Valley Zeeman Splitting and Valley Polarization of Neutral and Charged Excitons in Monolayer MoTe2 at High Magnetic Fields

Giant Faraday rotation in atomically thin semiconductors

Faraday rotation is a fundamental effect in the magneto-optical response of solids, liquids and gases. Materials with a large Verdet constant find applications in optical modulators, sensors and non-reciprocal devices, such as optical isolators. Here, we demonstrate that the plane of polarization of light exhibits a giant Faraday rotation of several degrees around the A exciton transition in hBN-encapsulated monolayers of WSe2 and MoSe2 under moderate magnetic fields. This results in the highest known Verdet constant of -1.9 × 107 deg T-1 cm-1 for any material in the visible regime. Additionally, interlayer excitons in hBN-encapsulated bilayer MoS2 exhibit a large Verdet constant (VIL ≈ +2 × 105 deg T-1 cm-2) of opposite sign compared to A excitons in monolayers. The giant Faraday rotation is due to the giant oscillator strength and high g-factor of the excitons in atomically thin semiconducting transition metal dichalcogenides. We deduce the complete in-plane complex dielectric tensor of hBN-encapsulated WSe2 and MoSe2 monolayers, which is vital for the prediction of Kerr, Faraday and magneto-circular dichroism spectra of 2D heterostructures. Our results pose a crucial advance in the potential usage of two-dimensional materials in ultrathin optical polarization devices.

Unconventional Piezoelectricity of Two-Dimensional Materials Driven by the Hall Effect

Piezoelectricity has been widely explored for nanoelectromechanical applications, yet its working modes are mainly limited in polar directions. Here we discover the intrinsic electro-mechanical response in crystal materials that is transverse to the conventional polarized direction, which is named unconventional piezoelectricity. A Hall-like mechanism is proposed to interpret unconventional piezoelectricity as charge polarization driven by a built-in electric field for systems with asymmetric Berry curvature distributions. Density functional theory simulations and statistical analyses justify such a mechanism and confirm that unconventional piezoelectricity is a general property for various two-dimensional materials with spin splitting or valley splitting. An empirical formula is derived to connect the conventional and unconventional piezoelectricity. The extended understanding of the piezoelectric tensor in quantum materials opens an opportunity for applications in multidirectional energy conversion, broadband operation, and multifunctional sensing.

Piezoelectricity and valley polarization in a semilithiated 2H-TiTe2 monolayer with near room-temperature ferromagnetism

Two-dimensional ferromagnetic semiconductors with coupled valley physics and piezoelectric responses offer unprecedented opportunities to miniaturize low-power multifunctional integrated devices. Prompted by epitaxial fabrication of nonmagnetic 2H-TiTe2 monolayer on the Au(111) substrate, we predict through both density functional theory and Monte Carlo simulations that the semilithiated 2H-TiTe2 monolayer (Li@2H-TiTe2) is a stable near room-temperature semiconducting ferromagnet. Under an out-of-plane magnetization, Li@2H-TiTe2 exhibits a clean valley polarization up to 160 meV in its conduction band and a valley-contrasting Berry curvature due to the broken inversion and time-reversal symmetries, in favor of achievable anomalous valley Hall effect. Alternatively, the simultaneous charge, spin, valley Hall currents can be realized as well in the ferromagnetic system with circularly polarized light. Furthermore, the missing mirror symmetry generates a scarce vertical piezoelectricity as large as 0.89 pm V-1. These findings indicate that asymmetric surface functionalization by Li deposition on the 2H-TiTe2 monolayer opens up a vital avenue to predesign superior and tailored multifunctional materials.

Rydberg Excitons and Trions in Monolayer MoTe2

Monolayer transition metal dichalcogenide (TMDC) semiconductors exhibit strong excitonic optical resonances, which serve as a microscopic, noninvasive probe into their fundamental properties. Like the hydrogen atom, such excitons can exhibit an entire Rydberg series of resonances. Excitons have been extensively studied in most TMDCs (MoS₂, MoSe₂, WS₂, and WSe₂), but detailed exploration of excitonic phenomena has been lacking in the important TMDC material molybdenum ditelluride (MoTe₂). Here, we report an experimental investigation of excitonic luminescence properties of monolayer MoTe₂ to understand the excitonic Rydberg series, up to 3s. We report a significant modification of emission energies with temperature (4 to 300 K), thereby quantifying the exciton-phonon coupling. Furthermore, we observe a strongly gate-tunable exciton-trion interplay for all the Rydberg states governed mainly by free-carrier screening, Pauli blocking, and band gap renormalization in agreement with the results of first-principles GW plus Bethe-Salpeter equation approach calculations. Our results help bring monolayer MoTe₂ closer to its potential applications in near-infrared optoelectronics and photonic devices.

Valley-optical absorption in planar transition metal dichalcogenide superlattices

In this study, we investigate the optical absorption of a planar superlattice comprising alternatively arranged two-dimensional Transition Metal DiChalcogenide semiconductors. Within a semi-classical model and using the Dirac-like equation in the presence of light interaction as a perturbation, we obtained the governing Hamiltonian. Using this Hamiltonian, we derived a fully analytical relationship for the absorption coefficient of the structure. By calculating the effective mass for different bands and using the Drude-Lorentz model, our approach is able to determine the oscillator strength and the effective refractive index of the structure. We found that the spin-orbit coupling has important effect on the absorption coefficient and energy bands where it reduces the absorption coefficient of the structure from typical value of [Formula: see text]-[Formula: see text], also the valence band experiences a significant blue shift, while the conduction band shows minor changes due to spin orbit coupling. Moreover, the role of incident light angle and light polarization were studied in details at different valleys of [Formula: see text] and [Formula: see text]. The most important finding is that by changing the polarization of incident light, it is possible to increase the absorption coefficients of [Formula: see text] and [Formula: see text] valleys by up to 30 times. For light propagation direction close to perpendicular to the plane of the superlattice, the right-circular polarization is absorbed only by [Formula: see text] valley in contrast to the left-circular polarization, which is absorbed by the [Formula: see text] valley. Our model might be used to design newly developed 2D optovalleytronic devices.

Spontaneous Valley Polarization in a Ferromagnetic Fe(OH)2 Monolayer

At present, creating sizable spontaneous valley polarization is at the center of the study of valleytronics, which, however, is still a huge challenge. In this work, we determined that the ferromagnetic Fe(OH)₂ monolayer of the hexagonal lattice is a highly appealing candidate for valleytronics by using first-principles calculations in conjunction with tight-binding model analysis. In light of the simultaneous inversion symmetry breaking and time-reversal symmetry breaking, we illustrated that the strong spin-orbit coupling and robust ferromagnetic exchange interaction cause a spontaneous valley polarization as large as 67 meV for Fe(OH)₂, indicative of room-temperature application. In addition, the physics of valley-selective circular dichroism, spin/valley Hall effects, and topological phase transition were also discussed.

Spontaneous Valley Polarization Caused by Crystalline Symmetry Breaking in Nonmagnetic LaOMX2 Monolayers

In order to achieve valley polarization, breaking the time-reversal symmetry in two-dimensional hexagonal lattices with inversion asymmetry is the heart of current valleytronic research, which, however, has caused studies to stagnate due to the inevitable drawbacks. In this work, we go beyond the conventional paradigm and demonstrate the novel valley physics caused by lowering the crystalline symmetry instead of breaking the time-reversal symmetry. In particular, we translate our concept into concrete nonmagnetic LaOMX₂ monolayers with a tetragonal lattice, confirming that a spontaneous structure distortion can cause the long-sought, considerably large valley polarization. In detail, the physics of valley-orbital coupling, valley-orbital-layer coupling, valley-contrasting linear dichroism, and interlayer exciton valleytronics are discussed.

Prolonging valley polarization lifetime through gate-controlled exciton-to-trion conversion in monolayer molybdenum ditelluride

Monolayer 2D semiconductors provide an attractive option for valleytronics due to valley-addressability. But the short valley-polarization lifetimes for excitons have hindered potential valleytronic applications. In this paper, we demonstrate a strategy for prolonging the valley-polarization lifetime by converting excitons to trions through efficient gate control and exploiting the much longer valley-polarization lifetimes for trions than for excitons. At charge neutrality, the valley lifetime of monolayer MoTe₂ increases by a factor of 1000 to the order of nanoseconds from excitons to trions. The exciton-to-trion conversion changes the dominant depolarization mechanism from the fast electron-hole exchange for excitons to the slow spin-flip process for trions. Moreover, the degree of valley polarization increases to 38% for excitons and 33% for trions through electrical manipulation. Our results reveal the depolarization dynamics and the interplay of various depolarization channels for excitons and trions, providing an effective strategy for prolonging the valley polarization.

Here, the authors devise a strategy for prolonging the valley polarization lifetime in monolayer MoTe₂ by converting excitons to trions through gate control, and by taking advantage of the longer valley polarization lifetime of trions.

Janus 2H-VSSe monolayer: two-dimensional valleytronic semiconductor with nonvolatile valley polarization

Valleytronic as a hot topic in recent years focuses on electrons' valley degree of freedom as a quantum information carrier. Here, by combining two-bandk.pmodel with high-throughput density functional theory (DFT) calculations, the valley states of Janus 2H-VSSe monolayer are studied which have spontaneous polarization. Nonvolatile valley polarization state is mainly arises from intrinsic ferromagnetism contributed by V-3d electronic configuration and not the spontaneous out-of-plane dipole moment of VSSe monolayer. The effective Hamiltonian model and DFT calculations both showed that the valley splitting mainly originates from the smaller spin splitting coming from the spin-orbit coupling effect rather than the spin splitting of magnetic exchange field. By using the effective Dirac Hamiltonian and Kubo formula, we further calculated the longitudinal and transversal conductivities and absorption spectra of VSSe monolayer which exhibits an anomalous valley Hall effect and clear valley-selective circular dichroism. Our calculations indicate that the modification of valley and spin splitting related to Berry curvature by applying an external strain is more noticeable than by the change of the magnetic moment orientation and electric field. We found that carriers accumulation with particular spin and valley label can be manipulated by tuning effective Hamiltonian parameters. The coexistence of robust in-plane magnetic ordering and spontaneous valley polarization of 2H-VSSe monolayer supports the possibility of applications in spintronics, valleytronics and optoelectronics devices.

Enhanced Valley Polarization in WS2 /LaMnO3 Heterostructure

Monolayer transition metal dichalcogenides have attracted great attention for potential applications in valleytronics. However, the valley polarization degree is usually not high because of the intervalley scattering. Here, a largely enhanced valley polarization up to 80% in monolayer WS₂ under nonresonant excitation at 4.2 K is demonstrated using WS₂ /LaMnO₃ thin film heterostructure, which is much higher than that for monolayer WS₂ on SiO₂ /Si substrate with a valley polarization of 15%. Furthermore, the greatly enhanced valley polarization can be maintained to a high temperature of about 160 K with a valley polarization of 53%. The temperature dependence of valley polarization is strongly correlated with the thermomagnetic curve of LaMnO₃ , indicating an exciton-magnon coupling between WS₂ and LaMnO₃ . A simple model is introduced to illustrate the underlying mechanisms. The coupling of WS₂ and LaMnO₃ is further confirmed with an observation of two interlayer excitons with opposite valley polarizations in the heterostructure, resulting from the spin-orbit coupling induced splitting of the conduction bands in monolayer transition metal dichalcogenides. The results provide a pathway to control the valleytronic properties of transition metal dichalcogenides by means of ferromagnetic van der Waals engineering, paving a way to practical valleytronic applications.

Many-Body Exciton and Intervalley Correlations in Heavily Electron-Doped WSe2 Monolayers

In monolayer transition-metal dichalcogenide semiconductors, many-body correlations can manifest in optical spectra when electron-hole pairs (excitons) are photoexcited into a 2D Fermi sea of mobile carriers. At low carrier densities, the formation of charged excitons (X^±) is well documented. However, in WSe₂ monolayers, an additional absorption resonance, often called X^-', emerges at high electron density. Its origin is not understood. Here, we investigate the X^-' state via polarized absorption spectroscopy of gated WSe₂ monolayers in magnetic fields to 60T. Field-induced filling and emptying of the lowest optically active Landau level in the K' valley causes repeated quenching of the corresponding optical absorption. Surprisingly, these quenchings are accompanied by absorption changes to higher Landau levels in both K' and K valleys, which are unoccupied. These results cannot be reconciled within a single-particle picture, and demonstrate the many-body nature and intervalley correlations of the X^-' quasiparticle state.

Site-controlled telecom-wavelength single-photon emitters in atomically-thin MoTe2

Quantum emitters (QEs) in two-dimensional transition metal dichalcogenides (2D TMDCs) have advanced to the forefront of quantum communication and transduction research. To date, QEs capable of operating in O-C telecommunication bands have not been demonstrated in TMDCs. Here we report site-controlled creation of telecom QEs emitting over the 1080 to 1550 nm telecommunication wavelength range via coupling of 2D molybdenum ditelluride (MoTe₂) to strain inducing nano-pillar arrays. Hanbury Brown and Twiss experiments conducted at 10 K reveal clear photon antibunching with 90% single-photon purity. The photon antibunching can be observed up to liquid nitrogen temperature (77 K). Polarization analysis further reveals that while some QEs display cross-linearly polarized doublets with ~1 meV splitting resulting from the strain induced anisotropic exchange interaction, valley degeneracy is preserved in other QEs. Valley Zeeman splitting as well as restoring of valley symmetry in cross-polarized doublets are observed under 8 T magnetic field.

Single-photon emitters in 2D semiconductors hold promise for quantum applications, but usually operate in the 500-800 nm wavelength range. Here, the authors report site-controlled creation of quantum emitters in the telecommunication wavelength window by coupling 2D MoTe2 to strain inducing nano-pillar arrays.

Synthesis of Large-Scale Monolayer 1T'-MoTe2 and Its Stabilization via Scalable hBN Encapsulation

Out of the different structural phases of molybdenum ditelluride (MoTe2), the distorted octahedral 1T' possesses great interest for fundamental physics and is a promising candidate for the implementation of innovative devices such as topological transistors. Indeed, 1T'-MoTe2 is a semimetal with superconductivity, which has been predicted to be a Weyl semimetal and a quantum spin Hall insulator in bulk and monolayer form, respectively. Large instability of monolayer 1T'-MoTe2 in environmental conditions, however, has made its investigation extremely challenging so far. In this work, we demonstrate homogeneous growth of large single-crystal (up to 500 μm) monolayer 1T'-MoTe2 via chemical vapor deposition (CVD) and its stabilization in air with a scalable encapsulation approach. The encapsulant is obtained by electrochemically delaminating CVD hexagonal boron nitride (hBN) from copper foil, and it is applied on the freshly grown 1T'-MoTe2 via a top-down dry lamination step. The structural and electrical properties of encapsulated 1T'-MoTe2 have been monitored over several months to assess the degree of degradation of the material. We find that when encapsulated with hBN, the lifetime of monolayer 1T'-MoTe2 successfully increases from a few minutes to more than a month. Furthermore, the encapsulated monolayer can be subjected to transfer, device processing, and heating and cooling cycles without degradation of its properties. The potential of this scalable heterostack is confirmed by the observation of signatures of low-temperature phase transition in monolayer 1T'-MoTe2 by both Raman spectroscopy and electrical measurements. The growth and encapsulation methods reported in this work can be employed for further fundamental studies of this enticing material as well as facilitate the technological development of monolayer 1T'-MoTe2.

Strong valley splitting ind0two-dimensional SnO induced by magnetic proximity effect

Strong magnetic interfacial coupling in van der Waals heterostructures is important for designing novel electronic devices. Besides the most studied transition metal dichalcogenides (TMDCs) materials, we demonstrate that the valley splitting can be activated in two-dimensional tetragonald⁰metal oxide, SnO, via the magnetic proximity effect by EuBrO. In SnO/EuBrO, the valley splitting of SnO can reach ∼46 meV, which is comparable to many TMDCs and equivalent to an external magnetic field of 800 T. In addition, the valley splitting can be further enhanced by adjusting interlayer distance and applying uniaxial strains. A design principle of new spintronic device based on this unique electronic structure of SnO/EuBrO has been proposed. Our findings indicate that SnO is a promising material for future valleytronics applications.

Measurement of Conduction and Valence Bands g-Factors in a Transition Metal Dichalcogenide Monolayer

The electron valley and spin degree of freedom in monolayer transition-metal dichalcogenides can be manipulated in optical and transport measurements performed in magnetic fields. The key parameter for determining the Zeeman splitting, namely, the separate contribution of the electron and hole g factor, is inaccessible in most measurements. Here we present an original method that gives access to the respective contribution of the conduction and valence band to the measured Zeeman splitting. It exploits the optical selection rules of exciton complexes, in particular the ones involving intervalley phonons, avoiding strong renormalization effects that compromise single particle g-factor determination in transport experiments. These studies yield a direct determination of single band g factors. We measure g_{c1}=0.86±0.1, g_{c2}=3.84±0.1 for the bottom (top) conduction bands and g_{v}=6.1±0.1 for the valence band of monolayer WSe_{2}. These measurements are helpful for quantitative interpretation of optical and transport measurements performed in magnetic fields. In addition, the measured g factors are valuable input parameters for optimizing band structure calculations of these 2D materials.

Valley pseudospin relaxation of charged excitons in monolayer MoTe2

Zeeman effect induced by the magnetic field introduces a splitting between the two valleys at K ⁺ and K ^- points of the Brillouin zone in monolayer semiconducting transition metal dichalcogenides. In consequence, the photoluminescence signal exhibits a field dependent degree of circular polarization. We present a comprehensive study of this effect in the case of a trion in monolayer MoTe₂, showing that although time integrated data allows us to deduce a g-factor of the trion state, such an analysis cannot be substantiated by the timescales revealed in the time-resolved experiments.

Quasi-Binary Transition Metal Dichalcogenide Alloys: Thermodynamic Stability Prediction, Scalable Synthesis, and Application

Transition metal dichalcogenide (TMDCs) alloys could have a wide range of physical and chemical properties, ranging from charge density waves to superconductivity and electrochemical activities. While many exciting behaviors of unary TMDCs have been demonstrated, the vast compositional space of TMDC alloys has remained largely unexplored due to the lack of understanding regarding their stability when accommodating different cations or chalcogens in a single-phase. Here, a theory-guided synthesis approach is reported to achieve unexplored quasi-binary TMDC alloys through computationally predicted stability maps. Equilibrium temperature-composition phase diagrams using first-principles calculations are generated to identify the stability of 25 quasi-binary TMDC alloys, including some involving non-isovalent cations and are verified experimentally through the synthesis of a subset of 12 predicted alloys using a scalable chemical vapor transport method. It is demonstrated that the synthesized alloys can be exfoliated into 2D structures, and some of them exhibit: i) outstanding thermal stability tested up to 1230 K, ii) exceptionally high electrochemical activity for the CO₂ reduction reaction in a kinetically limited regime with near zero overpotential for CO formation, iii) excellent energy efficiency in a high rate Li-air battery, and iv) high break-down current density for interconnect applications. This framework can be extended to accelerate the discovery of other TMDC alloys for various applications.

2D materials beyond graphene toward Si integrated infrared optoelectronic devices

Since the discovery of graphene in 2004, it has become a worldwide hot topic due to its fascinating properties. However, the zero band gap and weak light absorption of graphene strictly restrict its applications in optoelectronic devices. In this regard, semiconducting two-dimensional (2D) materials are thought to be promising candidates for next-generation optoelectronic devices. Infrared (IR) light has gained intensive attention due to its vast applications, including night vision, remote sensing, target acquisition, optical communication, etc. Consequently, the generation, modulation, and detection of IR light are crucial for practical applications. Due to the van der Waals interaction between 2D materials and Si, the lattice mismatch of 2D materials and Si can be neglected; consequently, the integration process can be achieved easily. Herein, we review the recent progress of semiconducting 2D materials in IR optoelectronic devices. Firstly, we introduce the background and motivation of the review. Then, the suitable materials for IR applications are presented, followed by a comprehensive review of the applications of 2D materials in light emitting devices, optical modulators, and photodetectors. Finally, the problems encountered and further developments are summarized. We believe that milestone investigations of IR optoelectronics based on 2D materials beyond graphene will emerge soon, which will bring about great industrial revelations in 2D material-based integrated nanodevice commercialization.

Ab Initio Studies of Exciton g Factors: Monolayer Transition Metal Dichalcogenides in Magnetic Fields

The effect of a magnetic field on the optical absorption in semiconductors has been measured experimentally and modeled theoretically for various systems in previous decades. We present a new first-principles approach to systematically determine the response of excitons to magnetic fields, i.e., exciton g factors. By utilizing the GW-Bethe-Salpeter equation methodology we show that g factors extracted from the Zeeman shift of electronic bands are strongly renormalized by many-body effects which we trace back to the extent of the excitons in reciprocal space. We apply our approach to monolayers of transition metal dichalcogenides (MoS_{2}, MoSe_{2}, MoTe_{2}, WS_{2}, and WSe_{2}) with strongly bound excitons for which g factors are weakened by about 30%.

Synthesis of Co-Doped MoS2 Monolayers with Enhanced Valley Splitting

Internal magnetic moments induced by magnetic dopants in MoS₂ monolayers are shown to serve as a new means to engineer valley Zeeman splitting (VZS). Specifically, successful synthesis of monolayer MoS₂ doped with the magnetic element Co is reported, and the magnitude of the valley splitting is engineered by manipulating the dopant concentration. Valley splittings of 3.9, 5.2, and 6.15 meV at 7 T in Co-doped MoS₂ with Co concentrations of 0.8%, 1.7%, and 2.5%, respectively, are achieved as revealed by polarization-resolved photoluminescence (PL) spectroscopy. Atomic-resolution electron microscopy studies clearly identify the magnetic sites of Co substitution in the MoS₂ lattice, forming two distinct types of configurations, namely isolated single dopants and tridopant clusters. Density functional theory (DFT) and model calculations reveal that the observed enhanced VZS arises from an internal magnetic field induced by the tridopant clusters, which couples to the spin, atomic orbital, and valley magnetic moment of carriers from the conduction and valence bands. The present study demonstrates a new method to control the valley pseudospin via magnetic dopants in layered semiconducting materials, paving the way toward magneto-optical and spintronic devices.

Polarization-Dependent Optical Properties and Optoelectronic Devices of 2D Materials

The development of optoelectronic devices requires breakthroughs in new material systems and novel device mechanisms, and the demand recently changes from the detection of signal intensity and responsivity to the exploration of sensitivity of polarized state information. Two-dimensional (2D) materials are a rich family exhibiting diverse physical and electronic properties for polarization device applications, including anisotropic materials, valleytronic materials, and other hybrid heterostructures. In this review, we first review the polarized-light-dependent physical mechanism in 2D materials, then present detailed descriptions in optical and optoelectronic properties, involving Raman shift, optical absorption, and light emission and functional optoelectronic devices. Finally, a comment is made on future developments and challenges. The plethora of 2D materials and their heterostructures offers the promise of polarization-dependent scientific discovery and optoelectronic device application.

Momentum-Dark Intervalley Exciton in Monolayer Tungsten Diselenide Brightened via Chiral Phonon

Inversion symmetry breaking and 3-fold rotation symmetry grant the valley degree of freedom to the robust exciton in monolayer transition-metal dichalcogenides, which can be exploited for valleytronics applications. However, the short lifetime of the exciton significantly constrains the possible applications. In contrast, the dark exciton could be long-lived but does not necessarily possess the valley degree of freedom. In this work, we report the identification of the momentum-dark, intervalley exciton in monolayer WSe₂ through low-temperature magneto-photoluminescence spectra. Interestingly, the intervalley exciton is brightened through the emission of a chiral phonon at the corners of the Brillouin zone (K point), and the pseudoangular momentum of the phonon is transferred to the emitted photon to preserve the valley information. The chiral phonon energy is determined to be ∼23 meV, based on the experimentally extracted exchange interaction (∼7 meV), in excellent agreement with the theoretical expectation of 24.6 meV. The long-lived intervalley exciton with valley degree of freedom adds an exciting quasiparticle for valleytronics, and the coupling between the chiral phonon and intervalley exciton furnishes a venue for valley spin manipulation.

Direct Observation of Gate-Tunable Dark Trions in Monolayer WSe2

Spin-forbidden intravalley dark excitons in tungsten-based transition-metal dichalcogenides (TMDCs), because of their unique spin texture and long lifetime, have attracted intense research interest. Here, we show that we can control the dark exciton electrostatically by dressing it with one free electron or free hole, forming the dark trions. The existence of the dark trions is suggested by the unique magneto-photoluminescence spectroscopy pattern of the boron nitride (BN)-encapsulated monolayer WSe₂ device at low temperature. The unambiguous evidence of the dark trions is further obtained by directly resolving the radiation pattern of the dark trions through back focal plane imaging. The dark trions possess a binding energy of ∼15 meV, and they inherit the long lifetime and large g-factor from the dark exciton. Interestingly, under the out-of-plane magnetic field, dressing the dark exciton with one free electron or hole results in distinctively different valley polarization of the emitted photon, as a result of the different intervalley scattering mechanism for the electron and hole. Finally, the lifetime of the positive dark trion can be further tuned from ∼50 ps to ∼215 ps by controlling the gate voltage. The gate-tunable dark trions usher in new opportunities for excitonic optoelectronics and valleytronics.

Enhancing and controlling valley magnetic response in MoS2/WS2 heterostructures by all-optical route

Van der Waals heterostructures of transition metal dichalcogenides with interlayer coupling offer an exotic platform to realize fascinating phenomena. Due to the type II band alignment of these heterostructures, electrons and holes are separated into different layers. The localized electrons induced doping in one layer, in principle, would lift the Fermi level to cross the spin-polarized upper conduction band and lead to strong manipulation of valley magnetic response. Here, we report the significantly enhanced valley Zeeman splitting and magnetic tuning of polarization for the direct optical transition of MoS₂ in MoS₂/WS₂ heterostructures. Such strong enhancement of valley magnetic response in MoS₂ stems from the change of the spin-valley degeneracy from 2 to 4 and strong many-body Coulomb interactions induced by ultrafast charge transfer. Moreover, the magnetic splitting can be tuned monotonically by laser power, providing an effective all-optical route towards engineering and manipulating of valleytronic devices and quantum-computation.

Van der Waals heterostructures may offer a suitable platform for all-optical manipulation of valleytronic devices. Here, the authors observe a strong enhancement of the valley magnetic response in MoS₂, and magnetic tuning of the polarization of MoS₂ direct optical transition

Revealing exciton masses and dielectric properties of monolayer semiconductors with high magnetic fields

In semiconductor physics, many essential optoelectronic material parameters can be experimentally revealed via optical spectroscopy in sufficiently large magnetic fields. For monolayer transition-metal dichalcogenide semiconductors, this field scale is substantial-tens of teslas or more-due to heavy carrier masses and huge exciton binding energies. Here we report absorption spectroscopy of monolayer [Formula: see text], and [Formula: see text] in very high magnetic fields to 91 T. We follow the diamagnetic shifts and valley Zeeman splittings of not only the exciton's [Formula: see text] ground state but also its excited [Formula: see text] Rydberg states. This provides a direct experimental measure of the effective (reduced) exciton masses and dielectric properties. Exciton binding energies, exciton radii, and free-particle bandgaps are also determined. The measured exciton masses are heavier than theoretically predicted, especially for Mo-based monolayers. These results provide essential and quantitative parameters for the rational design of opto-electronic van der Waals heterostructures incorporating 2D semiconductors.

Hyperfine interaction in atomically thin transition metal dichalcogenides

The spin dynamics of localized charge carriers is mainly driven by hyperfine interaction with nuclear spins. Here we develop a theory of hyperfine interaction in transition metal dichalcogenide monolayers. Using group representation theory and the tight binding model we derive effective Hamiltonians of the intervalley hyperfine interaction in the conduction and valence bands. The spin-valley locking and pronounced spin-orbit splitting lead to a specific form of hyperfine interaction, which we call "helical". We also demonstrate that the hyperfine interaction is noncollinear for chalcogen atoms in the general case. At the same time in the upper valence band the hyperfine interaction is purely of the Ising type, which suggests that the spin-valley polarization of localized holes in transition metal dichalcogenide monolayers can be conserved for a particularly long time.

Modifying the Band Gap of Semiconducting Two-Dimensional Materials by Polymer Assembly into Different Structures

Polyethylene glycol (PEG) assembled on the surface of two-dimensional tungsten disulfide (WS₂) into a limited number of nanoislands (NIs), nanoshells (NSs), and granular nanoparticulates (GNPs) depending on its chain length. NI assemblies showed a nonmeasurable shift of photoluminescence (PL) and the A and B absorption peaks of WS₂. This confirmed that the electronic doping by thiol is not effective. The PEG NS assembly displayed a smaller red shift of the PL and a slight decrease of the energy difference between the A and B absorption peaks of WS₂. However, increasing the dielectric function on the surface of WS₂ has a small influence on their optical properties. The PEG NP assembly on WS₂ exhibited a significant red shift of the PL spectrum and a large decrease of the energy difference between A and B absorption peaks. Deforming the WS₂ sheet by the PEG NP assembly decreased the orbital coupling and lowered the electronic direct band gap significantly. Raman bands of WS₂ are shifted to a higher frequency on improving its mechanical strength after the PEG assembly.

Engineering Valley Polarization of Monolayer WS2 : A Physical Doping Approach

The emerging field of valleytronics has boosted intensive interests in investigating and controlling valley polarized light emission of monolayer transition metal dichalcogenides (1L TMDs). However, so far, the effective control of valley polarization degree in monolayer TMDs semiconductors is mostly achieved at liquid helium cryogenic temperature (4.2 K), with the requirements of high magnetic field and on-resonance laser, which are of high cost and unwelcome for applications. To overcome this obstacle, it is depicted that by electrostatic and optical doping, even at temperatures far above liquid helium cryogenic temperature (80 K) and under off-resonance laser excitation, a competitive valley polarization degree of monolayer WS₂ can be achieved (more than threefold enhancement). The enhanced polarization is understood by a general doping dependent valley relaxation mechanism, which agrees well with the unified theory of carrier screening effects on intervalley scattering process. These results demonstrate that the tunability corresponds to an effective magnet field of ≈10 T at 4.2 K. This work not only serves as a reference to future valleytronic studies based on monolayer TMDs with various external or native carrier densities, but also provides an alternative approach toward enhanced polarization degree, which denotes an essential step toward practical valleytronic applications.

Valley-contrasting optics of interlayer excitons in Mo- and W-based bulk transition metal dichalcogenides

Recently, spatially indirect ("interlayer") excitons have been discovered in bulk 2H-MoTe2. They are theoretically predicted to exist in other Mo-based transition metal dichalcogenides (TMDCs) and are expected to be present in W-based TMDCs as well. We investigate interlayer excitons (XIL) in bulk 2H-MoSe2 and 2H-WSe2 using valley-resolved magneto-reflectance spectroscopy under high magnetic fields of up to 29 T combined with ab initio GW-BSE calculations. In the experiments, we observe interlayer excitons in MoSe2, while their signature is surprisingly absent in WSe2. In the calculations, we find that interlayer excitons exist in both Mo- and W-based TMDCs. However, their energetic positions and their oscillator strengths are remarkably different. In Mo-based compounds, the interlayer exciton resonance XIL is clearly separated from the intralayer exciton X1sA and has a high amplitude. In contrast, in W-based compounds, XIL is close in energy to the intralayer A exciton X1sA and possesses a small oscillator strength, which explains its absence in the experimental data of WSe2. Our combined experimental and theoretical observations demonstrate that interlayer excitons can gain substantial oscillator strength by mixing with intralayer states and hence pave the way for exploring interlayer exciton physics in Mo-based bulk transition metal dichalcogenides.

Large valley polarization in monolayer MoTe2 on a magnetic substrate

Very large valley polarization and anomalous valley Hall effects were found in MoTe₂ monolayers deposited on RbMnCl₃ magnetic substrates.

Giant Valley Splitting and Valley Polarized Plasmonics in Group V Transition-Metal Dichalcogenide Monolayers

Two-dimensional group VI transition-metal dichalcogenides (TMDs) provide a promising platform to encode and manipulate quantum information in the valleytronics. However, the two valleys are energetically degenerate, protected by time-reversal symmetry (TRS). To lift this degeneracy, one needs to break the TRS by either applying an external magnetic field or using a magnetic rare-earth oxide substrate. Here, we predict a different strategy to achieve this goal. We propose that the ferromagnetic group V TMD monolayer, in which the TRS is intrinsically broken, can produce a larger valley and spin splitting. A polarized ZnS(0001) surface is also used as a substrate, which shifts the valleys to the low-energy regime (near the Fermi level). Moreover, by calculating its collective electronic excitation behaviors, we show that such a system hosts a giant valley polarized terahertz plasmonics. Our results demonstrate a new way to design and use valleytronic devices, which are both fundamentally and technologically significant.

Electronic and Optoelectronic Applications Based on 2D Novel Anisotropic Transition Metal Dichalcogenides

With the continuous exploration of 2D transition metal dichalcogenides (TMDs), novel high-performance devices based on the remarkable electronic and optoelectronic natures of 2D TMDs are increasingly emerging. As fresh blood of 2D TMD family, anisotropic MTe2 and ReX2 (M = Mo, W, and X = S, Se) have drawn increasing attention owing to their low-symmetry structures and charming properties of mechanics, electronics, and optoelectronics, which are suitable for the applications of field-effect transistors (FETs), photodetectors, thermoelectric and piezoelectric applications, especially catering to anisotropic devices. Herein, a comprehensive review is introduced, concentrating on their recent progresses and various applications in recent years. First, the crystalline structure and the origin of the strong anisotropy characterized by various techniques are discussed. Specifically, the preparation of these 2D materials is presented and various growth methods are summarized. Then, high-performance applications of these anisotropic TMDs, including FETs, photodetectors, and thermoelectric and piezoelectric applications are discussed. Finally, the conclusion and outlook of these applications are proposed.

Zeeman splitting via spin-valley-layer coupling in bilayer MoTe2

Atomically thin monolayer transition metal dichalcogenides possess coupling of spin and valley degrees of freedom. The chirality is locked to identical valleys as a consequence of spin-orbit coupling and inversion symmetry breaking, leading to a valley analog of the Zeeman effect in presence of an out-of-plane magnetic field. Owing to the inversion symmetry in bilayers, the photoluminescence helicity should no longer be locked to the valleys. Here we show that the Zeeman splitting, however, persists in 2H-MoTe₂ bilayers, as a result of an additional degree of freedom, namely the layer pseudospin, and spin-valley-layer locking. Unlike monolayers, the Zeeman splitting in bilayers occurs without lifting valley degeneracy. The degree of circularly polarized photoluminescence is tuned with magnetic field from -37% to 37%. Our results demonstrate the control of degree of freedom in bilayer with magnetic field, which makes bilayer a promising platform for spin-valley quantum gates based on magnetoelectric effects.Monolayer transition metal dichalcogenides host a valley splitting in magnetic field analogous to the Zeeman effect. Here, the authors report that the Zeeman splitting still persists in bilayers of MoTe₂ without lifting the valley degeneracy, due to spin-valley-layer coupling.

Magnetic Proximity Effects in Transition-Metal Dichalcogenides: Converting Excitons

The two-dimensional character and reduced screening in monolayer transition-metal dichalcogenides (TMDs) lead to the ubiquitous formation of robust excitons with binding energies orders of magnitude larger than in bulk semiconductors. Focusing on neutral excitons, bound electron-hole pairs that dominate the optical response in TMDs, it is shown that they can provide fingerprints for magnetic proximity effects in magnetic heterostructures. These proximity effects cannot be described by the widely used single-particle description but instead reveal the possibility of a conversion between optically inactive and active excitons by rotating the magnetization of the magnetic substrate. With recent breakthroughs in fabricating Mo- and W-based magnetic TMD heterostructures, this emergent optical response can be directly tested experimentally.

Interlayer excitons in a bulk van der Waals semiconductor

Bound electron-hole pairs called excitons govern the electronic and optical response of many organic and inorganic semiconductors. Excitons with spatially displaced wave functions of electrons and holes (interlayer excitons) are important for Bose-Einstein condensation, superfluidity, dissipationless current flow, and the light-induced exciton spin Hall effect. Here we report on the discovery of interlayer excitons in a bulk van der Waals semiconductor. They form due to strong localization and spin-valley coupling of charge carriers. By combining high-field magneto-reflectance experiments and ab initio calculations for 2H-MoTe₂, we explain their salient features: the positive sign of the g-factor and the large diamagnetic shift. Our investigations solve the long-standing puzzle of positive g-factors in transition metal dichalcogenides, and pave the way for studying collective phenomena in these materials at elevated temperatures.Excitons, quasi-particles of bound electron-hole pairs, are at the core of the optoelectronic properties of layered transition metal dichalcogenides. Here, the authors unveil the presence of interlayer excitons in bulk van der Waals semiconductors, arising from strong localization and spin-valley coupling of charge carriers.

The magnetic proximity effect and electrical field tunable valley degeneracy in MoS2/EuS van der Waals heterojunctions

We report the magnetic proximity effect (MPE) and valley non-degeneracy in monolayer MoS₂ and magnetic semiconductor EuS thin film heterojunctions studied by density functional theory (DFT) with the vdW-DF2 correlations. Magnetic moments are observed in MoS₂ due to the MPE when forming chemical or van der Waals (vdW) adsorption states with EuS. Spin-orbit coupling (SOC) leads to observable valley non-degeneracy of MoS₂ at the K (K') points in the Brillouin zone. The valley Zeeman splitting energy E_z can reach 5.1 meV and 37.3 meV for the vdW and chemical adsorption states, corresponding to a magnetic exchange field (MEF) of 22 T and 160 T respectively. By applying a gate voltage across the MoS₂/EuS interface, it is found that E_z can be tuned from 1.8 meV to 8.2 meV and from 24.5 meV to 53.8 meV for vdW and chemical adsorption states respectively. The strong MPE, large and tunable valley degeneracy in 2D material and ferromagnetic semiconductor/insulator vdW heterojunctions demonstrate their promising potential for novel optoelectronic and valleytronic device applications.

Intrinsic valley polarization of magnetic VSe2 monolayers

Intrinsic valley polarization can be obtained in VSe₂ monolayers with broken inversion symmetry and time reversal symmetry. First-principles investigations reveal that the magnitude of the valley splitting in magnetic VSe₂ induced by spin-orbit coupling reaches as high as 78.2 meV and can be linearly tuned by biaxial strain. Besides conventional polarized light, hole doping or illumination with light of proper frequency can offer effective routes to realize valley polarization. Moreover, spin-orbit coupling in monolayer VSe₂ breaks not only the valley degeneracy but also the three-fold rotational symmetry in band structure. The intrinsic and tunable valley splitting and the breaking of optical isotropy bring additional benefits to valleytronic and optoelectronic applications.

Emptying Dirac valleys in bismuth using high magnetic fields

The Fermi surface of elemental bismuth consists of three small rotationally equivalent electron pockets, offering a valley degree of freedom to charge carriers. A relatively small magnetic field can confine electrons to their lowest Landau level. This is the quantum limit attained in other dilute metals upon application of sufficiently strong magnetic field. Here we report on the observation of another threshold magnetic field never encountered before in any other solid. Above this field, B_empty, one or two valleys become totally empty. Drying up a Fermi sea by magnetic field in the Brillouin zone leads to a manyfold enhancement in electric conductance. We trace the origin of the large drop in magnetoresistance across B_empty to transfer of carriers between valleys with highly anisotropic mobilities. The non-interacting picture of electrons with field-dependent mobility explains most results but the Coulomb interaction may play a role in shaping the fine details.

In-Plane 2H-1T' MoTe2 Homojunctions Synthesized by Flux-Controlled Phase Engineering

The fabrication of in-plane 2H-1T' MoTe₂ homojunctions by the flux-controlled, phase-engineering of few-layer MoTe₂ from Mo nanoislands is reported. The phase of few-layer MoTe₂ is controlled by simply changing Te atomic flux controlled by the temperature of the reaction vessel. Few-layer 2H MoTe₂ is formed with high Te flux, while few-layer 1T' MoTe₂ is obtained with low Te flux. With medium flux, few-layer in-plane 2H-1T' MoTe₂ homojunctions are synthesized. As-synthesized MoTe₂ is characterized by Raman spectroscopy and X-ray photoelectron spectroscopy. Kelvin probe force microscopy and Raman mapping confirm that in-plane 2H-1T' MoTe₂ homojunctions have abrupt interfaces between 2H and 1T' MoTe₂ domains, possessing a potential difference of about 100 mV. It is further shown that this method can be extended to create patterned metal-semiconductor junctions in MoTe₂ in a two-step lithographic synthesis. The flux-controlled phase engineering method could be utilized for the large-scale controlled fabrication of 2D metal-semiconductor junctions for next-generation electronic and optoelectronic devices.

Strain engineering of phonon thermal transport properties in monolayer 2H-MoTe2

The effect of strain on the phonon properties such as phonon group velocity, phonon anharmonicity, phonon lifetime, and lattice thermal conductivity of monolayer 2H-MoTe₂is studied by solving the Boltzmann transport equation based on first principles calculations.

Excitonic Valley Effects in Monolayer WS2 under High Magnetic Fields

Transition-metal dichalcogenides can be easily produced as atomically thin sheets, exhibiting the possibility to optically polarize and read out the valley pseudospin of extremely stable excitonic quasiparticles present in these 2D semiconductors. Here, we investigate a monolayer of tungsten disulfide in high magnetic fields up to 30 T via photoluminescence spectroscopy at low temperatures. The valley degeneracy is lifted for all optical features, particularly for excitons, singlet and triplet trions, for which we determine the g factor separately. While the observation of a diamagnetic shift of the exciton and trion resonances gives us insight into the real-space extension of these quasiparticles, magnetic field-induced valley polarization effects shed light onto the exciton and trion dispersion relations in reciprocal space. The field dependence of the trion valley polarizations is in line with the predicted trion splitting into singlet and triplet configurations.

Control of Exciton Valley Coherence in Transition Metal Dichalcogenide Monolayers

The direct gap interband transitions in transition metal dichalcogenide monolayers are governed by chiral optical selection rules. Determined by laser helicity, optical transitions in either the K^{+} or K^{-} valley in momentum space are induced. Linearly polarized laser excitation prepares a coherent superposition of valley states. Here, we demonstrate the control of the exciton valley coherence in monolayer WSe_{2} by tuning the applied magnetic field perpendicular to the monolayer plane. We show rotation of this coherent superposition of valley states by angles as large as 30° in applied fields up to 9 T. This exciton valley coherence control on the ps time scale could be an important step towards complete control of qubits based on the valley degree of freedom.