hall insulators. However, yet to date, the door is locked for realizing versatile spin-valley based phenomena due to inversion symmetry in this family. By exploiting the inversion symmetry using different strategies such as placing the jacutingaite family in the vertical electric field or growing its composites with some suitable well-matched systems, we reveal several promising valley spin based phenomena in the jacutingaite family. Overall, we achieve the coupled spin valley Hall effect, valley spin-valve effect, Rashba spin splitting around the low-symmetric $M$ point, layer crossover accompanied by spin crossover, and selective-excitation of carriers from opposite valleys in this family. More interestingly, swapping of the induced spin splittings, Berry curvatures, and the spin texture between the two valleys occur upon the reversal of electric field from ${E}_{z}>0$ to ${E}_{z}<0$ without destroying the ${\mathcal{Z}}_{2}$ topological hallmarks. Meanwhile, considerable hexagonal trigonal warping effects around the ${K}_{+}$ and ${K}_{\ensuremath{-}}$ valleys are realized. Furthermore, by applying vertical electric field through interfacial coupling with ferroelectric ${\mathrm{III}}_{2}\ensuremath{-}{\mathrm{VI}}_{3}$ film, valley contrasting Berry curvature in the ${\mathrm{Pt}}_{2}{\mathrm{HgSe}}_{3}$ layer with a larger spin splitting in the lower conduction band $(\ensuremath{\sim}188\phantom{\rule{0.16em}{0ex}}\mathrm{meV})$ is achieved in the $+P$ polarization state. By inverting the polarization state from $+P$ to $\ensuremath{-}P$, the Fermi level shifts down into the valence band of the ${\mathrm{Pt}}_{2}{\mathrm{HgSe}}_{3}$ layer $(\ensuremath{\sim}82\phantom{\rule{0.16em}{0ex}}\mathrm{meV})$ revealing a hole doping in the ${\mathrm{Pt}}_{2}{\mathrm{HgSe}}_{3}$ layer. This could establish an effective mechanism to control doping levels in the ${\mathrm{Pt}}_{2}{\mathrm{HgSe}}_{3}$ layer as desirable for achieving superconductivity at finite doping in the jacutingaite family. Our paper provides a path towards integrating valleytronics and spintronics in multivalley materials with broken inversion symmetry.

Spin-valley-coupled quantum spin Hall insulator with topological Rashba-splitting edge states in Janus monolayer CSb1.5Bi1.5

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.

Spin-valley polarized edge states and quantum anomalous Hall states controlled by side potential in two-dimensional honeycomb lattices

Based on the tight-binding formalism, we study the effect of side potential on the spin- and valley-related electronic property of $2\mathrm{D}$ honeycomb lattices with intrinsic spin-orbit coupling, such as silicene and germanene. The side potential is composed of potential field and exchange field applied on the boundaries of the zigzag nanoribbon. It is found that the side potential could greatly affect the helical edge states with different spin indices and the spin and valley are locked to each other. By adjusting the side potential and ribbon width, the system shows a quantum spin-valley Hall effect, valley-polarized quantum spin Hall effect, and spin-polarized quantum anomalous Hall effect. Due to the side potential and the coupling of edge states in the narrow ribbon, a band gap could be opened for specific spin and the time-reversal symmetry could be broken, leading to a spin-polarized quantum anomalous Hall phase. Various kinds of spin-valley polarized edge states are formed at the two boundaries. Furthermore, the spin-valley polarized insulating states can be used to realize a perfect spin-valley switch.

Quantum anomalous Hall octet driven by orbital magnetism in bilayer graphene.

The quantum anomalous Hall (QAH) effect-a macroscopic manifestation of chiral band topology at zero magnetic field-has been experimentally realized only by the magnetic doping of topological insulators1-3 and the delicate design of moiré heterostructures4-8. However, the seemingly simple bilayer graphene without magnetic doping or moiré engineering has long been predicted to host competing ordered states with QAH effects9-11. Here we explore states in bilayer graphene with a conductance of 2 e2 h-1 (where e is the electronic charge and h is Planck's constant) that not only survive down to anomalously small magnetic fields and up to temperatures of fivekelvin but also exhibit magnetic hysteresis. Together, the experimental signatures provide compelling evidence for orbital-magnetism-driven QAH behaviour that is tunable via electric and magnetic fields as well as carrier sign. The observed octet of QAH phases is distinct from previous observations owing to its peculiar ferrimagnetic and ferrielectric order that is characterized by quantized anomalous charge, spin, valley and spin-valley Hall behaviour9.

Quantum Spin-Valley Hall Kink States: From Concept to Materials Design.

We propose a general and tunable platform to realize high-density arrays of quantum spin-valley Hall kink (QSVHK) states with spin-valley-momentum locking based on a two-dimensional hexagonal topological insulator. Through the analysis of Berry curvature and topological charge, the QSVHK states are found to be topologically protected by the valley-inversion and time-reversal symmetries. Remarkably, the conductance of QSVHK states remains quantized against both nonmagnetic short- and long-range and magnetic long-range disorder, verified by the Green-function calculations. Based on first-principles results and our fabricated samples, we show that QSVHK states, protected with a gap up to 287meV, can be realized in bismuthene by alloy engineering, surface functionalization, or electric field, supporting nonvolatile applications of spin-valley filters, valves, and waveguides even at room temperature.

Orbitronics: Orbital currents in solids

In solids, electronic Bloch states are formed by atomic orbitals. While it is natural to expect that orbital composition and information about Bloch states can be manipulated and transported, in analogy to the spin degree of freedom extensively studied in past decades, it has been assumed that orbital quenching by the crystal field prevents significant dynamics of orbital degrees of freedom. However, recent studies reveal that an orbital current, given by the flow of electrons with a finite orbital angular momentum, can be electrically generated and transported in wide classes of materials despite the effect of orbital quenching in the ground state. Orbital currents also play a fundamental role in the mechanisms of other transport phenomena such as spin Hall effect and valley Hall effect. Most importantly, it has been proposed that orbital currents can be used to induce magnetization dynamics, which is one of the most pivotal and explored aspects of magnetism. Here, we give an overview of recent progress and the current status of research on orbital currents. We review proposed physical mechanisms for generating orbital currents and discuss candidate materials where orbital currents are manifest. We review recent experiments on orbital current generation and transport and discuss various experimental methods to quantify this elusive object at the heart of orbitronics —an area which exploits the orbital degree of freedom as an information carrier in solid-state devices.

Optically Reconfigurable Spin-Valley Hall Effect of Light in Coupled Nonlinear Ring Resonator Lattice.

Scattering immune propagation of light in topological photonic systems may revolutionize the design of integrated photonic circuits for information processing and communications. In optics, various photonic topological circuits have been developed, which were based on classical emulation of either quantum spin Hall effect or quantum valley Hall effect. On the other hand, the combination of both the valley and spin degrees of freedom can lead to a new kind of topological transport phenomenon, dubbed spin-valley Hall effect (SVHE), which can further expand the number of topologically protected edge channels and would be useful for information multiplexing. However, it is challenging to realize SVHE in most known material platforms, due to the requirement of breaking both the (pseudo)fermionic time-reversal (T) and parity symmetries (P) individually, but leaving the combined symmetry S≡TP intact. Here, we propose an experimentally feasible platform to realize SVHE for light, based on coupled ring resonators mediated by optical Kerr nonlinearity. Thanks to the inherent flexibility of cross-mode modulation, the coupling between the probe light can be engineered in a controllable way such that spin-dependent staggered sublattice potential emerges in the effective Hamiltonian. With delicate yet experimentally feasible pump conditions, we show the existence of spin-valley Hall-induced topological edge states. We further demonstrate that both degrees of freedom, i.e., spin and valley, can be manipulated simultaneously in a reconfigurable manner to realize spin-valley photonics, doubling the degrees of freedom for enhancing the information capacity in optical communication systems.

Optically induced topological spin-valley Hall effect for exciton polaritons

We consider exciton-polaritons in a honeycomb lattice of micropillars subjected to circularly polarized (${\sigma_\pm}$) incoherent pumps, which are arranged to form two domains in the lattice. We predict that the nonlinear interaction between the polaritons and the reservoir excitons gives rise to the topological valley Hall effect where in each valley two counterpropagating helical edge modes appear. Under a resonant pump, ${\sigma_\pm}$ polaritons propagate in different directions without being reflected around bends. The polaritons propagating along the interface have extremely high effective lifetimes and show fair robustness against disorder. This paves the way for robust exciton-polariton spin separating and transporting channels in which polaritons attain and maintain high degrees of spin polarization, even in the presence of spin relaxation.

Transport properties of the organic Dirac electron system α−(BEDT−TSeF)2I3

Motivated by the insulating behavior of $\alpha$-(BEDT-TSeF)$_2$I$_3$ at low temperatures ($T$'s), we first performed first-principles calculations based on the crystal structural data at 30 K under ambient pressure, and we constructed a two-dimensional effective model using maximally localized Wannier functions. As possible causes of the insulating behavior, we studied the effects of the on-site Coulomb interaction $U$ and spin-orbit interaction (SOI) by investigating the electronic state and the transport coefficient using the Hartree approximation and the $T$-matrix approximation. The calculations at a finite $T$ demonstrated that a spin-ordered massive Dirac electron (SMD) appeared due to the on-site Coulomb interaction. We had an interest in the anomalous competitive effect with $U$ and SOI when the SMD phase is present in $\alpha$-(BETS)$_2$I$_3$, and we investigated these contributions to the electronic state and conductivity. The SMD is not a conventional spin order, but it exhibits the spin-valley Hall effect. Direct current resistivity in the presence of a spin order gap increased divergently and exhibited negative magnetoresistance in the low $T$ region with decreasing $T$. The charge density hardly changed below and above the $T$ at which this insulating behavior appeared. However, when considering the SOI alone, the state changed to a topological insulator phase, and the electrical resistivity is saturated by edge conduction at quite low $T$. When considering both the SMD and the SOI, the spin order gap was suppressed by the SOI, and gaps with different sizes opened in the left and right Dirac cones. This phase transition leads to distinct changes in microwave conductivity, such as a discontinuous jump and a peak structure.

Spin\u2013valley Hall phenomena driven by Van Hove singularities in blistered graphene

Using first-principles calculations, we investigate the possibility of realizing valley Hall effects (VHE) in blistered graphene sheets. We show that the Van Hove singularities (VHS) induced by structural deformations can give rise to interesting spin–valley Hall phenomena. The broken degeneracy of spin degree of freedom results in spin-filtered VH states and the valley conductivity have a Hall plateau of ±e2/2h, while the blistered structures with time-reversal symmetry show the VHE with the opposite sign of sigma _{xy}^{K/K^{prime}} (e2/2h) in the two valleys. Remarkably, these results show that the distinguishable chiral valley pseudospin state can occur even in the presence of VHS induced spin splitting. The robust chiral spin–momentum textures in both massless and massive Dirac cones of the blistered systems indicate significant suppression of carrier back-scattering. Our study provides a different approach to realize spin-filtered and spin-valley contrasting Hall effects in graphene-based devices without any external field.