Spin Valley Research Articles

Valley- and spin-polarized broken-symmetry states of interacting electrons in gatedMoS2quantum dots

Understanding strongly interacting electrons enables the design of materials, nanostructures and devices. Developing this understanding relies on the ability to tune and control electron-electron interactions by, e.g., confining electrons to atomically thin layers of 2D crystals with reduced screening. The interplay of strong interactions on a hexagonal lattice with two nonequivalent valleys, topological moments, and the Ising-like spin-orbit interaction gives rise to a variety of phases of matter corresponding to valley and spin polarized broken symmetry states. In this work we describe a highly tunable strongly interacting system of electrons laterally confined to monolayer transition metal dichalcogenide MoS$_2$ by metalic gates. We predict the existence of valley and spin polarized broken symmetry states tunable by the parabolic confining potential using exact diagonalization techniques for up to $N=6$ electrons. We find that the ground state is formed by one of two phases, either both spin and valley polarized or valley unpolarised but spin intervalley antiferromagnetic, which compete as a function of electronic shell spacing. This finding can be traced back to the combined effect of Ising-like spin-orbit coupling and weak intervalley exchange interaction. These results provide an explanation for interaction-driven symmetry-breaking effects in valley systems and highlight the important role of electron-electron interactions for designing valleytronic devices.

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.

Valley interference and spin exchange at the atomic scale in silicon

Tunneling is a fundamental quantum process with no classical equivalent, which can compete with Coulomb interactions to give rise to complex phenomena. Phosphorus dopants in silicon can be placed with atomic precision to address the different regimes arising from this competition. However, they exploit wavefunctions relying on crystal band symmetries, which tunneling interactions are inherently sensitive to. Here we directly image lattice-aperiodic valley interference between coupled atoms in silicon using scanning tunneling microscopy. Our atomistic analysis unveils the role of envelope anisotropy, valley interference and dopant placement on the Heisenberg spin exchange interaction. We find that the exchange can become immune to valley interference by engineering in-plane dopant placement along specific crystallographic directions. A vacuum-like behaviour is recovered, where the exchange is maximised to the overlap between the donor orbitals, and pair-to-pair variations limited to a factor of less than 10 considering the accuracy in dopant positioning. This robustness remains over a large range of distances, from the strongly Coulomb interacting regime relevant for high-fidelity quantum computation to strongly coupled donor arrays of interest for quantum simulation in silicon.

Spin-valley locked topological edge states in a staggered chiral photonic crystal

Engineering pseudo-spin and valley degrees of freedom using quantum spin Hall and valley Hall effects has opened up remarkable possibilities for highly efficient and robust signal transport in time-reversal invariant photonic systems. Here we present a spin-valley locked photonic crystal that has distinct signs of chirality of sublattices in a honeycomb unit cell. We show that the photonic crystal has an insulating bulk dispersion and sublattice-dependent spin-valley coupled gapless edge states by exploiting a coupled dipole method and demonstrate valley-selective propagation by controlling spin state of an external dipole source. The interplay between spin, valley and sublattice shows a judicious way for one-way photon transport by using multiple degrees of freedom.

Band-Gap Sensitived Seebeck Effect in Heavy Group-IV Monolayers

We have systematically investigated the spin- and valley-dependent Seebeck effect in irradiated heavy group-IV monolayers including silicene, germanene, and stanene by means of semi-classical Boltzmann equation in diffusive regime. Due to the interplay of strong intrinsic spin-orbit coupling, perpendicular electric field, and off-resonant light field, the temperature-driven spin and valley conductivity can be controllable effectively. Except for numerical results, the amplitude of Seebeck coefficient is analyzed and found to be in direct proportion to the band gap at high temperature. It supplies a flexible method to modulate the Seebeck effect. In addition, we have compared the thermoelectric transport properties of different group-IV materials and found that the figure of merit shows great enhancement from silicene to stanene. These findings are excepted to provide a platform for the heavy group-IV materials in future spin–valley thermal and energy-saving devices.

Valley depolarization in downconversion and upconversion emission of monolayer WS2 at room temperature

Abstract Benefiting from strong photon–exciton and phonon–exciton interactions in atomic thickness, transition metal dichalcogenides (TMDCs) are viewed as one promising platform for exploring elementary excitonic photoluminescence (PL) and intrinsic spin–valley properties at the monolayer limit. Despite well-studied Stokes downconversion (DC) PL, the anti-Stokes upconversion (UC) PL has been recently reported in TMDC monolayers, which mainly focus on UC mechanisms while detailed valley-related dynamical processes are unwittingly less concerned. Here, we carry out an in-depth investigation on both DC and UC emission features of monolayer WS2 at room temperature, where UC PL persists with energy gain up to 190 meV. The PL excitation and power-dependent experiments clearly distinguish the origins of DC PL and UC PL, which refer to saturated absorption and phonon-assisted transition from charged trions to neutral A-excitons. And contrast valley properties are observed in DC and UC scenarios with polarization-resolved PL and pump–probe measurements. According to the experimental facts, phenomenological dynamical DC and UC scenarios are modeled with intervalley depolarization taken into consideration, in which intermediates from spontaneous intervalley depolarization account for the observed emission and valley properties. This work can help understand the light–matter interactions and valley properties in monolayer TMDCs.

Coupled spin and valley polarization in monolayer HfN2 and valley-contrasting physics at the HfN2−WSe2 interface

Despite extensive studies on coupled spin and valley physics, occurrence of these properties is currently limited to transition-metal dichalcogenides (TMDCs) and graphene. Therefore, exploration of materials beyond TMDCs and graphene is necessary for a further advancement in valleytronics. In this work, the $\mathrm{Hf}{\mathrm{N}}_{2}$ monolayer, a theoretically reported semiconductor having a direct band gap has been investigated in-depth for its applications in valleytronics and spintronics. It exhibits a large valley spin splitting (VSS) \ensuremath{\sim}314 meV at the conduction band (CB) due to strong spin-orbit coupling (SOC). Such a large VSS at the CB is unique and comparable to that of tungsten-based dichalcogenide monolayers at its valence band (VB). The spin splitting is nearly insensitive to small in-plane strain, whereas the optical transition frequencies between the spin states $({\ensuremath{\omega}}_{\mathrm{up}},\phantom{\rule{4pt}{0ex}}{\ensuremath{\omega}}_{\mathrm{down}})$ in the CB and VB is effectively strain tunable. Inspired by the experimentally observed higher exciton lifetime 1.8 ns in $\mathrm{MoS}{\mathrm{e}}_{2}/\mathrm{WS}{\mathrm{e}}_{2}$ type-II van der Waals heterostructure (vdWH) than in the monolayers \ensuremath{\sim}2.1 (2.5) $ps$ in monolayer $\mathrm{Mo}{\mathrm{S}}_{2}$ $(\mathrm{W}{\mathrm{S}}_{2})$, a type-II (vdWH) prototype has been demonstrated by stacking $\mathrm{Hf}{\mathrm{N}}_{2}$ monolayer over $1\mathrm{H}\ensuremath{-}\mathrm{WS}{\mathrm{e}}_{2}$ monolayer for an extended lifetime of valley polarized excitons and large magnitude of spin splitting at both CB and VB. The elastic properties highlight the robustness of $\mathrm{Hf}{\mathrm{N}}_{2}$ monolayer and vdWH, as the bending modulus and critical buckling strain are found to be superior to that in graphene. Further, carrier mobility calculated using the deformation potential theory in $\mathrm{Hf}{\mathrm{N}}_{2}/\mathrm{WS}{\mathrm{e}}_{2}$ is as high as ${\ensuremath{\mu}}_{h}=16\phantom{\rule{4pt}{0ex}}\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{2}{\mathrm{V}}^{1}{\mathrm{s}}^{\ensuremath{-}1}$. Moreover, this work introduces the $\mathrm{Hf}{\mathrm{N}}_{2}$ monolayer as an exceptionally promising valleytronic material having valley properties complementary to that of Group VI TMDC. This is a report on valley contrasting physics and VSS at the CB, which would strongly motivate experimentalists to synthesize and explore this predicted two-dimensional material.

Controlled giant magnetoresistance and spin–valley transport in an asymmetrical MoS2 tunnel junction

We study the effects of asymmetrical magnetization and an optoelectronic tunable band structure on the transmission of particles in a MoS2 tunnel junction. Based on the results, we propose a model for a multifunctional coupler as a single system incorporating giant magnetoresistance, a spin–valley filter, and a spin–valley valve. The device is made up of ferromagnetic/ferromagnetic/normal junctions, with an off-resonant light and an electric gate potential functioning as the spin–valley filter and spin–valley valve, respectively. Increasing the asymmetrical magnetization is found to substantially enhance the tunneling magnetoresistance (TMR) of the system, leading to giant TMR. The spin–valley filtering is based on the spin imbalance modulation that arises from asymmetrical magnetization and the valley degeneracy breaking of off-resonant light, and the spin–valley valve is produced by altering the effective density of states of spin/valley polarized bands via the gate potential that controls the flow of spin/valley polarized particles. By fixing the magnetization configurations, one specific spin–valley filter and spin–valley valve can be acquired by tuning an external parameter to the corresponding spin/valley polarized energy windows.

Giant Stark splitting of an exciton in bilayer MoS2.

Transition metal dichalcogenides (TMDs) constitute a versatile platform for atomically thin optoelectronics devices and spin-valley memory applications. In monolayer TMDs the optical absorption is strong, but the transition energy cannot be tuned as the neutral exciton has essentially no out-of-plane static electric dipole1,2. In contrast, interlayer exciton transitions in heterobilayers are widely tunable in applied electric fields, but their coupling to light is substantially reduced. In this work, we show tuning over 120 meV of interlayer excitons with a high oscillator strength in bilayer MoS2 due to the quantum-confined Stark effect3. We optically probed the interaction between intra- and interlayer excitons as they were energetically tuned into resonance. Interlayer excitons interact strongly with intralayer B excitons, as demonstrated by a clear avoided crossing, whereas the interaction with intralayer A excitons is substantially weaker. Our observations are supported by density functional theory (DFT) calculations, which include excitonic effects. In MoS2 trilayers, our experiments uncovered two types of interlayer excitons with and without in-built electric dipoles. Highly tunable excitonic transitions with large in-built dipoles and oscillator strengths will result in strong exciton-exciton interactions and therefore hold great promise for non-linear optics with polaritons.

Room-Temperature Valley Polarization in Atomically Thin Semiconductors via Chalcogenide Alloying.

Room-temperature manipulation and processing of information encoded in the electronic valley pseudospin and spin degrees of freedoms lie at the heart of the next technological quantum revolution. In atomically thin layers of transition-metal dichalcogenides (TMDs) with hexagonal lattices, valley-polarized excitations and valley quantum coherence can be generated by simply shining with adequately polarized light. In turn, the polarization states of light can induce topological Hall currents in the absence of an external magnetic field, which underlies the fundamental principle of opto-valleytronics devices. However, demonstration of optical generation of valley polarization at room temperature has remained challenging and not well understood. Here, we demonstrate control of strong valley polarization (valley quantum coherence) at room temperature of up to ∼50% (∼20%) by strategically designing Coulomb forces and spin-orbit interactions in atomically thin TMDs via chalcogenide alloying. We show that tailor making the carrier density and the relative order between optically active (bright) and forbidden (dark) states by key variations on the chalcogenide atom ratio allows full control of valley pseudospin dynamics. Our findings set a comprehensive approach for intrinsic and efficient manipulation of valley pseudospin and spin degree of freedom toward realistic opto-valleytronics devices.

Bipolar and unipolar valley filter effects in graphene-based P/N junction

We use the spin and valley degrees of freedom to design the bipolar and unipolar valley filter effects based on the graphene-based P/N junction. When the modified Haldane model and staggered potential are applied on the region P, while the off-resonant circularly polarized light and staggered ferromagnetic exchange field are applied on the region N, the unipolar valley filter effect emerges with the unidirectional spin–valley current. The direction and type of the unidirectional spin–valley current depend on the phase of the modified Haldane model and the direction of polarized light. Other types of the bipolar valley filter effects are also reported, such as the valley-mixed bipolar spin filter effect, valley-mixed bipolar filter effect, valley-locked bipolar spin filter effect and valley-locked bipolar filter effect. These bipolar filter effects have the similarity that the spin–valley currents flow bidirectionally. These types of the unipolar and bipolar valley filter effects can be also mutually switched by modulating the external fields. Moreover, these unipolar and bipolar valley filter effects are robust against a weak temperature. This work reveals that the graphene-based junction has the potential applications in designing the valley filter device and improving the reprogrammable spin logic.

Topological spin–valley filtering effects based on hybrid silicene-like nanoribbons

Topological edge states have crucial applications in nano spintronics and valleytronics devices, while topological inner-edge states have seldom been extensively researched in this field. Based on the inner-edge states of the hybridized zigzag silicene-like nanoribbons, we investigate their transport properties. We propose two types of spin–valley filters. The first type can generate two different spin–valley polarized currents in output leads, respectively. The second type outputs the specific spin–valley polarized current in only one of the output leads. All these inner-edge states have the spin–valley-momentum locking property. These types of filters can switch the output spin–valley polarizations by modulating the external fields. Besides, we also find that the device size plays a crucial role in designing these spin–valley filters. Moreover, the local current distributions are calculated to visualize the detailed transport process and understand the mechanism. The mechanism lies that the spin–valley polarized current can nearly freely pass through the system with the same momentum, spin and valley degrees of freedom. The small reflection of the current results from the inter-valley scattering. In particular, we also consider the realistic (disorder) effects on the performance of these filters to ensure the robustness of our systems. We believe these spin–valley current filtering effects have potential applications in the future spintronics and valleytronics device designs.

Fine structures of valley-polarized excitonic states in monolayer transitional metal dichalcogenides

Abstract Monolayer transitional metal dichalcogenides (TMDCs), a new class of atomically thin semiconductor, respond to optical excitation strongly with robust excitons, which stem from the reduced screening in two dimensions. These excitons also possess a new quantum degree of freedom known as valley spin, which has inspired the field of valleytronics. The strongly enhanced Coulomb interaction allows the exciton to bind with other particles to form new excitonic states. However, despite the discovery of trions, most of the excitonic states in monolayer TMDCs remain elusive until recently, when new light was shed into the fascinating excitonic fine structures with drastically improved sample quality through boron nitride encapsulation. Here, we review the latest research progress on fine structures of excitonic states in monolayer TMDCs, with a focus on tungsten-based TMDCs and related alloy. Many of the new excitonic complexes inherit the valley degree of freedom, and the valley-polarized dark excitonic states are of particular interest because of their long lifetime and possible long valley coherence time. The capability of resolving the excitonic fine structures also enables the investigation of exciton–phonon interactions. The knowledge of the interlayer between excitons and other particles not only advances our understanding of many-body effects in the monolayer TMDCs but also provides guidance on future applications based on TMDCs.

Enhanced valleytronic properties in germanene by direct proximity to heavy metal layer

Germanene, though with Dirac valleys, is not deemed as a good valleytronic material due to its minute band gap, negligible spin–orbit coupling and spatial inversion symmetry. In comparison of interfacing germanene with MoS2, we proposed that forming heterostructure with Tl2S, an anti-MoS2 material with two outer heavy metal layers, could be more effective in raising spin–orbit coupling and band gap in germanene due to the direct Ge-metal contact. By carrying out first-principles calculations, we studied the valleytronic properties of germanene enhanced by monolayer Tl2S. It is found that the Ge–Tl direct interaction is strong to a proper extent so that the valleys of germanene still persist and simultaneously the valley gap is drastically increased from 23 to 370 meV. The valley spin splitting, being zero in pristine germanene, become 45 meV, which is opposite at inequivalent valleys owing to the time reversal symmetry. The inversion symmetry of germanene is broken by Tl2S, resulting in large Berry curvature near the valleys and hence laying the ground for Berry phase physics in germanene, e.g., valley spin Hall effect and valley–spin locking, as revealed in our study. The calculations found a perfect valley-selective circular dichroism, by which the valley and spin degrees of freedom can be manipulated selectively and correlatively.

Valley polarization in monolayer CrX2 (X = S, Se) with magnetically doping and proximity coupling

Manipulating the valley degree of freedom as an information carrier has been a focused topic for both fundamental and applied research. Here, using first-principles calculations, we report the identification of monolayer CrX2 (X = S, Se) as a novel two-dimensional valleytronic crystal. It shows large valley spin splitting in the valence band, attractive for the integration of valleytronics and spintronics. More importantly, through proximity coupling with monolayer CrCl3, the valley polarization in monolayer CrX2 is achieved, which can be further engineered by stacking patterns. Also, the valley polarization in monolayer CrX2 can be obtained via magnetically doping V and Mn. Specially for V-doped monolayer CrSe2, there are no impurity states in the band gap, beneficial for its practical applications. Our works thus provide not only exceptional two-dimensional valleytronic crystals but also promising ways for realizing valley polarizations in them.

Many-body effects due to the electron–electron interaction in silicene under an applied exchange field: The case of valley–spin coupling

We investigate the many-body effects induced by the electron–electron interaction in a valley–spin-polarized silicene under a perpendicularly applied exchange field. We calculate the real and imaginary parts of the self-energy within the leading order dynamical screening approximation where the screened interaction is obtained from the random phase approximation. Our study on the valley- and spin-dependent real and imaginary parts of the self-energy indicates that the different coupled valley–spin subbands may exhibit distinct characteristics. Moreover, we obtain the corresponding spectral functions and find that the plasmaron and quasiparticle peaks have different spectral weights and broadenings in all states. Interestingly, it seems that there are clear dependencies for the position and broadening of the peaks on valley–spin indexes. In addition, we study the effect of the electron–electron interaction on the renormalized velocity in the on-shell approximation and show that the renormalized velocity in gapped states becomes greater, and in gapless states, it becomes smaller as the wave vector grows.

Collective Excitations of Quantum Anomalous Hall Ferromagnets in Twisted Bilayer Graphene

We present a microscopic theory for collective excitations of quantum anomalous Hall ferromagnets (QAHF) in twisted bilayer graphene. We calculate the spin magnon and valley magnon spectra by solving Bethe-Salpeter equations and verify the stability of QAHF. We extract the spin stiffness from the gapless spin wave dispersion and estimate the energy cost of a skyrmion-antiskyrmion pair, which is found to be comparable in energy with the Hartree-Fock gap. The valley wave mode is gapped, implying that the valley polarized state is more favorable compared to the valley coherent state. Using a nonlinear sigma model, we estimate the valley ordering temperature, which is considerably reduced from the mean-field transition temperature due to thermal excitations of valley waves.

Possible realization and protection of valley-polarized quantum Hall effect in Mn/WS2

By using the first-principles calculations and model analyses, we found that the combination of defected tungsten disulfide monolayer and sparse manganese adsorption may give a KK` valley spin splitting up to 210 meV. This system also has a tunable magnetic anisotropy energy, a clean band gap, and an appropriate band alignment, with the Fermi level sitting right above the top of valence bands at the K-valleys. Therefore, it can be used for the realization of the valley-polarized anomalous Hall effect and for the exploration of other valley related physics without using optical methods. A protective environment can be formed by covering it with a hexagonal BN layer, without much disturbance to the benign properties of Mn/WS2.

Modulation of spin–valley splitting in a two-dimensional MnPSe3/CrBr3 van der Waals heterostructure

We perform a systematic investigation of MnPSe3/CrBr3 two-dimensional (2D) van der Waals heterostructures through first-principles calculations. The most stable stacking configuration of MnPSe3/CrBr3 heterostructures is found to have an indirect type-II band structure. Biaxial tensile strain is employed to tailor the spin–valley properties of the heterostructures in terms of the momentum, energy and spin components of the valleys. A novel opposite spin splitting evolution appears at the K and K′ valleys of the top valance band (TVB) with increasing tensile strain. A change from an indirect to a direct band gap is found at 7% tensile strain. A maximum spin splitting of 34.7 meV at the K′ valley is produced simultaneously with valley polarization under a tensile strain of 10%. The spin components distributed at the TVB are found to be controlled by strain-related competition between direct exchange interaction and indirect superexchange interaction of Se (px + py ) and Se pz orbitals. Spin polarization precisely regulated by strain can facilitate the manipulation of valley and spin degrees of freedom in MnPSe3/CrBr3 heterostructures, which opens up great potential for novel applications, such as strained sensor, spintronic and valleytronic devices.

Tailoring excitonic states of van der Waals bilayers through stacking configuration, band alignment, and valley spin.

Excitons in monolayer semiconductors have a large optical transition dipole for strong coupling with light. Interlayer excitons in heterobilayers feature a large electric dipole that enables strong coupling with an electric field and exciton-exciton interaction at the cost of a small optical dipole. We demonstrate the ability to create a new class of excitons in hetero- and homobilayers that combines advantages of monolayer and interlayer excitons, i.e., featuring both large optical and electric dipoles. These excitons consist of an electron confined in an individual layer, and a hole extended in both layers, where the carrier-species-dependent layer hybridization can be controlled through rotational, translational, band offset, and valley-spin degrees of freedom. We observe different species of layer-hybridized valley excitons, which can be used for realizing strongly interacting polaritonic gases and optical quantum controls of bidirectional interlayer carrier transfer.