Valleytronics. The valley Hall effect in MoS₂ transistors

Quantum Transport and Observation of Dyakonov-Perel Spin-Orbit Scattering in Monolayer MoS_{2}

Monolayers of group 6 transition metal dichalcogenides are promising candidates for future spin-, valley-, and charge-based applications. Quantum transport in these materials reflects a complex interplay between real spin and pseudospin (valley) relaxation processes, which leads to either positive or negative quantum correction to the classical conductivity. Here we report experimental observation of a crossover from weak localization to weak antilocalization in highly n-doped monolayer MoS_{2}. We show that the crossover can be explained by a single parameter associated with electron spin lifetime of the system. At low temperatures and high carrier densities, the spin lifetime is inversely proportional to momentum relaxation time; this indicates that spin relaxation occurs via a Dyakonov-Perel mechanism.

Fast and large-area growth of uniform MoS2 monolayers on molybdenum foils

A controllable synthesis of two-dimensional crystal monolayers in a large area is a prerequisite for potential applications, but the growth of transition metal dichalcogenide monolayers in a large area with spatial homogeneity remains a great challenge. Here we report a novel and efficient method to fabricate large-scale MoS2 monolayers by direct sulfurization of pre-annealed molybdenum foil surfaces with large grain boundaries of more than 50 μm in size at elevated temperatures. Continuous MoS2 monolayers can be formed uniformly by sulfurizing the Mo foils in sulfur vapor at 600 °C within 1 min. At a lower temperature even down to 500 °C, uniform MoS2 monolayers can still be obtained but in a much longer sulfurizing duration. It is demonstrated that the formed monolayers can be nondestructively transferred onto arbitrary substrates by removing the Mo foil using diluted ferric chloride solution and can be successfully fabricated into photodetectors. The results show a novel avenue to efficiently fabricate two-dimensional crystals in a large area in a highly controllable way and should have great potential for the development of large-scale applications of two-dimensional crystals in electrophotonic systems.

Does p-type ohmic contact exist in WSe2-metal interfaces?

Formation of low-resistance metal contacts is the biggest challenge that masks the intrinsic exceptional electronic properties of two dimensional WSe2 devices. We present the first comparative study of the interfacial properties between monolayer/bilayer (ML/BL) WSe2 and Sc, Al, Ag, Au, Pd, and Pt contacts by using ab initio energy band calculations with inclusion of the spin-orbital coupling (SOC) effects and quantum transport simulations. The interlayer coupling tends to reduce both the electron and hole Schottky barrier heights (SBHs) and alters the polarity for the WSe2-Au contact, while the SOC chiefly reduces the hole SBH. In the absence of the SOC, the Pd contact has the smallest hole SBH. Dramatically, the Pt contact surpasses the Pd contact and becomes the p-type ohmic or quasi-ohmic contact with inclusion of the SOC. Therefore, p-type ohmic or quasi-ohmic contact exists in WSe2-metal interfaces. Our study provides a theoretical foundation for the selection of favorable metal electrodes in ML/BL WSe2 devices.

Floquet-Engineered Valleytronics in Dirac Systems

Valley degrees of freedom offer a potential resource for quantum information processing if they can be effectively controlled. We discuss an optical approach to this problem in which intense light breaks electronic symmetries of a two-dimensional Dirac material. The resulting quasienergy structures may then differ for different valleys, so that the Floquet physics of the system can be exploited to produce highly polarized valley currents. This physics can be utilized to realize a valley valve whose behavior is determined optically. We propose a concrete way to achieve such valleytronics in graphene as well as in a simple model of an inversion-symmetry broken Dirac material. We study the effect numerically and demonstrate its robustness against moderate disorder and small deviations in optical parameters.

Anomalous temperature-dependent spin-valley polarization in monolayer WS2

Single layers of transition metal dichalcogenides (TMDs) are direct gap semiconductors with nondegenerate valley indices. An intriguing possibility for these materials is the use of their valley index as an alternate state variable. Several limitations to such a utility include strong intervalley scattering, as well as multiparticle interactions leading to multiple emission channels. We prepare single-layer WS₂ films such that the photoluminescence is from either the neutral or charged exciton (trion). After excitation with circularly polarized light, the neutral exciton emission has zero polarization. However, the trion emission has a large polarization (28%) at room temperature. The trion emission also has a unique, non-monotonic temperature dependence that is a consequence of the multiparticle nature of the trion. This temperature dependence enables us to determine that intervalley scattering, electron-hole radiative recombination, and Auger processes are the dominant mechanisms at work in this system. Because this dependence involves trion systems, one can use gate voltages to modulate the polarization (or intensity) emitted from TMD structures.

Probing thermal expansion coefficients of monolayers using surface enhanced Raman scattering

A non-destructive method has been proposed to probe thermal expansion coefficients of the monolayer materials using surface-enhanced Raman spectroscopy.

Pressure evolution of the potential barriers of phase transition of MoS2, MoSe2 and MoTe2

Two-dimensional crystals with weak layer interactions, such as transitional metal dichalcogenides, have been a focus of research recently.

Photoinduced doping and photoluminescence signature in an exfoliated WS2 monolayer semiconductor

Photoinduced doping effect in a mechanically-exfoliated high-quality tungsten disulfide (WS₂) monolayer.

Interactions between lasers and two-dimensional transition metal dichalcogenides

We review the interactions between lasers and TMDs with a focus on the use of laser-based technologies as effective tools for the characterization, modification, and manipulation of TMDs.

Tunable electronic structures in MPX3 (M = Zn, Cd; X = S, Se) monolayers by strain engineering

Tunable electronic structures in MPX₃ (M = Zn, Cd; X = S, Se) monolayers by strain are investigated, and the substitution of MX monolayers by MPX₃ is proposed.

The polarization-dependent anisotropic Raman response of few-layer and bulk WTe2under different excitation wavelengths

WTe₂, which is an orthorhombic semimetal crystallized in Td phase, exhibts distinct in-plane anisotropy. The Raman modes depict different anisotropic response by rotating the incident polarization under different excitation wavelengths.

Recent Advances in Two-Dimensional Materials beyond Graphene

The isolation of graphene in 2004 from graphite was a defining moment for the "birth" of a field: two-dimensional (2D) materials. In recent years, there has been a rapidly increasing number of papers focusing on non-graphene layered materials, including transition-metal dichalcogenides (TMDs), because of the new properties and applications that emerge upon 2D confinement. Here, we review significant recent advances and important new developments in 2D materials "beyond graphene". We provide insight into the theoretical modeling and understanding of the van der Waals (vdW) forces that hold together the 2D layers in bulk solids, as well as their excitonic properties and growth morphologies. Additionally, we highlight recent breakthroughs in TMD synthesis and characterization and discuss the newest families of 2D materials, including monoelement 2D materials (i.e., silicene, phosphorene, etc.) and transition metal carbide- and carbon nitride-based MXenes. We then discuss the doping and functionalization of 2D materials beyond graphene that enable device applications, followed by advances in electronic, optoelectronic, and magnetic devices and theory. Finally, we provide perspectives on the future of 2D materials beyond graphene.

Experimental Evidence for Dark Excitons in Monolayer WSe_{2}

Transition metal dichalcogenides in the class MX_{2} (M=Mo, W; X=S, Se) have been identified as direct-gap semiconductors in the monolayer limit. Here, we examine light emission of monolayer WSe_{2} using temperature-dependent photoluminescence and time-resolved photoluminescence spectroscopy. We present experimental evidence for the existence of an optically forbidden dark state of the band-gap exciton that lies tens of meV below the optically bright state. The presence of the dark state is manifest in the strong quenching of light emission observed at reduced temperatures. The experimental findings are consistent with theoretical predictions of spin-polarized conduction and valence bands at the K point of the Brillouin zone, with the minimum gap occurring between bands of opposite electron spin.

Spin-orbit engineering in transition metal dichalcogenide alloy monolayers

Binary transition metal dichalcogenide monolayers share common properties such as a direct optical bandgap, spin-orbit splittings of hundreds of meV, light-matter interaction dominated by robust excitons and coupled spin-valley states. Here we demonstrate spin-orbit-engineering in Mo(1-x)WxSe2 alloy monolayers for optoelectronics and applications based on spin- and valley-control. We probe the impact of the tuning of the conduction band spin-orbit spin-splitting on the bright versus dark exciton population. For MoSe2 monolayers, the photoluminescence intensity decreases as a function of temperature by an order of magnitude (4-300 K), whereas for WSe2 we measure surprisingly an order of magnitude increase. The ternary material shows a trend between these two extreme behaviours. We also show a non-linear increase of the valley polarization as a function of tungsten concentration, where 40% tungsten incorporation is sufficient to achieve valley polarization as high as in binary WSe2.

Thermally Driven Pure Spin and Valley Currents via the Anomalous Nernst Effect in Monolayer Group-VI Dichalcogenides

The spin and valley-dependent anomalous Nernst effects are analyzed for monolayer MoS_{2} and other group-VI dichalcogenides. We find that pure spin and valley currents can be generated perpendicular to the applied thermal gradient in the plane of these two-dimensional materials. This effect provides a versatile platform for applications of spin caloritronics. A spin current purity factor is introduced to quantify this effect. When time reversal symmetry is violated, e.g., two-dimensional materials on an insulating magnetic substrate, a dip-peak feature appears for the total Nernst coefficient. For the dip state it is found that carriers with only one spin and from one valley are driven by the temperature gradient.

WSe₂ Light-Emitting Tunneling Transistors with Enhanced Brightness at Room Temperature

Monolayers of molybdenum and tungsten dichalcogenides are direct bandgap semiconductors, which makes them promising for optoelectronic applications. In particular, van der Waals heterostructures consisting of monolayers of MoS2 sandwiched between atomically thin hexagonal boron nitride (hBN) and graphene electrodes allows one to obtain light emitting quantum wells (LEQWs) with low-temperature external quantum efficiency (EQE) of 1%. However, the EQE of MoS2- and MoSe2-based LEQWs shows behavior common for many other materials: it decreases fast from cryogenic conditions to room temperature, undermining their practical applications. Here we compare MoSe2 and WSe2 LEQWs. We show that the EQE of WSe2 devices grows with temperature, with room temperature EQE reaching 5%, which is 250× more than the previous best performance of MoS2 and MoSe2 quantum wells in ambient conditions. We attribute such different temperature dependences to the inverted sign of spin-orbit splitting of conduction band states in tungsten and molybdenum dichalcogenides, which makes the lowest-energy exciton in WSe2 dark.

Electrical contacts to two-dimensional semiconductors

The performance of electronic and optoelectronic devices based on two-dimensional layered crystals, including graphene, semiconductors of the transition metal dichalcogenide family such as molybdenum disulphide (MoS2) and tungsten diselenide (WSe2), as well as other emerging two-dimensional semiconductors such as atomically thin black phosphorus, is significantly affected by the electrical contacts that connect these materials with external circuitry. Here, we present a comprehensive treatment of the physics of such interfaces at the contact region and discuss recent progress towards realizing optimal contacts for two-dimensional materials. We also discuss the requirements that must be fulfilled to realize efficient spin injection in transition metal dichalcogenides.

Simulation Evidence of Hexagonal-to-Tetragonal ZnSe Structure Transition: A Monolayer Material with a Wide-Range Tunable Direct Bandgap

2D material with tunable direct bandgap in the intermediate region (i.e., ≈2-3 eV) is key to the achievement of high efficiency in visible-light optical devices. Herein, a simulation evidence of structure transition of monolayer ZnSe from the experimental pseudohexagonal structure to the tetragonal structure (t-ZnSe) under lateral pressure is shown, suggesting a possible fabrication route to achieve the t-ZnSe monolayer. The as-produced t-ZnSe monolayer exhibits highly tunable bandgap under the biaxial strains, allowing strain engineering of t-ZnSe's bandgap over a wide range of 2-3 eV. Importantly, even under the biaxial strain up to 7%, the t-ZnSe monolayer still keeps its direct-gap property in the desirable range of 2.40-3.17 eV (corresponding to wavelength of green light to ultraviolet). The wide-range tunability of direct bandgap appears to be a unique property of the t-ZnSe monolayer, suggesting its potential application as a light-emitting 2D material in red-green-blue light emission diodes or as complementary light-absorption material in the blue-yellow region for multijunction solar cells. The straddling of the band edge of the t-ZnSe monolayer over the redox potential of water splitting reaction also points to its plausible application for visible-light-driven water splitting.

Optically initialized robust valley-polarized holes in monolayer WSe2

A robust valley polarization is a key prerequisite for exploiting valley pseudospin to carry information in next-generation electronics and optoelectronics. Although monolayer transition metal dichalcogenides with inherent spin–valley coupling offer a unique platform to develop such valleytronic devices, the anticipated long-lived valley pseudospin has not been observed yet. Here we demonstrate that robust valley-polarized holes in monolayer WSe₂ can be initialized by optical pumping. Using time-resolved Kerr rotation spectroscopy, we observe a long-lived valley polarization for positive trion with a lifetime approaching 1 ns at low temperatures, which is much longer than the trion recombination lifetime (∼10–20 ps). The long-lived valley polarization arises from the transfer of valley pseudospin from photocarriers to resident holes in a specific valley. The optically initialized valley pseudospin of holes remains robust even at room temperature, which opens up the possibility to realize room-temperature valleytronics based on transition metal dichalcogenides.

The long associated lifetimes required to exploit valley polarization in electronic devices, along with charge and spin, have yet to be observed. Here, the authors demonstrate the photoexcitation of long-lived valley-polarized holes in WSe₂.

Anomalous Light Cones and Valley Optical Selection Rules of Interlayer Excitons in Twisted Heterobilayers

We show that, because of the inevitable twist and lattice mismatch in heterobilayers of transition metal dichalcogenides, interlayer excitons have sixfold degenerate light cones anomalously located at finite velocities on the parabolic energy dispersion. The photon emissions at each light cone are elliptically polarized, with the major axis locked to the direction of exciton velocity, and helicity specified by the valley indices of the electron and the hole. These finite-velocity light cones allow unprecedented possibilities for optically injecting valley polarization and valley current, and the observation of both direct and inverse valley Hall effects, by exciting interlayer excitons. Our findings suggest potential excitonic circuits with valley functionalities, and unique opportunities to study exciton dynamics and condensation phenomena in semiconducting 2D heterostructures.

High-Mobility Holes in Dual-Gated WSe2 Field-Effect Transistors

We demonstrate dual-gated p-type field-effect transistors (FETs) based on few-layer tungsten diselenide (WSe2) using high work-function platinum source/drain contacts and a hexagonal boron nitride top-gate dielectric. A device topology with contacts underneath the WSe2 results in p-FETs with ION/IOFF ratios exceeding 10(7) and contacts that remain ohmic down to cryogenic temperatures. The output characteristics show current saturation and gate tunable negative differential resistance. The devices show intrinsic hole mobilities around 140 cm(2)/(V s) at room temperature and approaching 4000 cm(2)/(V s) at 2 K. Temperature-dependent transport measurements show a metal-insulator transition, with an insulating phase at low densities and a metallic phase at high densities. The mobility shows a strong temperature dependence consistent with phonon scattering, and saturates at low temperatures, possibly limited by Coulomb scattering or defects.

Topological Imbert-Fedorov Shift in Weyl Semimetals

The Goos-Hänchen (GH) shift and the Imbert-Fedorov (IF) shift are optical phenomena which describe the longitudinal and transverse lateral shifts at the reflection interface, respectively. Here, we predict the GH and IF shifts in Weyl semimetals (WSMs)-a promising material harboring low energy Weyl fermions, a massless fermionic cousin of photons. Our results show that the GH shift in WSMs is valley independent, which is analogous to that discovered in a 2D relativistic material-graphene. However, the IF shift has never been explored in nonoptical systems, and here we show that it is valley dependent. Furthermore, we find that the IF shift actually originates from the topological effect of the system. Experimentally, the topological IF shift can be utilized to characterize the Weyl semimetals, design valleytronic devices of high efficiency, and measure the Berry curvature.

Microscopic basis for the band engineering of Mo1-xWxS2-based heterojunction

Transition-metal dichalcogenide layered materials, consisting of a transition-metal atomic layer sandwiched by two chalcogen atomic layers, have been attracting considerable attention because of their desirable physical properties for semiconductor devices, and a wide variety of pn junctions, which are essential building blocks for electronic and optoelectronic devices, have been realized using these atomically thin structures. Engineering the electronic/optical properties of semiconductors by using such heterojunctions has been a central concept in semiconductor science and technology. Here, we report the first scanning tunneling microscopy/spectroscopy (STM/STS) study on the electronic structures of a monolayer WS₂/Mo_1−xW_xS₂ heterojunction that provides a tunable band alignment. The atomically modulated spatial variation in such electronic structures, i.e., a microscopic basis for the band structure of a WS₂/Mo_1−xW_xS₂ heterojunction, was directly observed. The macroscopic band structure of Mo_1−xW_xS₂ alloy was well reproduced by the STS spectra averaged over the surface. An electric field of as high as 80 × 10⁶ Vm⁻¹ was observed at the interface for the alloy with x = 0.3, verifying the efficient separation of photoexcited carriers at the interface.

Gate-tunable diode and photovoltaic effect in an organic-2D layered material p-n junction

The semiconducting p-n junction is a simple device structure with great relevance for electronic and optoelectronic applications. The successful integration of low-dimensional materials in electronic circuits has opened the way forward for producing gate-tunable p-n junctions. In that context, we present here an organic (Cu-phthalocyanine)-2D layered material (MoS2) hybrid p-n junction with both gate-tunable diode characteristics and photovoltaic effect. Our proof-of-principle devices show multifunctional properties with diode rectifying factors of up to 10(4), while under light exposure they exhibit photoresponse with a measured external quantum efficiency of ∼11%. As for their photovoltaic properties, we found open circuit voltages of up to 0.6 V and optical-to-electrical power conversion efficiency of 0.7%. The extended catalogue of known organic semiconductors and two-dimensional materials offer the prospect for tailoring the properties and the performance of the resulting devices, making organic-2D p-n junctions promising candidates for future technological applications.

Local Spectroscopic Characterization of Spin and Layer Polarization in WSe_{2}

We report scanning tunneling microscopy and scanning tunneling spectroscopy (STS) measurements of monolayer and bilayer WSe_{2}. We measure a band gap of 2.21±0.08  eV in monolayer WSe_{2}, which is much larger than the energy of the photoluminescence peak, indicating a large excitonic binding energy. We additionally observe significant electronic scattering arising from atomic-scale defects. Using Fourier transform STS, we map the energy versus momentum dispersion relations for monolayer and bilayer WSe_{2}. Further, by tracking allowed and forbidden scattering channels as a function of energy we infer the spin texture of both the conduction and valence bands. We observe a large spin-splitting of the valence band due to strong spin-orbit coupling, and additionally observe spin-valley-layer coupling in the conduction band of bilayer WSe_{2}.

Electrical Tuning of Exciton Binding Energies in Monolayer WS_{2}

We demonstrate continuous tuning of the exciton binding energy in monolayer WS_{2} by means of an externally applied voltage in a field-effect transistor device. Using optical spectroscopy, we monitor the ground and excited excitonic states as a function of gate voltage and track the evolution of the quasiparticle band gap. The observed decrease of the exciton binding energy over the range of about 100 meV, accompanied by the renormalization of the quasiparticle band gap, is associated with screening of the Coulomb interaction by the electrically injected free charge carriers at densities up to 8×10^{12} cm^{-2}. Complete ionization of the excitons due to the electrical doping is estimated to occur at a carrier density of several 10^{13} cm^{-2}.

A tight-binding model for MoS2 monolayers

We propose an accurate tight-binding parametrization for the band structure of MoS2 monolayers near the main energy gap. We introduce a generic and straightforward derivation for the band energies equations that could be employed for other monolayer dichalcogenides. A parametrization that includes spin-orbit coupling is also provided. The proposed set of model parameters reproduce both the correct orbital compositions and location of valence and conductance band in comparison with ab initio calculations. The model gives a suitable starting point for realistic large-scale atomistic electronic transport calculations.

In situ degradation studies of two-dimensional WSe₂-graphene heterostructures

Heterostructures of two-dimensional materials can be vulnerable to thermal degradation due to structural and interfacial defects as well as thermal expansion mismatch, yet a systematic study does not exist in the literature. In this study, we investigate the degradation of freestanding WSe2-graphene heterostructures due to heat and charge flow by performing in situ experiments inside a transmission electron microscope. Experimental results show that purely thermal loading requires higher temperatures (>850 °C), about 150 °C higher than that under combined electrical and thermal loading. In both cases, selenium is the first element to decompose and migration of silicon atoms from the test structure to the freestanding specimen initiates rapid degradation through the formation of tungsten disilicide and silicon carbide. The role of the current flow is to enhance the migration of silicon from the sample holder and to knock-out the selenium atoms. The findings of this study provide fundamental insights into the degradation of WSe2-graphene heterostructures and inspire their application in electronics for use in harsh environments.

Double resonant Raman scattering and valley coherence generation in monolayer WSe_{2}

The electronic states at the direct band gap of monolayer transition metal dichalcogenides such as WSe_{2} at the K^{+} and K^{-} valleys are related by time reversal and may be viewed as pseudospins. The corresponding optical interband transitions are governed by robust excitons. Excitation with linearly polarized light yields the coherent superposition of exciton pseudospin states, referred to as coherent valley states. Here, we uncover how and why valley coherence can be generated efficiently. In double resonant Raman spectroscopy, we show that the optically generated 2s exciton state differs from the 1s state by exactly the energy of the combination of several prominent phonons. Superimposed on the exciton photoluminescence (PL), we observe the double resonant Raman signal. This spectrally narrow peak shifts with the excitation laser energy as incoming photons match the 2s and outgoing photons the 1s exciton transition. The multiphonon resonance has important consequences: following linearly polarized excitation of the 2s exciton, a superposition of valley states is efficiently transferred from the 2s to 1s state. This explains the high degree of valley coherence measured for the 1s exciton PL.

Chiral phonons at high-symmetry points in monolayer hexagonal lattices

In monolayer hexagonal lattices, the intravalley and intervalley scattering of electrons can involve chiral phonons at Brillouin-zone center and corners, respectively. At these high-symmetry points, there is a threefold rotational symmetry endowing phonon eigenmodes with a quantized pseudoangular momentum, which includes orbital and spin parts. Conservation of pseudoangular momentum yields selection rules for intravalley and intervalley scattering of electrons by phonons. Concrete predictions of helicity-resolved optical phenomena are made on monolayer molybdenum disulfide. The chiral phonons at Brillouin-zone corners excited by polarized photons can be detected by a valley phonon Hall effect. The chiral phonons, together with phonon circular polarization, phonon pseudoangular momentum, selection rules, and valley phonon Hall effect will extend the basis for valley-based electronics and phononics applications in the future.

Tunable Valley Polarization and Valley Orbital Magnetic Moment Hall Effect in Honeycomb Systems with Broken Inversion Symmetry

In this Letter, a tunable valley polarization is investigated for honeycomb systems with broken inversion symmetry such as transition-metal dichalcogenide MX2 (M = Mo, W; X = S, Se) monolayers through elliptical pumping. Compared to circular pumping, elliptical pumping is a more universal and effective method to create coherent valley polarization. When two valleys of MX2 monolayers are doped or polarized, a novel anomalous Hall effect (called valley orbital magnetic moment Hall effect) is predicted. Valley orbital magnetic moment Hall effect can generate an orbital magnetic moment current without the accompaniment of a charge current, which opens a new avenue for exploration of valleytronics and orbitronics. Valley orbital magnetic moment Hall effect is expected to overshadow spin Hall effect and is tunable under elliptical pumping.

New perspectives for Rashba spin-orbit coupling

In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade has been particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topological classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.

On Valence-Band Splitting in Layered MoS2

As a representative two-dimensional semiconducting transition-metal dichalcogenide (TMD), the electronic structure in layered MoS2 is a collective result of quantum confinement, interlayer interaction, and crystal symmetry. A prominent energy splitting in the valence band gives rise to many intriguing electronic, optical, and magnetic phenomena. Despite numerous studies, an experimental determination of valence-band splitting in few-layer MoS2 is still lacking. Here, we show how the valence-band maximum (VBM) splits for one to five layers of MoS2. Interlayer coupling is found to contribute significantly to phonon energy but weakly to VBM splitting in bilayers, due to a small interlayer hopping energy for holes. Hence, spin-orbit coupling is still predominant in the splitting. A temperature-independent VBM splitting, known for single-layer MoS2, is, thus, observed for bilayers. However, a Bose-Einstein type of temperature dependence of VBM splitting prevails in three to five layers of MoS2. In such few-layer MoS2, interlayer coupling is enhanced with a reduced interlayer distance, but thermal expansion upon temperature increase tends to decouple adjacent layers and therefore decreases the splitting energy. Our findings that shed light on the distinctive behaviors about VBM splitting in layered MoS2 may apply to other hexagonal TMDs as well. They will also be helpful in extending our understanding of the TMD electronic structure for potential applications in electronics and optoelectronics.

Topological Bloch bands in graphene superlattices

We outline a designer approach to endow widely available plain materials with topological properties by stacking them atop other nontopological materials. The approach is illustrated with a model system comprising graphene stacked atop hexagonal boron nitride. In this case, the Berry curvature of the electron Bloch bands is highly sensitive to the stacking configuration. As a result, electron topology can be controlled by crystal axes alignment, granting a practical route to designer topological materials. Berry curvature manifests itself in transport via the valley Hall effect and long-range chargeless valley currents. The nonlocal electrical response mediated by such currents provides diagnostics for band topology.

Quantum Spin-Quantum Anomalous Hall Insulators and Topological Transitions in Functionalized Sb(111) Monolayers

Electronic and topological behaviors of Sb(111) monolayers decorated with H and certain magnetic atoms are investigated by using ab initio methods. The drastic exchange field induced by the magnetic atoms, together with strong spin-orbit coupling (SOC) of Sb atoms, generates one new category of valley polarized topological insulators, called quantum spin-quantum anomalous Hall (QSQAH) insulators in the monolayer, with a band gap up to 53 meV. The strong SOC is closely related to Sb px and py orbitals, instead of pz orbitals in usual two-dimensional (2D) materials. Topological transitions from quantum anomalous Hall states to QSQAH states and then to time-reversal-symmetry-broken quantum spin Hall states are achieved by tuning the SOC strength. The behind mechanism is revealed. Our work is helpful for future valleytronic and spintronic applications in 2D materials.

Superconductivity Series in Transition Metal Dichalcogenides by Ionic Gating

Functionalities of two-dimensional (2D) crystals based on semiconducting transition metal dichalcogenides (TMDs) have now stemmed from simple field effect transistors (FETs) to a variety of electronic and opto-valleytronic devices, and even to superconductivity. Among them, superconductivity is the least studied property in TMDs due to methodological difficulty accessing it in different TMD species. Here, we report the systematic study of superconductivity in MoSe₂, MoTe₂ and WS₂ by ionic gating in different regimes. Electrostatic gating using ionic liquid was able to induce superconductivity in MoSe₂ but not in MoTe₂ because of inefficient electron accumulation limited by electronic band alignment. Alternative gating using KClO₄/polyethylene glycol enabled a crossover from surface doping to bulk doping, which induced superconductivities in MoTe₂ and WS₂ electrochemically. These new varieties greatly enriched the TMD superconductor families and unveiled critical methodology to expand the capability of ionic gating to other materials.

Raman shift and electrical properties of MoS2 bilayer on boron nitride substrate

We have fabricated a bilayer molybdenum disulphide (MoS2) transistor on boron nitride (BN) substrate and performed Raman spectroscopy and electrical measurements with this device. The characteristic Raman peaks show an upshift about 2.5 cm(-1) with the layer lying on BN, and a narrower line width in comparison with those on a SiO2 substrate. The device has a maximum drain current larger than 1 μA and a high current on/off ratio of greater than 10(8). In the temperature range of 100 K-293 K, the two terminal gate effect mobility and the carrier density do not change significantly with temperature. Results of the Raman and electrical measurements reveal that BN is a suitable substrate for atomic layer electrical devices.

Optical Investigation of Monolayer and Bulk Tungsten Diselenide (WSe₂) in High Magnetic Fields

Optical spectroscopy in high magnetic fields B ≤ 65 T is used to reveal the very different nature of carriers in monolayer and bulk transition metal dichalcogenides. In monolayer WSe2, the exciton emission shifts linearly with the magnetic field and exhibits a splitting that originates from the magnetic field induced valley splitting. The monolayer data can be described using a single particle picture with a Dirac-like Hamiltonian for massive Dirac Fermions, with an additional term to phenomenologically include the valley splitting. In contrast, in bulk WSe2 where the inversion symmetry is restored, transmission measurements show a distinctly excitonic behavior with absorption to the 1s and 2s states. Magnetic field induces a spin splitting together with a small diamagnetic shift and cyclotron like behavior at high fields, which is best described within the hydrogen model.

Dichroic spin-valley photocurrent in monolayer molybdenum disulphide

The aim of valleytronics is to exploit confinement of charge carriers in local valleys of the energy bands of semiconductors as an additional degree of freedom in optoelectronic devices. Thanks to strong direct excitonic transitions in spin-coupled K valleys, monolayer molybdenum disulphide is a rapidly emerging valleytronic material, with high valley polarization in photoluminescence. Here we elucidate the excitonic physics of this material by light helicity-dependent photocurrent studies of phototransistors. We demonstrate that large photocurrent dichroism (up to 60%) can also be achieved in high-quality molybdenum disulphide monolayers grown by chemical vapour deposition, due to the circular photogalvanic effect on resonant excitations. This opens up new opportunities for valleytonic applications in which selective control of spin-valley-coupled photocurrents can be used to implement polarization-sensitive light-detection schemes or integrated spintronic devices, as well as biochemical sensors operating at visible frequencies.

Rotation-misfit-free heteroepitaxial stacking and stitching growth of hexagonal transition-metal dichalcogenide monolayers by nucleation kinetics controls

2D vertical stacking and lateral stitching growth of monolayer (ML) hexagonal transition-metal dichalcogenides are reported. The 2D heteroepitaxial manipulation of MoS2 and WS2 MLs is achieved by control of the 2D nucleation kinetics during the sequential vapor-phase growth. It enables the creation of hexagon-on-hexagon unit-cell stacking and hexagon-by-hexagon stitching without interlayer rotation misfits.

Magnetoluminescence and valley polarized state of a two-dimensional electron gas in WS2 monolayers

Materials often exhibit fundamentally new phenomena in reduced dimensions that potentially lead to novel applications. This is true for single-layer, two-dimensional semiconductor crystals of transition-metal dichalcogenides, MX2 (M = Mo, W and X = S, Se). They exhibit direct bandgaps with energies in the visible region at the two non-equivalent valleys in the Brillouin zone. This makes them suitable for optoelectronic applications that range from light-emitting diodes to light harvesting and light sensors, and to valleytronics. Here, we report the results of a magnetoluminescence study of WS2 single-layer crystals in which the strong spin-orbit interaction additionally locks the valley and spin degrees of freedom. The recombination of the negatively charged exciton in the presence of a two-dimensional electron gas (2DEG) is found to be circularly polarized at zero magnetic field despite being excited with unpolarized light, which indicates that the existence of a valley polarized 2DEG is caused by valley and spin locking and strong electron-electron interactions.

Interlayer orientation-dependent light absorption and emission in monolayer semiconductor stacks

Two-dimensional stacks of dissimilar hexagonal monolayers exhibit unusual electronic, photonic and photovoltaic responses that arise from substantial interlayer excitations. Interband excitation phenomena in individual hexagonal monolayer occur in states at band edges (valleys) in the hexagonal momentum space; therefore, low-energy interlayer excitation in the hexagonal monolayer stacks can be directed by the two-dimensional rotational degree of each monolayer crystal. However, this rotation-dependent excitation is largely unknown, due to lack in control over the relative monolayer rotations, thereby leading to momentum-mismatched interlayer excitations. Here, we report that light absorption and emission in MoS2/WS2 monolayer stacks can be tunable from indirect- to direct-gap transitions in both spectral and dynamic characteristics, when the constituent monolayer crystals are coherently stacked without in-plane rotation misfit. Our study suggests that the interlayer rotational attributes determine tunable interlayer excitation as a new set of basis for investigating optical phenomena in a two-dimensional hexagonal monolayer system.

Single-Crystal Atomic-Layered Molybdenum Disulfide Nanobelts with High Surface Activity

Nanostructured molybdenum disulfide (MoS2) has emerged as a promising catalytic alternative to the widely used Pt in the hydrogen evolution reaction from water because it is inexpensive and earth-abundant. The central prerequisite in realizing its potential is to enhance the surface activities by increasing the concentration of metallic edge sites. However, MoS2 thermodynamics favors the presence of a two-dimensional basal plane, and therefore, the one-dimensional edge sites surrounding the basal plane are very limited. Herein, we report the first synthesis of single-crystal MoS2 nanobelts with the top surface fully covered by edge sites. The nanobelt structure comprises parallel stacked atomic layers with the basal plane vertical to the substrate, and these layer edges form the top surface of the nanobelt. The surface is highly active: it optically quenches all of the indirect band gap excitons and chemically leads to a high electrocatalytic hydrogen evolution efficiency (a low onset overpotential of 170 mV for an electrocatalytic current density of 20 mA/cm(2) and a Tafel slope of 70 mV/decade).

Optoelectronic crystal of artificial atoms in strain-textured molybdenum disulphide

The isolation of the two-dimensional semiconductor molybdenum disulphide introduced a new optically active material possessing a band gap that can be facilely tuned via elastic strain. As an atomically thin membrane with exceptional strength, monolayer molybdenum disulphide subjected to biaxial strain can embed wide band gap variations overlapping the visible light spectrum, with calculations showing the modified electronic potential emanating from point-induced tensile strain perturbations mimics the Coulomb potential in a mesoscopic atom. Here we realize and confirm this ‘artificial atom' concept via capillary-pressure-induced nanoindentation of monolayer molybdenum disulphide from a tailored nanopattern, and demonstrate that a synthetic superlattice of these building blocks forms an optoelectronic crystal capable of broadband light absorption and efficient funnelling of photogenerated excitons to points of maximum strain at the artificial-atom nuclei. Such two-dimensional semiconductors with spatially textured band gaps represent a new class of materials, which may find applications in next-generation optoelectronics or photovoltaics.

Periodically strained monolayer molybdenum disulphide funnels photogenerated electron-hole pairs across an electric field induced by a spatially graded band gap, mimicking a crystal of artificial atoms. Here, the authors experimentally demonstrate the artificial crystal in strain-textured molybdenum disulphide.

Single quantum emitters in monolayer semiconductors

Single quantum emitters (SQEs) are at the heart of quantum optics and photonic quantum-information technologies. To date, all the demonstrated solid-state single-photon sources are confined to one-dimensional (1D; ref. 3) or 3D materials. Here, we report a new class of SQEs based on excitons that are spatially localized by defects in 2D tungsten-diselenide (WSe2) monolayers. The optical emission from these SQEs shows narrow linewidths of ∼130 μeV, about two orders of magnitude smaller than those of delocalized valley excitons. Second-order correlation measurements revealed a strong photon antibunching, which unambiguously established the single-photon nature of the emission. The SQE emission shows two non-degenerate transitions, which are cross-linearly polarized. We assign this fine structure to two excitonic eigenmodes whose degeneracy is lifted by a large ∼0.71 meV coupling, probably because of the electron-hole exchange interaction in the presence of anisotropy. Magneto-optical measurements also reveal an exciton g factor of ∼8.7, several times larger than those of delocalized valley excitons. In addition to their fundamental importance, establishing new SQEs in 2D quantum materials could give rise to practical advantages in quantum-information processing, such as an efficient photon extraction and a high integratability and scalability.

Multi-terminal transport measurements of MoS2 using a van der Waals heterostructure device platform

Atomically thin two-dimensional semiconductors such as MoS2 hold great promise for electrical, optical and mechanical devices and display novel physical phenomena. However, the electron mobility of mono- and few-layer MoS2 has so far been substantially below theoretically predicted limits, which has hampered efforts to observe its intrinsic quantum transport behaviours. Potential sources of disorder and scattering include defects such as sulphur vacancies in the MoS2 itself as well as extrinsic sources such as charged impurities and remote optical phonons from oxide dielectrics. To reduce extrinsic scattering, we have developed here a van der Waals heterostructure device platform where MoS2 layers are fully encapsulated within hexagonal boron nitride and electrically contacted in a multi-terminal geometry using gate-tunable graphene electrodes. Magneto-transport measurements show dramatic improvements in performance, including a record-high Hall mobility reaching 34,000 cm(2) V(-1) s(-1) for six-layer MoS2 at low temperature, confirming that low-temperature performance in previous studies was limited by extrinsic interfacial impurities rather than bulk defects in the MoS2. We also observed Shubnikov-de Haas oscillations in high-mobility monolayer and few-layer MoS2. Modelling of potential scattering sources and quantum lifetime analysis indicate that a combination of short-range and long-range interfacial scattering limits the low-temperature mobility of MoS2.

Observation of Excitonic Rydberg States in Monolayer MoS2 and WS2 by Photoluminescence Excitation Spectroscopy

We have identified excited exciton states in monolayers of MoS2 and WS2 supported on fused silica by means of photoluminescence excitation spectroscopy. In monolayer WS2, the positions of the excited A exciton states imply an exciton binding energy of 0.32 eV. In monolayer MoS2, excited exciton transitions are observed at energies of 2.24 and 2.34 eV. Assigning these states to the B exciton Rydberg series yields an exciton binding energy of 0.44 eV.