Spontaneous Valley Polarization Research Articles

Chern Insulator States with Tunable Chern Numbers in a Graphene Moiré Superlattice.

Moiré superlattices, constituted by two-dimensional materials, demonstrate a variety of strongly correlated and topological phenomena including correlated insulators, superconductivity, and integer/fractional Chern insulators. In the realm of topological nontrivial Chern insulators within specific moiré superlattices, previous studies usually observe a single Chern number at a given filling factor in a device. Here we present the observation of gate-tunable Chern numbers within the Chern insulator state of an ABC-stacked trilayer graphene/hexagonal boron nitride moiré superlattice device. Near quarter filling, the moiré superlattice exhibits spontaneous valley polarization and distinct ferromagnetism associated with the Chern insulator states over a range of the displacement field. Surprisingly we find a transition of the Chern number from C = 3 to 4 as the displacement field is increased. Our observation of gate-tunable correlated Chern insulators suggests new ways to control and manipulate topological states in a moiré superlattice device.

Spontaneous and tunable valley polarization in two-dimensional single-layer LaCl2

Applying the valley contrasting properties of valleytronic materials to logical operations is the foundation of valleytronic device manufacturing. It is predicted that single-layer (SL) LaCl2 is an ferrovalley material with intrinsic and tunable valley polarization through first-principles calculations. It is a ferromagnetic semiconductor (bandgap 0.767 eV) with roughly 1.0 μ B per unit cell as well as out of plane magnetization, and the Curie temperature is about 149 K. The tight-binding model considering five orbitals as well as next nearest neighboring hopping get a consistent band structure with the first-principles calculation. The valley polarization changes from 40.49 to 98.51 meV under the biaxial strain of 5% ∼ −5%. Therefore, the biaxial strain can be a means to tune the valley polarization. In addition, the valley polarization of the double-layer (DL) structure (∼80 meV) is much greater than that of the SL structure (∼59 meV) due to the increased magnetic moment of the DL structure, indicating the potential tunable character by stacking few layers. We believe that SL LaCl2 has great potential for device manufacturing and application in the field of valley electronics.

Spontaneous polarization dynamics in V-doped monolayer MoS2

Valleytronics has drawn attention both for its fundamental aspects and potential applications in device technology. Lifting the valley degeneracy is an attractive route to achieve stable valley polarization and spontaneous valley polarization. Our first-principles calculations on V-doped monolayer MoS2 reveal a substantial permanent valley splitting of 174 meV, driven by the combined effects of spin-orbit coupling (SOC) and magnetic coupling with the doped atom. Non-adiabatic molecular dynamics simulations show that the spontaneous valley polarization dynamics depends on the SOC, electron-phonon (e-ph) coupling and the scattering with the impurity, and it varies notably with different initial spin orientations of excited holes. For spin-up holes, the process involves e-ph scattering and spin-flip induced by spinor-phonon scattering over several picoseconds. On the other hand, spin-down hole excitation leads to spontaneous polarization through e-ph and impurity scattering on a timescale shorter by an order of magnitude. This study provides insights into the distinct valley polarization dynamics of carriers with different spins, contributing to the design of ultrafast valleytronic and spintronic devices.

Magnetic proximity effect on the spin-valley coupling in two-dimensional Cr2Ge2Te6/2H-TMD van der Waals heterostructures

Two-dimensional (2D) transition metal dichalcogenides with 2H-phases, as a unique platform of valleytronics, display valley polarization and the well-known anomalous valley Hall effect when stacking with 2D magnetic substrates. In this study, we employ first-principles calculations to investigate the magnetic states, band structures, and magnetic proximity-dependent valley properties of 2D van der Waals heterostructures Cr2Ge2Te6/2H-MX2 (M = Mo, W, and X = S, Se, Te). Our findings reveal that the heterostructures possess stacking-dependent spontaneous valley polarization as well as pristine perpendicular magnetic anisotropy. Additionally, the Berry curvature and circular polarization demonstrate the presence of spin–momentum coupling characteristics, while the calculated non-zero Hall voltage indicates that the anomalous valley Hall effect can be achieved in valley-polarized systems. Furthermore, due to the strain effect and the electronic polarization at the interface, Cr2Ge2Te6/2H-MX2 heterostructures undergo the transition from semiconductors to semimetals upon substitution of early chalcogen elements. These calculations provide valuable insights for practical applications of valleytronics in 2D van der Waals heterostructure systems.

Chiral breathing-valley locking in two-dimensional kagome lattice Ta3I8

The exploration of valley-related physics is essential to the development and refinement of valleytronics. Here, a paradigm called chiral breathing-valley locking (CBVL) is proposed, in which two chiral “breathing” phases are completely locked to their valley indexes. Utilizing first-principles calculations, a two-dimensional (2D) kagome lattice with large spontaneous valley polarization (VP), namely, monolayer Ta3I8, is proposed to realize CBVL. There are two breathing phases with chiral symmetry in Ta3I8, and they can change to each other under some conditions. The valley indexes change between “−K” and “K” along the breathing of the two chiral symmetric phases, so CBVL can be obtained. Remarkably, the VP is up to 199.7 meV, so CBVL can cause the obvious switching of the anomalous valley Hall effect (AVHE). Additionally, a 2D Janus Kagome structure TaI4X4 is constructed to confirm experimentally the feasibility of electric field modulation on the CBVL. The built-in electric field and the breathing mode can mutually influence each other in TaI4X4, which provides a synergistic regulation of the AVHE. Our findings broaden the horizon for exploring AVHE materials and provide a platform for future valleytronic applications.

Tunable polarization properties of charge, spin, and valley in Janus VSiGeZ4 (Z = N, P, As) monolayers.

Polarization, as an important characterization of the symmetry breaking systems, has attracted tremendous attention in two-dimensional (2D) materials. Due to their significant symmetry breaking, Janus 2D ferrovalley materials provide a desirable platform to investigate the charge, spin, and valley polarization, as well as their coupling effects. Herein, using first-principles calculations, the polarization properties of charge, spin, and valley in Janus VSiGeZ4 (Z = N, P, and As) monolayers are systematically studied. The mirror symmetry breaking leads to a non-zero dipole moment and surface work function difference, indicating the presence of out-of-plane charge polarization. Magnetic properties calculations demonstrate that VSiGeN4 is a 2D-XY magnet with a Berezinskii-Kosterlitz-Thouless temperature of 342 K, while VSiGeP4 and VSiGeAs4 have an out-of-plane magnetization with a Curie temperature below room temperature. The magnetization can be rotated by applying biaxial strain, allowing manipulation of the spin polarization via nonmagnetic means. The spontaneous valley polarization is predicted to be 46, 49, and 70 meV for VSiGeN4, VSiGeP4, and VSiGeAs4, respectively, whose physical origin can be elucidated by employing the model analysis. In particular, the biaxial strain can induce the valley polarization switching from the valence (conduction) band to conduction (valence) band, but it hardly changes the valley polarization strength. Meanwhile, the valley extremum is transformed from the K' (K) to K (K') points. The present work not only provides an underlying insight into the polarization properties of Janus VSiGeZ4 but also offers a class of promising materials for spintronic and valleytronic devices.

Novel valley character and tunable quasi-half-valley metal state in Janus monolayer VSiGeP4.

The manipulation and regulation of valley characteristics have aroused widespread interest in emerging information fields and fundamental research. Realizing valley polarization is one crucial issue for spintronic and valleytronic applications, the concepts of a half-valley metal (HVM) and ferrovalley (FV) materials have been put forward. Then, to separate electron and hole carriers, a fresh concept of a quasi-HVM (QHVM) has been proposed, in which only one type of carrier is valley polarized for electron and hole carriers. Based on first-principles calculations, we demonstrate that the Janus monolayer VSiGeP4 has QHVM character. To well regulate the QHVM state, strain engineering is utilized to adjust the electronic and valley traits of monolayer VSiGeP4. In the discussed strain range, monolayer VSiGeP4 always favors the ferromagnetic ground state and out-of-plane magnetization, which ensures the appearance of spontaneous valley polarization. It is found that the QHVM state can be induced in different electronic correlations (U), and the strain can effectively tune the valley, magnetic, and electronic features to maintain the QHVM state under various U values. Our work opens up a new research idea in the design of multifunctional spintronic and valleytronic devices.

Tunable valley polarization effect and second-order topological state in monolayer FeClSH.

In two-dimensional (2D) materials, breaking the inversion symmetry plays an important role in valleytronics. Ferrovalley (FV) materials can achieve spontaneous valley polarization (VP) without additional modulation due to the magnetic exchange interaction and strong spin-orbit coupling. Using first-principles calculations, we predict a new 2D material, Janus FeClSH, which exhibits a large spontaneous VP. This monolayer is a perfect FV material, where the valence band maximum and conduction band minimum are located at the K/K' point. A large VP of 102.95 meV is spontaneously generated for the case of out-of-plane magnetization. Additionally, we propose that the irradiating circularly polarized light can be used to realize VP for the case of in-plane magnetization. Remarkably, a triangular nanoflake of FeClSH with armchair edges can show nontrivial corner states, exhibiting a second-order topological insulator (SOTI) state. The VP effect and SOTI state are tunable with the Hubbard U parameter, making the FeClSH monolayer promising for the study of the coupling between VP and SOTI.

Tunable abundant valley Hall effect and chiral spin-valley locking in Janus monolayer VCGeN4.

It is both conceptually and practically fascinating to explore fundamental research studies and practical applications of two-dimensional systems with the tunable abundant valley Hall effect. In this work, based on first-principles calculations, the tunable abundant valley Hall effect is proved to appear in Janus monolayer VCGeN4. When the magnetization is along the out-of-plane direction, VCGeN4 is an intrinsic ferromagnetic semiconductor with a valley feature. The intriguing spontaneous valley polarization exists in VCGeN4 due to the common influence of broken inversion and time-reversal symmetries, which makes it easier to realize the anomalous valley Hall effect. Furthermore, we observe that the valley-non-equilibrium quantum anomalous Hall effect is driven by external strain, which is located between two half-valley-metal states. When reversing the magnetization, the spin flipping makes the position of the edge state to change from one valley to another valley, demonstrating an intriguing behavior known as chiral spin-valley locking. Although the easy magnetic axis orientation is along the in-plane direction, we can utilize an external magnetic field to transform the magnetic axis orientation. Moreover, it is found that the valley state, electronic and magnetic properties can be well regulated by the electric field. Our works explore the mechanism of the tunable abundant valley Hall effect by applying an external strain and electric field, which provides a perfect platform to investigate the spin, valley, and topology.

Half‐Valley Ohmic Contact: Contact‐Limited Valley‐Contrasting Current Injection

AbstractThe 2D ferrovalley semiconductor (FVSC) with spontaneous valley polarization offers an exciting material platform for probing Berry phase physics. How FVSC can be incorporated in valleytronic device applications, however, remain an open question. Here, the concept of metal/semiconductor (MS) contact into the realm of valleytronics is generalized. A half‐valley Ohmic contact is proposed based on FVSC/graphene heterostructure, where the two valleys of FVSC separately forms Ohmic and Schottky contacts with those of graphene, thus allowing current to be valley‐selectively injected through the ‘Ohmic’ valley while being blocked in the ‘Schottky’ valley. A theory of contact‐limited valley‐contrasting current injection is developed and such transport mechanism can produce gate‐tunable valley‐polarized injection current. Using RuCl2/graphene heterostructure as an example, a device concept of valleytronic barristor is illustrated, where high valley polarization efficiency and sizable current on/off ratio, can be achieved under experimentally feasible electrostatic gating conditions. These findings uncover contact‐limited valley‐contrasting current injection as an efficient mechanism for valley polarization manipulation, and reveals the potential of valleytronic MS contact as a functional building block of valleytronic device technology.

Strain and stacking induced topological phase transition in bipolar ferromagnetic semiconductor OsClBr

The combination of valleytronics and topology has great potential significance in condensed matter and material physics. Here, based on first-principles calculations, we predict a dipolar ferromagnetic semiconductor OsClBr. Benefiting from strong spin–orbit coupling and the intrinsic exchange interaction of localized d electrons, spontaneous valley polarization occurs. In addition, the tensile strain can induce topological phase transitions between ferrovalley, half-valley-metal, and valley-polarization quantum anomalous Hall (VQAH) phases, which can be attributed to the band inversion between dz2 and dxy/dx2−y2 orbitals of Os atom. Moreover, stacking-dependent topological phase transitions can be found in bilayer OsClBr, and the robustness of VQAH phase in b − 1 configuration under a wide strain range has been proved, which is greatly beneficial for the regulation of quantum states. Our work provides a potential opportunity for the preparation and application of low-power consumption electronics devices.

First-principles prediction of two-dimensional Rare-earth intrinsic ferrovalley materials: Non-Janus GdXY (X≠Y=Cl,Br,I) monolayers

Two-dimensional ferrovalley magnetic materials have attracted much attention due to the applications in valley-based nonvolatile random access memories and valley filters. In this work, using first-principles calculations, we predict a promising class of bipolar magnetic semiconductors, namely non-Janus GdXY(X≠Y=Cl,Br,I) monolayers, which exhibit excellent mechanical and thermal stability, large magnetic moment (8 μB/Gd), and high Curie temperature (above 450 K). When magnetized along the ±z direction, a spontaneous valley polarization can be observed in non-Janus GdXY. Due to the non-zero Berry curvature, the anomalous Hall effect will be able to be observed in non-Janus GdXY. In addition, the system transforms into a semi-semiconductor from a bipolar magnetic semiconductor with increasing biaxial tensile strain. Under the strain of -4%∼+4%, the ferrovalley characteristics can be well maintained. Our findings not only reveal that non-Janus GdXY is a novel room-temperature ferrovalley semiconductor material, but also provide a new platform for designing spintronics and valley electronics devices.

First-principles prediction of the two-dimensional intrinsic ferrovalley material CeX2 (X=F,Cl,Br)

Two-dimensional (2D) ferrovalley semiconductor materials with intrinsic spontaneous valley polarization offer new prospects for valley electronics applications. However, there are only a limited number of known promising candidate materials, which are in urgent need of expansion. In particular, the room-temperature 2D ferrovalley materials are still lacking. In this study, we predicted novel 2D ferromagnetic CeX2 (X=Fe,Cl,Br) monolayers by using first-principles calculations. The monolayer CeX2 is a bipolar magnetic semiconductor with robust dynamical and thermal stabilities, and easy magnetization direction is in the plane. Due to the simultaneous breaking of both inversion symmetry and time-reversal symmetry, the monolayer CeX2 is exhibiting a spontaneous intrinsic valley polarization when magnetized along the out-of-plane z direction. Interestingly, monolayer CeBr2 is a spontaneous intrinsic ferrovalley material with a room temperature of 334 K and an obvious valley splitting of 32 meV. Due to the non-zero valley-contrast Berry curvature, monolayer CeBr2 is a candidate materials for realizing the anomalous valley Hall effect under a suitable applied electric field. Our study provides a theoretical reference for the design of valley electronic devices with anomalous valley Hall effect based on hole-doped CeX2.

Stacking order modulated anomalous valley Hall effect in antiferromagnetic MXene

The valley index is a promising degree of freedom for information processing in electronic devices. However, the researches on valley polarization are mainly focused on ferromagnetic order, which breaks the time reversal symmetry simultaneously. Here, a novel paradigm for achieving stacking order modulated anomalous valley Hall (AVH) effect is proposed in antiferromagnetic monolayers. The paradigm involves the introduction and reversal of nonuniform potentials by modulating the position of substrate, to break the combined symmetry of spatial inversion and time reversal (PT symmetry) and achieve stacking-dependent valley spin splitting. Based on first-principles calculations, we discover spontaneous valley polarization in antiferromagnetic Cr2CH2 MXene and stacking-dependent valley spin splitting in Cr2CH2/Sc2CO2 heterostructure. Furthermore, switching the ferroelectric polarization of monolayer Sc2CO2 results in a semiconductor-metal transition in Cr2CH2/Sc2CO2, accompanied by the disappearance of valley physics. Our findings provide an alternative way to develop controllable valleytronics devices based on antiferromagnetic monolayers.

Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe_{2}.

The pursuit of exotic phases of matter outside of the extreme conditions of a quantizing magnetic field is a long-standing quest of solid state physics. Recent experiments have observed spontaneous valley polarization and fractional Chern insulators in zero magnetic field in twisted bilayers of MoTe_{2}, at partial filling of the topological valence band (ν=-2/3 and -3/5). We study the topological valence band at half filling, using exact diagonalization and density matrix renormalization group calculations. We discover a composite Fermi liquid (CFL) phase even at zero magnetic field that covers a large portion of the phase diagram near twist angle ∼3.6°. The CFL is a non-Fermi liquid phase with metallic behavior despite the absence of Landau quasiparticles. We discuss experimental implications including the competition between the CFL and a Fermi liquid, which can be tuned with a displacement field. The topological valence band has excellent quantum geometry over a wide range of twist angles and a small bandwidth that is, remarkably, reduced by interactions. These key properties stabilize the exotic zero field quantum Hall phases. Finally, we present an optical signature involving "extinguished" optical responses that detects Chern bands with ideal quantum geometry.

Optical spectrum of ferrovalley materials: A case study of Janus H-VSSe

As opposed to the prototypical MoS2 with centroasymmetry, Janus ferrovalley materials such as H-VSSe are less symmetric with the mirror symmetry and time reversal symmetry broken, and hence possess spontaneous valley polarization and strong ferroelasticity. The optical transition is an important means to excite the valley carriers. We investigate the optical spectrum of H-VSSe by using the many-body perturbation-based GW approach and solving the Bethe–Salpeter equation (BSE) to include the electron–hole interactions. It is found that after the GW correction, the band gaps of the quasiparticle bands are much larger than those obtained by the normal density functional theory. The system is ferromagnetic and the valley gaps become non-degenerate due to spin–orbit coupling (SOC). The position of the lowest BSE peak is much lower than the quasiparticle band gap, indicating that the excitonic effect is large. The peak is split into two peaks by the SOC. The binding energy difference between these two BSE peaks is about the same as the difference between the inequivalent valley gaps. Our results show that in Janus H-VSSe the two lowest exciton peaks are from the two inequivalent valleys with different gaps, in contrast to the A and B exciton peaks of MoS2 which are from the same valley.

Janus monolayer ScXY (X≠Y = Cl, Br and I) for piezoelectric and valleytronic application: a first-principle prediction

Coexistence of ferromagnetism, piezoelectricity and valley in two-dimensional (2D) materials is crucial to advance multifunctional electronic technologies. Here, Janus ScXY (X≠Y = Cl, Br and I) monolayers are predicted to be piezoelectric ferromagnetic semiconductors with dynamical, mechanical and thermal stabilities. They all show an in-plane easy axis of magnetization by calculating magnetic anisotropy energy (MAE) including magnetocrystalline anisotropy energy and magnetic shape anisotropy energy. The MAE results show that they intrinsically have no spontaneous valley polarization. The predicted piezoelectric strain coefficients d 11 and d 31 (absolute values) are higher than ones of most 2D materials. Moreover, the d 31 (absolute value) of ScClI reaches up to 1.14 pm V−1, which is highly desirable for ultrathin piezoelectric device application. To obtain spontaneous valley polarization, charge doping are explored to tune the direction of magnetization of ScXY. By appropriate hole doping, their easy magnetization axis can change from in-plane to out-of-plane, resulting in spontaneous valley polarization. Taking ScBrI with 0.20 holes per f.u. as an example, under the action of an in-plane electric field, the hole carriers of K valley turn towards one edge of the sample, which will produce anomalous valley Hall effect, and the hole carriers of Γ valley move in a straight line. These findings could pave the way for designing piezoelectric and valleytronic devices.

Giant spontaneous valley polarization in two-dimensional ferromagnetic heterostructures

Screening two-dimensional (2D) materials with inherent out-of-plane magnetization is the key to spontaneous valley polarization. Based on first-principles calculations, the thermodynamic stability, magnetic orders and electronic band structures of 2D ScX2 (X = Cl, Br and I) monolayers and their van der Waals junctions are studied to identify potential valley materials, while their monolayers and homo-structural bilayers exhibit intrinsic in-plane magnetization. Particularly, ScI2 is found to have a strongest valley polarization effect when its magnetization direction is shifted to the z direction. A strategy is proposed to achieve out-of-plane magnetization by creating hetero-structures with monolayer MSe2 (M=Zr, Hf and Sn). All these constructed heterostructures display out-of-plane magnetization with enhanced valley splitting. The predicted strongest valley splitting reaches about 121 meV in the heterostructure ScI2/ZrSe2, which is much larger than that in the pristine ScI2 monolayer, demonstrating enhanced valley polarization that results from both the compressed ScI2 lattice and the interlayer interaction with MSe2. It is noted that the hybridization of px and py orbitals of I atoms is increased in heterostructures and is responsible for magnetization variation. Our study not only extends the family of 2D spontaneous valley polarization, but also provides in-depth insights for the fundamental investigations of 2D valleytronics.

Large valley polarization and high Curie temperature in single layer XI2 (X = Sc, Y)

Ferrovalley materials with spontaneous valley polarization are the key to valleytronics applications. Therefore, it is important to find materials with relatively large valley polarization. In this work, we theoretically designed two novel two-dimensional ferrovalley materials namely XI2 (X = Sc, Y), which have both high Curie temperature and large valley polarization. The Curie temperature of monolayer ScI2 and YI2 are 138 K and 58 K, the large valley polarization of 97 meV and 108 meV are also predicted in monolayer ScI2 and YI2. The anomalous valley Hall effect is also proposed based on the valley contrasting Berry curvature. In addition, strain engineering can effectively modulate the valley polarization and Curie temperature of monolayer XI2 (X = Sc, Y). The Curie temperature of ScI2 increases with increasing strain, and the valley polarization of YI2 increases with increasing strain. Our findings suggest that monolayer XI2 (X = Sc, Y) is a promising material for valleytronics.

Spin–valley splitting and spontaneous valley polarization in antiferromagnetic Mn2P2X3Y3 monolayers

In the current stage, valley-contrasting physics is mainly rooted in nonmagnetic and/or ferromagnetic hexagonal lattices and is rarely used to observe the simultaneous spin and valley polarization in antiferromagnetic materials. In this work, we propose a general scheme that can be achieved easily in experiments to break the PT joint symmetry of antiferromagnetic structures, that is, introducing an out-of-plane potential gradient to realize spin–valley splitting and spontaneous valley polarization. In combination of the model analysis and first-principles calculations, we translate the concept into Mn2P2X3Y3 monolayers and clarify the valley-related physics. It is obvious that our finding significantly extends the scope of valleytronics in both theory and experiments.