Spin Valley Research Articles

Tunable quantum criticalities in an isospin extended Hubbard model simulator

Studying strong electron correlations has been an essential driving force for pushing the frontiers of condensed matter physics. In particular, in the vicinity of correlation-driven quantum phase transitions (QPTs), quantum critical fluctuations of multiple degrees of freedom facilitate exotic many-body states and quantum critical behaviours beyond Landau’s framework1. Recently, moiré heterostructures of van der Waals materials have been demonstrated as highly tunable quantum platforms for exploring fascinating, strongly correlated quantum physics2–22. Here we report the observation of tunable quantum criticalities in an experimental simulator of the extended Hubbard model with spin–valley isospins arising in chiral-stacked twisted double bilayer graphene (cTDBG). Scaling analysis shows a quantum two-stage criticality manifesting two distinct quantum critical points as the generalized Wigner crystal transits to a Fermi liquid by varying the displacement field, suggesting the emergence of a critical intermediate phase. The quantum two-stage criticality evolves into a quantum pseudo criticality as a high parallel magnetic field is applied. In such a pseudo criticality, we find that the quantum critical scaling is only valid above a critical temperature, indicating a weak first-order QPT therein. Our results demonstrate a highly tunable solid-state simulator with intricate interplay of multiple degrees of freedom for exploring exotic quantum critical states and behaviours.

Emergence of Rashba splitting and spin-valley properties in Janus MoGeSiP2As2 and WGeSiP2As2 monolayers

First-principles calculations are performed to study the structural stability and spintronics properties of Janus MoGeSiP2As2 and WGeSiP2As2 monolayers. The high cohesive energies and the stable phonon modes confirm that both these structures are experimentally accessible. In contrast to pristine MoSi2P4, the Janus monolayers demonstrate reduced direct bandgaps and large spin-split states at K/K’. For the monolayered Janus structure, the broken mirror symmetry with respect to the Mo/W-plane gives rise to a potential gradient normal to the basal plane, which causes difference in the work function for the two surfaces. In addition, the spin textures exposed that breaking the mirror symmetry brings Rashba-type spin splitting in the systems which can be increased by using higher atomic spin–orbit coupling. The large valley spin splitting together with the Rashba splitting in these Janus monolayer structures can make a remarkable contribution to semiconductor valleytronics and spintronics.

Theoretical studies of valleytronic and optical properties in monolayer MoP2X2Y2 (XY=BTe,AlS,andGaS)

Motivated by recent extensive studies on the $M{A}_{2}{Z}_{4}$ family materials, we have predicted three ${\mathrm{MoP}}_{2}{X}_{2}{Y}_{2}$-type monolayers, including ${\mathrm{MoP}}_{2}{\mathrm{B}}_{2}{\mathrm{Te}}_{2}, {\mathrm{MoP}}_{2}{\mathrm{Al}}_{2}{\mathrm{S}}_{2}$, and ${\mathrm{MoP}}_{2}{\mathrm{Ga}}_{2}{\mathrm{S}}_{2}$, which possess excellent dynamic and thermal stabilities and peculiar electronic properties. According to first-principle calculations, the band structures show that the three monolayers are direct band-gap semiconductors with a direct band gap of $\ensuremath{\sim}1\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$. The band energy extrema occurs at $K/{K}^{\ensuremath{'}}$ points, giving rise to a pair of degenerate valleys. A large valley spin splitting is found at the valence band under the spin-orbit coupling effect, resulting in valley-contrasting Berry curvature. Moreover, these materials have strong optical absorption intensity in the visible light regions, especially ${\mathrm{MoP}}_{2}{\mathrm{Ga}}_{2}{\mathrm{S}}_{2}$. Our research shows that these three ${\mathrm{MoP}}_{2}{X}_{2}{Y}_{2}$ monolayers, as close relatives of $M{A}_{2}{Z}_{4}$ family materials, have potential valleytronics and photovoltaics applications.

Strengthened spin–valley polarization and negative magnetoresistance based on an asymmetrical double-ferromagnetic WSe2 junction

The spin–valley transport and tunneling magnetoresistance (TMR) are studied in an off-resonant circularly polarized light (CPL)-modulated asymmetrical double-ferromagnetic (FM) WSe 2 junction. Based on the results, we propose a device that can simultaneously operate as spin–valley filter and exhibit giant magnetoresistance in a single system. For the antiparallel configuration, the broken spin degeneracy and optical Stark effect in the first FM barrier produce 100% spin (valley)-polarized particles. Subsequently, the spin valve effect from the second FM barrier gives rise to a 100% spin (valley)-selective polarization in the strengthened polarized energy windows of the first CPL. Furthermore, increasing the asymmetrical magnetization of such a junction is found to substantially enhance the TMR, leading to a positive 100% TMR. The TMR can be tuned from −100% to 100% and is sensitively dependent on the chirality of the second CPL due to the coupling between the spin valve effect and the optical Stark effect. Our findings indicate that double-FM barriers combined with off-resonant CPL modulation can be an excellent option to improve the spin–valley polarization and magnetoresistance of transition metal dichalcogenide-based structures. • A model was proposed to improve the magnetoresistance response as well as obtain two well-defined spin–valley polarization states. • The structure gives rise to a 100% spin (valley)-selective polarization in strengthened polarized energy windows of light. • Increasing the asymmetrical magnetization of this junction is found to substantially enhance the tunnel magnetoresistance to 100%. • The magnetoresistance can be tuned from −100% to 100% and is sensitively dependent on the chirality of light.

Chiral SO(4) spin-valley density wave and degenerate topological superconductivity in magic-angle twisted bilayer graphene

Starting from a realistic extended Hubbard model for a ${p}_{x,y}$-orbital tight-binding model on the Honeycomb lattice, we perform a thorough investigation of the possible electron instabilities in magic-angle twisted bilayer graphene near the van Hove (VH) dopings. Here we focus on the interplay between the two symmetries of the system. One is the approximate $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry which leads to the degeneracy between the intervalley spin density wave (SDW) and valley density wave (VDW) as well as that between the intervalley singlet and triplet superconductivities (SCs). The other is the ${D}_{3}$ symmetry which leads to the degeneracy among the three symmetry-related wave vectors of the density-wave (DW) orders, originating from the Fermi-surface nesting. The interplay between these two degeneracies leads to intriguing quantum states relevant to recent experiments, as revealed by our systematic random-phase-approximation based calculations followed by a succeeding mean-field energy minimization for the groundstate energy. At the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetric point, the degenerate intervalley SDW and VDW are mixed into a new state of matter dubbed as the chiral SO(4) spin-valley DW. This state simultaneously hosts three four-component vectorial spin-valley DW orders with each adopting one wave vector, and the polarization directions of the three DW orders are mutually perpendicular to one another. In the presence of a tiny intervalley exchange interaction with coefficient ${J}_{H}\ensuremath{\rightarrow}{0}^{\ensuremath{-}}$ which breaks the $\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}\mathrm{SU}(2)$ symmetry, a pure chiral SDW state is obtained. In the case of ${J}_{H}\ensuremath{\rightarrow}{0}^{+}$, although a nematic VDW order is favored, the two SDW orders with equal amplitudes are accompanied simultaneously. This nematic $\mathrm{VDW}+\mathrm{SDW}$ state possesses a stripy distribution of the charge density, consistent with the recent STM observations. On the aspect of SC, while the triplet $p+ip$ and singlet $d+id$ topological SCs are degenerate at ${J}_{H}=0$ near the VH dopings, the former (latter) is favored for ${J}_{H}\ensuremath{\rightarrow}{0}^{\ensuremath{-}}$ (${J}_{H}\ensuremath{\rightarrow}{0}^{+}$). In addition, the two asymmetric doping-dependent behaviors of the obtained pairing phase diagram are well consistent with experiments.

Stacking-dependent exciton multiplicity in WSe2 bilayers

Twisted layers of atomically thin two-dimensional materials realize a broad range of quantum materials with engineered optical and transport phenomena arising from spin and valley degrees of freedom and strong electron correlations in hybridized interlayer bands. Here, we report on experimental and theoretical studies of ${\mathrm{WSe}}_{2}$ homobilayers obtained in two stable configurations of $2H$ (${60}^{\ensuremath{\circ}}$ twist) and $3R$ (${0}^{\ensuremath{\circ}}$ twist) stackings by controlled chemical vapor synthesis of high-quality large-area crystals. Using optical absorption and photoluminescence (PL) spectroscopy at cryogenic temperatures, we uncover marked differences in the optical characteristics of $2H$ and $3R$ bilayer ${\mathrm{WSe}}_{2}$ which we explain on the basis of beyond-density functional theory calculations. Our results highlight the role of layer stacking for the spectral multiplicity of momentum-direct intralayer exciton transitions in absorption and relate the multiplicity of phonon sidebands in the PL to momentum-indirect excitons with different spin valley and layer character. Our comprehensive study generalizes to other layered homobilayer and heterobilayer semiconductor systems and highlights the role of crystal symmetry and stacking for interlayer hybrid states.

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.

Electrical and thermal transport in a twisted heterostructure of transition metal dichalcogenide and CrI3 connected to a superconductor

The broad tunability of the proximity exchange effect between transition-metal dichalcogenides (TMDCs) and chromium iodide (CrI$_3$) heterostructures offers intriguing possibilities for the use of TMDCs in two-dimensional magnetoelectrics. In this work, the influence of the twist angle and the gate electric field on the electric and thermal transport in a TMDC/CrI$_3$ junction is investigated using the Dirac -Bogoliubov-de Gennes equation. We show that significant amounts can be controlled by spin-splitting of band structures due to spin-orbit interaction, and that the exchange-splitting of bands arises from the proximity effect. The property of the Andreev reflection (AR) process is highly dependent on the spin valley polarized states due to spin-orbit coupling. Remarkably, perfect spin valley polarized AR is possible over a wide bias range by using a gate voltage to tune the local Fermi energy and varying the type of charge doping. The proposed structure with $p$-type doping is found to have larger spin valley polarized Andreev conductance and high thermal conductance. We further show that, depending on the TMDC material and chemical potential of the TMDC/CrI$_3$ layer, twisting can lead to suppression or a significant increase in Andreev conductance as well as enhancement of thermal conductance for chemical potentials smaller than that of the superconducting regime.

Moments and multiplets in moiré materials

The observation of strongly correlated states in moiré systems has renewed the conceptual interest in magnetic systems with higher SU(4) spin symmetry, e.g., to describe Mott insulators where the local moments are coupled spin–valley degrees of freedom. Here, we discuss a numerical renormalization group scheme to explore the formation of spin–valley ordered and unconventional spin–valley liquid states at zero temperature based on a pseudo-fermion representation. Our generalization of the conventional pseudo-fermion functional renormalization group approach for {{mathfrak {s}}}{{mathfrak {u}}}(2) spins is capable of treating diagonal and off-diagonal couplings of generic spin–valley exchange Hamiltonians in the self-conjugate representation of the {{mathfrak {s}}}{{mathfrak {u}}}(4) algebra. To achieve proper numerical efficiency, we derive a number of symmetry constraints on the flow equations that significantly limit the number of ordinary differential equations to be solved. As an example system, we investigate a diagonal SU(2)_{text {spin}}otimes U(1)_{text {valley}} model on the triangular lattice which exhibits a rich phase diagram of spin and valley ordered phases.Graphic

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.

Electric field induced pure spin-photo current in zigzag stanene and germanene nanoribbons

The spin-photo current in single layer stanene and germanene under a linearly polarized light is theoretically investigated based on the tight-binding Hamiltonian combined with the nonequilibrium Green’s function at room temperature. The results show that by considering the simultaneous effect of the linear illumination and a vertical external electric field without any magnetic exchange element, pure spin-photo current without charge current is generated in two-dimensional lattices with a large intrinsic spin–orbit coupling. The necessity of enhanced spin life-time for detection of spin polarization can be explained by spin-valley locking concept. Spin-valley locking arises in buckled two-dimensional materials as a result of the large spin–orbit coupling and electric-field reversible valley spin polarization. Equal absorption of the linearly illumination at both valleys with different spin polarization, leads to pure spin-photo current injection. In addition, an acceptable photoresponsivity has been reported in a broad range of photon energy. The numerical results indicate high quantum efficiency with a maximum of nearly 83% and 50% for stanene and germanene, respectively. This work may pave theoretical reference toward design of new spin-optoelectronic devices based on satanene and germanene junctions with high performance.

Gate‐Controlled Quantum Dots Based on 2D Materials

Abstract2D materials are a family of layered materials exhibiting rich exotic phenomena, such as valley‐contrasting physics. Down to single‐particle level, unraveling fundamental physics and potential applications including quantum information processing in these materials attracts significant research interests. To unlock these great potentials, gate‐controlled quantum dot architectures have been applied in 2D materials and their heterostructures. Such systems provide the possibility of electrical confinement, control, and manipulation of single carriers in these materials. In this review, efforts in gate‐controlled quantum dots in 2D materials are presented. Following basic introductions to valley degree of freedom and gate‐controlled quantum dot systems, the up‐to‐date progress in etched and gate‐defined quantum dots in 2D materials, especially in graphene and transition metal dichalcogenides, is provided. The challenges and opportunities for future developments in this field, from views of device design, fabrication scheme, and control technology, are discussed. The rapid progress in this field not only sheds light on the understanding of spin–valley physics but also provides an ideal platform for investigating diverse condensed matter physics phenomena and realizing quantum computation in the 2D limit.

Utilizing Valley–Spin Hall Effect in Monolayer WSe2 for Designing Low Power Nonvolatile Spintronic Devices and Flip-Flops

In this article, we propose low power nonvolatile flip-flops (NVFFs) utilizing valley–spin Hall effect (VSHE) in monolayer tungsten diselenide (WSe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ). The proposed designs are based on nonvolatile spintronic devices comprising of WSe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -based charge-to-spin converter coupled with magnetic tunnel junctions. The proposed devices have an integrated back-gate to control the flow of charge and spin currents. VSHE leads to the flow of opposite spins in divergent directions perpendicular to the WSe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> layer with valley/spin Hall angle ~1. This enables encoding true and complementary bits in a single device utilizing magnets with perpendicular magnetic anisotropy (PMA). By introducing exchange coupling between PMA magnets mediated by Ta and FeCo-oxide layers, we electrically isolate but magnetically couple the PMA free layers, which enable the design of backup/restore module of NVFFs with minimal number of transistors. Using object-oriented micromagnetic framework (OOMMF) simulation, we establish the robustness of the exchange-coupled PMA systems and show that the misalignment and reduction in exchange coupling strength, induced by process variations, have a minimal impact on their functionality. Exploiting the unique features of the proposed devices, we design two flavors of VSHE-based NVFFs (VSHE-NVFFs) and carry out their energy–delay characterization, including an extensive variation analysis. The proposed VSHE-NVFFs achieve 74%–75% lower backup energy and 55%–59% lower restore energy than the existing NVFFs based on giant spin Hall effect (GSHE).

Plasmonic Nanocavity Induced Coupling and Boost of Dark Excitons in Monolayer WSe2 at Room Temperature.

Spin-forbidden excitons in monolayer transition metal dichalcogenides are optically inactive at room temperature. Probing and manipulating these dark excitons are essential for understanding exciton spin relaxation and valley coherence of these 2D materials. Here, we show that the coupling of dark excitons to a metal nanoparticle-on-mirror cavity leads to plasmon-induced resonant emission with the intensity comparable to that of the spin-allowed bright excitons. A three-state quantum model combined with full-wave electrodynamic calculations reveals that the radiative decay rate of the dark excitons can be enhanced by nearly 6 orders of magnitude through the Purcell effect, therefore compensating its intrinsic nature of weak radiation. Our nanocavity approach provides a useful paradigm for understanding the room-temperature dynamics of dark excitons, potentially paving the road for employing dark exciton in quantum computing and nanoscale optoelectronics.

Valley spin polarization in two-dimensional h−MN (M=Nb,Ta) monolayers: Merger of valleytronics with spintronics

The search for new two-dimensional (2D) semiconductors with strong spin-orbit coupling, merging Rashba effect with valley physics, is essential for advancing the emerging fields of spintronics and valleytronics. $h\text{\ensuremath{-}}M\mathrm{N}$ $(M=\mathrm{Nb},\mathrm{Ta})$ monolayers are found to host valley physics together with Rashba effect. $h$-NbN (TaN) monolayers show Zeeman-type valley spin splitting of 32 (112) meV and 130 (406) meV at valence-band and conduction-band edges, respectively, based on density-functional theory calculations. One of the three degenerate valleys around the $K/{K}^{\ensuremath{'}}$ point in the first Brillouin zone (BZ) lies fully enclosed within the first BZ. Berry curvature $\ensuremath{\sim}50(73)\phantom{\rule{0.16em}{0ex}}{\AA{}}^{2}$ shown by h-NbN (TaN) monolayers is much higher than that in ${\mathrm{MoS}}_{2}$ monolayer $(\ensuremath{\sim}11\phantom{\rule{0.16em}{0ex}}{\AA{}}^{2})$, owing to the lower band gap and wave vector magnitude in $h$-NbN (TaN) monolayers. The Rashba energy splitting and Rashba constant induced by strong spin-orbit coupling (SOC) in $h$-NbN (TaN) monolayer is found to be 52 (74) meV and 2.9 (4.23) eV \AA{} respectively, which are amongst the giant Rashba spin-splitting parameters observed so far in 2D materials. The degree of Zeeman-type valley spin splitting and Rashba-type spin splitting is substantially tunable via in-plane biaxial strain and out of-plane electric field. Higher SOC in $h$-TaN monolayer relative to $h$-NbN monolayer caused by the heavier Ta atoms gives rise to a higher Berry curvature, valley-, and Rashba spin splitting in the former as compared to the latter. Valleytronic and spintronic properties in the studied monolayers are found to be superior to that in $h\text{\ensuremath{-}}{\mathrm{MoS}}_{2}$ and Janus MoSSe monolayers and are therefore proposed for an effective coupling of spin and valley physics.

Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene.

In conventional superconductors, Cooper pairing occurs between electrons of opposite spin. We observe spin-polarized superconductivity in Bernal bilayer graphene when doped to a saddle-point van Hove singularity generated by large applied perpendicular electric field. We observe a cascade of electrostatic gate-tuned transitions between electronic phases distinguished by their polarization within the isospin space defined by the combination of the spin and momentum-space valley degrees of freedom. Although all of these phases are metallic at zero magnetic field, we observe a transition to a superconducting state at finite B‖ ≈ 150mT applied parallel to the two-dimensional sheet. Superconductivity occurs near a symmetry breaking transition, and exists exclusively above the B‖-limit expected of a paramagnetic superconductor with the observed transition temperature TC ≈ 30mK, consistent with a spin-triplet order parameter.

Janus Monolayers of Transition Metal Dichalcogenides: A DFT Study

MXY (M = W, Mo; X, Y = S, Se, Te) Janus monolayers are noncentrosymmetric systems with strong spin–orbit coupling effects, giving rise to interesting physical phenomena. By using the full-potential linearized augmented plane-wave method (FP-LAPW), Daniel Olguín and co-workers study the electronic properties of the MoXY (X, Y = S, Se, Te) Janus monolayers (see article number 2100248). These Janus monolayers are found to present a spin polarization near the high symmetry Γ, K–, and K+ points of the valence band. Among the studied systems, MoSeTe and MoSSe present spin–valley polarization, Rashba spin-splitting, and a direct bandgap, representing an interesting atomically thin material that can be exploited in different applications such as spintronics, spin-orbitronics, and nanoelectronics.

Prediction of a new two-dimensional valleytronic semiconductor MoGe2P4 with large valley spin splitting.

Recently, MoSi2N4 with large valley spin splitting was experimentally synthesized. However, materials with large valley spin splitting are still rare. We predict a new two-dimensional (2D) MoGe2P4 material. It has large valley spin splitting and excellent optical absorption properties. The results show that 2D MoGe2P4 is a direct semiconductor with a bandgap of 887 meV. Its valley spin splitting (ΔV) at the top of the valence band is 153 meV because of the inversion symmetry breaking and spin-orbit coupling (SOC). 2D MoGe2P4 transforms from a semiconductor to a metal under a biaxial strain of 6%. ΔV increases monotonically from 137 meV to 157 meV under biaxial strain. In addition, the lowest exciton state of 2D MoGe2P4 is near 770 nm, and the optical absorption coefficient in the ultraviolet range is higher than that of MoS2. Our results suggest that 2D MoGe2P4 has excellent potential for applications in valley electronics and optoelectronic devices.

Large valley polarization in a novel two-dimensional semiconductor H-ZrX2 (X = Cl, Br, I)

Inspired by the new progress in the research field of two-dimensional valleytronics materials, we propose a new class of transition metal halides, i.e. H-ZrX2 (X = Cl, Br, I), and investigated their valleytronics properties under the first-principles calculations. It harbors the spin-valley coupling at K and K′ points in the top of valence band, in which the valley spin splitting of ZrI2 can reach up to 115 meV. By carrying out the strain engineering, the valley spin splitting and Berry curvature can be effectively tuned. The long-sought valley polarization reaches up to 108 meV by doping Cr atom, which corresponds to the large Zeeman magnetic field of 778 T. Furthermore, the valley polarization in ZrX2 can be lineally adjusted or flipped by manipulating the magnetization orientation of the doped magnetic atoms. All the results demonstrate the well-founded application prospects of single-layer ZrX2, which can be considered as great candidate for the development of valleytronics and spintronics.

Giant Spin Lifetime Anisotropy and Spin-Valley Locking in Silicene and Germanene from First-Principles Density-Matrix Dynamics.

Through first-principles real-time density-matrix (FPDM) dynamics simulations, we investigated spin relaxation due to electron-phonon and electron-impurity scatterings with spin-orbit coupling (SOC) in two-dimensional Dirac materials silicene and germanene at finite temperatures. We discussed the applicability of conventional descriptions of spin relaxation mechanisms by Elliott-Yafet (EY) and D'yakonov-Perel' (DP) compared to the FPDM method, which is determined by a complex interplay of intrinsic SOC, external fields, and scattering strength. For example, the electric field dependence of the spin lifetime by FPDM is close to the DP mechanism for silicene at room temperature but similar to the EY mechanism for germanene. Because of its stronger SOC strength and buckled structure in contrast to graphene, germanene has a giant spin lifetime anisotropy and spin-valley locking effect under nonzero Ez and low temperatures. More importantly, germanene has a long spin lifetime (∼100 ns at 50 K) and an ultrahigh carrier mobility, making it advantageous for spin-valleytronic applications.