Valleytronics. The valley Hall effect in MoS₂ transistors

Polariton Anomalous Hall Effect in Transition-Metal Dichalcogenides

We analyze the properties of strongly coupled excitons and photons in systems made of semiconducting two-dimensional transition-metal dichalcogenides embedded in optical cavities. Through a detailed microscopic analysis of the coupling, we unveil novel, highly tunable features of the spectrum that result in polariton splitting and a breaking of light-matter selection rules. The dynamics of the composite polaritons is influenced by the Berry phase arising both from their constituents and from the confinement-enhanced coupling. We find that light-matter coupling emerges as a mechanism that enhances the Berry phase of polaritons well beyond that of its elementary constituents, paving the way to achieve a polariton anomalous Hall effect.

Biexcitons in monolayer transition metal dichalcogenides tuned by magnetic fields

We present time-integrated four-wave mixing measurements on monolayer MoSe₂ in magnetic fields up to 25 T. The experimental data together with time-dependent density function theory calculations provide interesting insights into the biexciton formation and dynamics. In the presence of magnetic fields the coherence at negative and positive time delays is dominated by intervalley biexcitons. We demonstrate that magnetic fields can serve as a control to enhance the biexciton formation and help search for more exotic states of matter, including the creation of multiple exciton complexes and excitonic condensates.

Biexciton complexes in atomically thin transition metal dichalcogenides have unusually large binding energies. Here, the authors explore biexciton formation dynamics in monolayer MoSe₂ in the presence of magnetic fields up to 25 T.

Valleytronics: Opportunities, Challenges, and Paths Forward

A lack of inversion symmetry coupled with the presence of time-reversal symmetry endows 2D transition metal dichalcogenides with individually addressable valleys in momentum space at the K and K' points in the first Brillouin zone. This valley addressability opens up the possibility of using the momentum state of electrons, holes, or excitons as a completely new paradigm in information processing. The opportunities and challenges associated with manipulation of the valley degree of freedom for practical quantum and classical information processing applications were analyzed during the 2017 Workshop on Valleytronic Materials, Architectures, and Devices; this Review presents the major findings of the workshop.

Midinfrared Plasmonic Valleytronics in Metagate-Tuned Graphene

A valley plasmonic crystal for graphene surface plasmons is proposed. We demonstrate that a designer metagate, placed within a few nanometers of graphene, can be used to impose a periodic Fermi energy landscape on graphene. For specific metagate geometries and bias voltages, the combined metagate-graphene structure is shown to produce complete propagation band gaps for the plasmons, and to impart them with nontrivial valley-linked topological properties. Sharply curved domain walls between differently patterned metagates are shown to guide highly localized plasmons without any reflections owing to suppressed intervalley scattering. Our approach paves the way for nonmagnetic and dynamically reconfigurable topological nanophotonic devices.

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.

Measurement of complex optical susceptibility for individual carbon nanotubes by elliptically polarized light excitation

The complex optical susceptibility is the most fundamental parameter characterizing light-matter interactions and determining optical applications in any material. In one-dimensional (1D) materials, all conventional techniques to measure the complex susceptibility become invalid. Here we report a methodology to measure the complex optical susceptibility of individual 1D materials by an elliptical-polarization-based optical homodyne detection. This method is based on the accurate manipulation of interference between incident left- (right-) handed elliptically polarized light and the scattering light, which results in the opposite (same) contribution of the real and imaginary susceptibility in two sets of spectra. We successfully demonstrate its application in determining complex susceptibility of individual chirality-defined carbon nanotubes in a broad optical spectral range (1.6-2.7 eV) and under different environments (suspended and in device). This full characterization of the complex optical responses should accelerate applications of various 1D nanomaterials in future photonic, optoelectronic, photovoltaic, and bio-imaging devices.

Hybridization induced metallic and magnetic edge states in noble transition-metal-dichalcogenides of PtX2 (X = S, Se) nanoribbons

The semiconducting transition metal dichalcogenide (TMD) 2H-MoS2 zigzag nanoribbon has two different edges, and only one edge shows metallic properties due to symmetric protection. In the present work, a nanoribbon with two parallel metallic and magnetic edges was designed from a noble TMD 1T-PtX2 (X = S, Se) by employing first-principles calculations based on density functional theory (DFT). The band structure, density of states (DOS), and simulated scanning tunneling microscopy (STM) of three possible zigzag edge states of monolayer semiconducting PtX2 were systematically studied. Detailed calculations showed that the Pt-terminated edge state among the three zigzag edge states was metallic. The Pt-terminated edge state designed from monolayer PtS2 showed both metallic and magnetic properties. These metallic and magnetic properties were mainly contributed to by the hybridization of the 5d orbitals of Pt atoms and the 3p orbitals of S atoms located at the edges. However, hybridization of the 5d orbitals of Pt atoms and the 4p orbitals of Se atoms located at the edges does not bring magnetic properties to the zigzag metallic PtSe2 nanoribbon. The interesting electronic and magnetic properties of 1T-PtX2 nanoribbons indicate that they may have promising applications as zigzag nanoribbons in spin electronics and photovoltaic cells.

Symmetry regimes for circular photocurrents in monolayer MoSe2

In monolayer transition metal dichalcogenides helicity-dependent charge and spin photocurrents can emerge, even without applying any electrical bias, due to circular photogalvanic and photon drag effects. Exploiting such circular photocurrents (CPCs) in devices, however, requires better understanding of their behavior and physical origin. Here, we present symmetry, spectral, and electrical characteristics of CPC from excitonic interband transitions in a MoSe2 monolayer. The dependence on bias and gate voltages reveals two different CPC contributions, dominant at different voltages and with different dependence on illumination wavelength and incidence angles. We theoretically analyze symmetry requirements for effects that can yield CPC and compare these with the observed angular dependence and symmetries that occur for our device geometry. This reveals that the observed CPC effects require a reduced device symmetry, and that effects due to Berry curvature of the electronic states do not give a significant contribution.

Spontaneous valley splitting and valley pseudospin field effect transistors of monolayer VAgP2Se6

Valleytronics has attracted much attention due to its potential applications in the information processing industry. Creation of permanent valley polarization (PVP), i.e. unbalanced occupation at different valleys, is a vital requirement for practical devices in valleytronics. However, the development of an appropriate material with PVP remains a main challenge. Here we used first-principles calculations to predict that the spin-orbit coupling and magnetic ordering allow spontaneous valley Zeeman-type splitting in the pristine monolayer of VAgP₂Se₆. After suitable doping of VAgP₂Se₆, the Zeeman-type valley splitting results in a PVP, similar to the effect of spin polarization in spintronics. The VAgP₂Se₆ monolayer has nonequivalent valleys which can emit or absorb circularly polarized photons with opposite chirality. It thus shows great potential to be used as a photonic chirality filter and a circularly polarized light source. We then designed a valley pseudospin field effect transistor (VPFET) based on the monolayer VAgP₂Se₆, akin to the spin field effect transistors. In contrast to the current common transistors, VPFETs carry information of not only the electrons but also the valley pseudospins, far beyond common transistors.

Probing the nanoscale light emission properties of a CVD-grown MoS2 monolayer by tip-enhanced photoluminescence

Two-dimensional transition metal dichalcogenides are gaining increasing interest due to their promising optical properties. In particular, molybdenum disulfide (MoS₂) which displays a band-gap change from indirect at 1.29 eV for bulk materials to direct at 1.8 eV for the material monolayer. This particular effect can lead to a strong light interaction which can pave the way for a new approach to the next generation of visible light emitting devices. In this work we show the nanoscale variation of light emission properties by tip-enhanced photoluminescence microscopy and spectroscopy in the MoS₂ monolayer, grown by chemical vapour deposition. The variations of the light emission properties are due to different effects depending on the shape of the MoS₂ single layer, for instance, a different concentration of point defect in an irregularly shaped flake and the presence of a nanoscale terrace in a triangular monolayer. Simultaneously, atomic force microscopy reveals indeed the presence of a nanometric terrace, composed of an additional layer of MoS₂, and tip-enhanced PL intensity imaging shows a localized intensity decrease.

Microsecond Valley Lifetime of Defect-Bound Excitons in Monolayer WSe_{2}

In atomically thin two-dimensional semiconductors such as transition metal dichalcogenides (TMDs), controlling the density and type of defects promises to be an effective approach for engineering light-matter interactions. We demonstrate that electron-beam irradiation is a simple tool for selectively introducing defect-bound exciton states associated with chalcogen vacancies in TMDs. Our first-principles calculations and time-resolved spectroscopy measurements of monolayer WSe_{2} reveal that these defect-bound excitons exhibit exceptional optical properties including a recombination lifetime approaching 200 ns and a valley lifetime longer than 1  μs. The ability to engineer the crystal lattice through electron irradiation provides a new approach for tailoring the optical response of TMDs for photonics, quantum optics, and valleytronics applications.

Spoof Plasmonics: From Metamaterial Concept to Topological Description

Advances in metamaterials have offered the opportunity of engineering electromagnetic properties beyond the limits of natural materials. A typical example is "spoof" surface plasmon polaritons (SPPs), which mimic features of SPPs without penetrating into metal, but only with periodic corrugations on metal surfaces. They hold considerable promise in device applications from microwaves to the far infrared, where real SPP modes do not exist. The original spoof SPP concept is derived from the description of corrugated surfaces by a metamaterial that hosts an effective plasma frequency. Later, studies have attempted to describe spoof SPP modes with the band structure by strictly solving Maxwell's equations, which can possess band gaps from polaritonic anticrossing principle or Bragg interference. More recently, as inspired by the development of topological framework in condensed matter physics, the topological description of spoof SPPs is used to propose topologically protected waveguiding phenomena. Here, the developments of spoof SPPs from both practical and fundamental perspectives are reviewed.

Valley-Selective Response of Nanostructures Coupled to 2D Transition-Metal Dichalcogenides

Monolayer (1L) transition-metal dichalcogenides (TMDCs) are attractive materials for several optoelectronic applications because of their strong excitonic resonances and valley-selective response. Valley excitons in 1L-TMDCs are formed at opposite points of the Brillouin zone boundary, giving rise to a valley degree of freedom that can be treated as a pseudospin, and may be used as a platform for information transport and processing. However, short valley depolarization times and relatively short exciton lifetimes at room temperature prevent using valley pseudospins in on-chip integrated valley devices. Recently, it was demonstrated how coupling these materials to optical nanoantennas and metasurfaces can overcome this obstacle. Here, we review the state-of-the-art advances in valley-selective directional emission and exciton sorting in 1L-TMDC mediated by nanostructures and nanoantennas. We briefly discuss the optical properties of 1L-TMDCs paying special attention to their photoluminescence/absorption spectra, dynamics of valley depolarization, and the valley Hall effect. Then, we review recent works on nanostructures for valley-selective directional emission from 1L-TMDCs.

Persistent spin texture enforced by symmetry

Persistent spin texture (PST) is the property of some materials to maintain a uniform spin configuration in the momentum space. This property has been predicted to support an extraordinarily long spin lifetime of carriers promising for spintronics applications. Here, we predict that there exists a class of noncentrosymmetric bulk materials, where the PST is enforced by the nonsymmorphic space group symmetry of the crystal. Around certain high symmetry points in the Brillouin zone, the sublattice degrees of freedom impose a constraint on the effective spin-orbit field, which orientation remains independent of the momentum and thus maintains the PST. We illustrate this behavior using density-functional theory calculations for a handful of promising candidates accessible experimentally. Among them is the ferroelectric oxide BiInO3-a wide band gap semiconductor which sustains a PST around the conduction band minimum. Our results broaden the range of materials that can be employed in spintronics.

Hubbard Model Physics in Transition Metal Dichalcogenide Moiré Bands

Flexible long period moiré superlattices form in two-dimensional van der Waals crystals containing layers that differ slightly in lattice constant or orientation. In this Letter we show theoretically that isolated flat moiré bands described by generalized triangular lattice Hubbard models are present in twisted transition metal dichalcogenide heterobilayers. The hopping and interaction strength parameters of the Hubbard model can be tuned by varying the twist angle and the three-dimensional dielectric environment. When the flat moiré bands are partially filled, candidate many-body ground states at some special filling factors include spin-liquid states, quantum anomalous Hall insulators, and chiral d-wave superconductors.

Effective Theory of Nonadiabatic Quantum Evolution Based on the Quantum Geometric Tensor

We study the role of the quantum geometric tensor (QGT) in the evolution of two-band quantum systems. We show that all its components play an important role on the extra phase acquired by a spinor and on the trajectory of an accelerated wave packet in any realistic finite-duration experiment. While the adiabatic phase is determined by the Berry curvature (the imaginary part of the tensor), the nonadiabaticity is determined by the quantum metric (the real part of the tensor). We derive, for geodesic trajectories (corresponding to acceleration from zero initial velocity), the semiclassical equations of motion with nonadiabatic corrections. The particular case of a planar microcavity in the strong coupling regime allows us to extract the QGT components by direct light polarization measurements and to check their effects on the quantum evolution.

Valley-selective circular dichroism and high carrier mobility of graphene-like BC6N

The two-dimensional (2D) hybrid structures of boron nitride (BN) and graphene with properties superior to the individuals are long desired. In this work, we demonstrate theoretically that this goal can be reached in a new graphene-like borocarbonitride (g-BC6N) whose domain has been synthesized in recent experiments. It has a direct band gap of 1.833 eV and a high carrier mobility comparable to that of black phosphorene. The inversion symmetry breaking in g-BC6N leads to a pair of inequivalent valleys with opposite Berry curvatures in the vicinities of the vertices (K and K') of the Brillouin zone. The coexistence of valley-selective circular dichroism and high carrier mobility in g-BNC6 is beneficial to realize the valley Hall effect. We also propose a tight-binding (TB) model to describe the intrinsic features of this type of lattice, revealing a new class of 2D valleytronic materials.

Nondegenerate Chiral Phonons in Graphene/Hexagonal Boron Nitride Heterostructure from First-Principles Calculations

Triggered by the recent successful observation of previously predicted phonon chirality in the monolayer tungsten diselenide [ Science 2018 , 359 , 579 ], we systematically study the chiral phonons in the classical heterostructure of graphene/hexagonal boron nitride (G/ h-BN) by first-principles calculations. It is found that the broken inversion symmetry and the interlayer interaction of G/ h-BN not only open the phononic gaps but also lift the degeneracy of left-handed and right-handed chiral phonons at the first-Brillouin-zone corners (valleys). At valleys, the hybridization makes chiral phonon modes solely contributed from one individual layer. Moreover, we demonstrate that the vertical stress is effective to tune the degenerated phononic gap while keeping the valley-phonon chirality of G/ h-BN heterostructure, which is favorable for the Raman or ultrafast infrared spectroscopy measurement. We also analyze the pseudoangular momentum of valley-phonon modes, which provide important references for the excitation and measurement of the chiral phonons in the process of electronic intervalley scattering. Collectively, our results on the chiral phonons in the G/ h-BN heterostructure system could stimulate more experimental and theoretical studies and promote the future applications on the phonon-chirality-based phononics.

Tailoring MoS2 Valley-Polarized Photoluminescence with Super Chiral Near-Field

Transition metal dichalcogenides with intrinsic spin-valley degrees of freedom hold great potentials for applications in spintronic and valleytronic devices. MoS2 monolayer possesses two inequivalent valleys in the Brillouin zone, with each valley coupling selectively with circularly polarized photons. The degree of valley polarization (DVP) is a parameter to characterize the purity of valley-polarized photoluminescence (PL) of MoS2 monolayer. Usually, the detected values of DVP in MoS2 monolayer show achiral property under optical excitation of opposite helicities due to reciprocal phonon-assisted intervalley scattering process. Here, it is reported that valley-polarized PL of MoS2 can be tailored through near-field interaction with plasmonic chiral metasurface. The resonant field of the chiral metasurface couples with valley-polarized excitons, and tailors the measured PL spectra in the far-field, resulting in observation of chiral DVP of MoS2 -metasurface under opposite helicities excitations. Valley-contrast PL in the chiral heterostructure is also observed when illuminated by linearly polarized light. The manipulation of valley-polarized PL in 2D materials using chiral metasurface represents a viable route toward valley-polaritonic devices.

Semiconducting edges and flake-shape evolution of monolayer GaSe: role of edge reconstructions

Group-III metal monochalcogenides have emerged as a new class of two-dimensional (2D) semiconductor materials. For the integration of 2D materials for various potential device applications, there is an inevitable need to reduce their dimensionality into specific sized nanostructures with edges. Owing to the properties of finite-sized 2D nanostructures strongly related to the edge configurations, the precise understanding of the edge geometric structures at an atomic level is of particular importance. By means of first-principles calculations, the geometric structures and electronic properties of stable zigzag and armchair edges in a prototype example GaSe monolayer have been identified. Our results demonstrate that both Ga- and Se-terminated zigzag edges prefer to the (3 × 1) reconstructions, and the armchair edges with the perfect flat configuration are energetically favorable. It is unexpectedly found that both zigzag and armchair GaSe nanoribbons with reconstructed edges are semiconductors, which is different from previous recognition where the zigzag edges are metallic. Moreover, the edge-dependent flake shape in GaSe has been plotted using the Wulff construction theory, and the shape evolution with chemical potentials can be applied to explain broad experimental observations on the morphologies of GaSe flakes. Importantly, similar reconstructions and electronic properties also appeared at InSe edges, suggesting that the reconstruction induced semiconducting edges are a fundamental phenomenon for 2D group-III metal monochalcogenides.

Optically dark excitonic states mediated exciton and biexciton valley dynamics in monolayer WSe2

We present a theory to address the photoluminescence (PL) intensity and valley polarization (VP) dynamics in monolayer WSe₂, under the impact of excitonic dark states of both excitons and biexcitons. We find that the PL intensity of all excitonic channels including intravalley exciton (X_b), intravalley biexciton (XX_k,k) and intervalley biexciton (XX[Formula: see text]) in particular for the XX_k,k PL is enhanced by laser excitation fluence. In addition, our results indicate the anomalous temperature dependence of PL, i.e. increasing with temperature, as a result of favored phonon assisted dark-to-bright scatterings at high temperatures. Moreover, we observe that the PL is almost immune to intervalley scatterings, which trigger the exchange of excitonic states between the two valleys. As far as the valley polarization is concerned, we find that the VP of X_b shrinks as temperature increases, exhibiting opposite temperature response to PL, while the intravalley XX_k,k VP is found almost independent of temperature. In contrast to both X_b and XX_k,k, the intervalley XX[Formula: see text] VP identically vanishes, because of equal populations of excitons in the K and [Formula: see text] valleys bounded to form intervalley biexcitons. Notably, it is found that the X_b VP much more strongly depends on bright-dark scattering than that of XX_k,k, making dark state act as a robust reservoir for valley polarization against intervalley scatterings for X_b at strong bright-dark scatterings, but not for XX_k,k. Dark excitonic states enabled enhancement of VP benefits quantum technology for information processing based on the valley degree of freedom in valleytronic devices. Furthermore, the VP has strong dependence on intervalley scattering but maintains essentially constant with excitation fluence. Finally, the dependence of time evolution of PL and VP on temperature and excitation fluence is discussed.

Evidence for line width and carrier screening effects on excitonic valley relaxation in 2D semiconductors

Monolayers of transition metal dichalcogenides (TMDC) have recently emerged as excellent platforms for exploiting new physics and applications relying on electronic valley degrees of freedom in two-dimensional (2D) systems. Here, we demonstrate that Coulomb screening by 2D carriers plays a critical role in excitonic valley pseudospin relaxation processes in naturally carrier-doped WSe₂ monolayers (1L-WSe₂). The exciton valley relaxation times were examined using polarization- and time-resolved photoluminescence spectroscopy at temperatures ranging from 10 to 160 K. We show that the temperature-dependent exciton valley relaxation times in 1L-WSe₂ under various exciton and carrier densities can be understood using a unified framework of intervalley exciton scattering via momentum-dependent long-range electron-hole exchange interactions screened by 2D carriers that depend on the carrier density and the exciton linewidth. Moreover, the developed framework was successfully applied to engineer the valley polarization of excitons in 1L-WSe₂. These findings may facilitate the development of TMDC-based opto-valleytronic devices.

The role of momentum-dark excitons in the elementary optical response of bilayer WSe2

Monolayer transition metal dichalcogenides (TMDs) undergo substantial changes in the single-particle band structure and excitonic optical response upon the addition of just one layer. As opposed to the single-layer limit, the bandgap of bilayer (BL) TMD semiconductors is indirect which results in reduced photoluminescence with richly structured spectra that have eluded a detailed understanding to date. Here, we provide a closed interpretation of cryogenic emission from BL WSe2 as a representative material for the wider class of TMD semiconductors. By combining theoretical calculations with comprehensive spectroscopy experiments, we identify the crucial role of momentum-indirect excitons for the understanding of BL TMD emission. Our results shed light on the origin of quantum dot formation in BL crystals and will facilitate further advances directed at opto-electronic applications of layered TMD semiconductors in van der Waals heterostructures and devices.

Gap-Mode Surface-Plasmon-Enhanced Photoluminescence and Photoresponse of MoS2

2D materials hold great potential for designing novel electronic and optoelectronic devices. However, 2D material can only absorb limited incident light. As a representative 2D semiconductor, monolayer MoS₂ can only absorb up to 10% of the incident light in the visible, which is not sufficient to achieve a high optical-to-electrical conversion efficiency. To overcome this shortcoming, a "gap-mode" plasmon-enhanced monolayer MoS₂ fluorescent emitter and photodetector is designed by squeezing the light-field into Ag shell-isolated nanoparticles-Au film gap, where the confined electromagnetic field can interact with monolayer MoS₂ . With this gap-mode plasmon-enhanced configuration, a 110-fold enhancement of photoluminescence intensity is achieved, exceeding values reached by other plasmon-enhanced MoS₂ fluorescent emitters. In addition, a gap-mode plasmon-enhanced monolayer MoS₂ photodetector with an 880% enhancement in photocurrent and a responsivity of 287.5 A W^-1 is demonstrated, exceeding previously reported plasmon-enhanced monolayer MoS₂ photodetectors.

Valley Physics in Non-Hermitian Artificial Acoustic Boron Nitride

The valley can serve as a new degree of freedom in the manipulation of particles or waves in condensed matter physics, whereas systems containing combinations of gain and loss elements constitute rich building units that can mimic non-Hermitian properties. By introducing gain and loss in artificial acoustic boron nitride, we show that the acoustic valley states and the valley-projected edge states display exotic behaviors in that they sustain either attenuated or amplified wave propagation. Our findings show how non-Hermiticity introduces a mechanism in tuning topological protected valley transports, which may have significance in advanced wave control for sensing and communication applications.

Monolayer Transition Metal Dichalcogenides as Light Sources

Reducing the dimensions of materials is one of the key approaches to discovering novel optical phenomena. The recent emergence of 2D transition metal dichalcogenides (TMDCs) has provided a promising platform for exploring new optoelectronic device applications, with their tunable electronic properties, structural controllability, and unique spin valley-coupled systems. This progress report provides an overview of recent advances in TMDC-based light-emitting devices discussed from several aspects in terms of device concepts, material designs, device fabrication, and their diverse functionalities. First, the advantages of TMDCs used in light-emitting devices and their possible functionalities are presented. Second, conventional approaches for fabricating TMDC light-emitting devices are emphasized, followed by introducing a newly established, versatile method for generating light emission in TMDCs. Third, current growing technologies for heterostructure fabrication, in which distinct TMDCs are vertically stacked or laterally stitched, are explained as a possible means for designing high-performance light-emitting devices. Finally, utilizing the topological features of TMDCs, the challenges for controlling circularly polarized light emission and its device applications are discussed from both theoretical and experimental points of view.

Effect of Distance on Photoluminescence Quenching and Proximity-Induced Spin-Orbit Coupling in Graphene/WSe2 Heterostructures

Spin-orbit coupling (SOC) in graphene can be greatly enhanced by proximity coupling it to transition metal dichalcogenides (TMDs) such as WSe₂. We find that the strength of the acquired SOC in graphene depends on the stacking order of the heterostructures when using hexagonal boron nitride ( h-BN) as the capping layer, i.e., SiO₂/graphene/WSe₂/ h-BN exhibiting stronger SOC than SiO₂/WSe₂/graphene/ h-BN. We utilize photoluminescence (PL) as an indicator to characterize the interaction between graphene and monolayer WSe₂ grown by chemical vapor deposition. We observe much stronger PL quenching in the SiO₂/graphene/WSe₂/ h-BN stack than in the SiO₂/WSe₂/graphene/ h-BN stack and, correspondingly, a much larger weak antilocalization (WAL) effect or stronger induced SOC in the former than in the latter. We attribute these two effects to the interlayer distance between graphene and WSe₂, which depends on whether graphene is in immediate contact with h-BN. Our observations and hypothesis are further supported by first-principles calculations, which reveal a clear difference in the interlayer distance between graphene and WSe₂ in these two stacks.

Nanophotonics with 2D transition metal dichalcogenides [Invited]

Two-dimensional semiconducting transition metal dichalcogenides (TMDCs) have recently become attractive materials for several optoelectronic applications, such as photodetection, light harvesting, phototransistors, light-emitting diodes, and lasers. Their bandgap lies in the visible and near-IR range, and they possess strong excitonic resonances, high oscillator strengths, and valley-selective response. Coupling these materials to optical nanocavities enhances the quantum yield of exciton emission, enabling advanced quantum optics and nanophotonics devices. Here, we review the state-of-the-art advances of hybrid exciton-polariton structures based on monolayer TMDCs coupled to plasmonic and dielectric nanocavities. We discuss the optical properties of 2D WS₂, WSe₂, MoS₂ and MoSe₂ materials, paying special attention to their energy bands, photoluminescence/absorption spectra, excitonic fine structure, and to the dynamics of exciton formation and valley depolarization. We also discuss light-matter interactions in such hybrid exciton-polariton structures. Finally, we focus on weak and strong coupling regimes in monolayer TMDCs-based exciton-polariton systems, envisioning research directions and future opportunities for this material platform.

In situ edge engineering in two-dimensional transition metal dichalcogenides

Exerting synthetic control over the edge structure and chemistry of two-dimensional (2D) materials is of critical importance to direct the magnetic, optical, electrical, and catalytic properties for specific applications. Here, we directly image the edge evolution of pores in Mo1-xW x Se2 monolayers via atomic-resolution in situ scanning transmission electron microscopy (STEM) and demonstrate that these edges can be structurally transformed to theoretically predicted metastable atomic configurations by thermal and chemical driving forces. Density functional theory calculations and ab initio molecular dynamics simulations explain the observed thermally induced structural evolution and exceptional stability of the four most commonly observed edges based on changing chemical potential during thermal annealing. The coupling of modeling and in situ STEM imaging in changing chemical environments demonstrated here provides a pathway for the predictive and controlled atomic scale manipulation of matter for the directed synthesis of edge configurations in Mo1-x W x Se2 to achieve desired functionality.

Imaging of pure spin-valley diffusion current in WS2-WSe2 heterostructures

Transition metal dichalcogenide (TMDC) materials are promising for spintronic and valleytronic applications because valley-polarized excitations can be generated and manipulated with circularly polarized photons and the valley and spin degrees of freedom are locked by strong spin-orbital interactions. In this study we demonstrate efficient generation of a pure and locked spin-valley diffusion current in tungsten disulfide (WS₂)-tungsten diselenide (WSe₂) heterostructures without any driving electric field. We imaged the propagation of valley current in real time and space by pump-probe spectroscopy. The valley current in the heterostructures can live for more than 20 microseconds and propagate over 20 micrometers; both the lifetime and the diffusion length can be controlled through electrostatic gating. The high-efficiency and electric-field-free generation of a locked spin-valley current in TMDC heterostructures holds promise for applications in spin and valley devices.

Exciton Diffusion and Halo Effects in Monolayer Semiconductors

We directly monitor exciton propagation in freestanding and SiO_{2}-supported WS_{2} monolayers through spatially and time-resolved microphotoluminescence under ambient conditions. We find a highly nonlinear behavior with characteristic, qualitative changes in the spatial profiles of the exciton emission and an effective diffusion coefficient increasing from 0.3 to more than 30  cm^{2}/s, depending on the injected exciton density. Solving the diffusion equation while accounting for Auger recombination allows us to identify and quantitatively understand the main origin of the increase in the observed diffusion coefficient. At elevated excitation densities, the initial Gaussian distribution of the excitons evolves into long-lived halo shapes with μm-scale diameter, indicating additional memory effects in the exciton dynamics.

Temperature-dependent Raman spectroscopy studies of the interface coupling effect of monolayer ReSe2 single crystals on Au foils

Rhenium diselenide (ReSe₂), which bears in-plane anisotropic optical and electrical properties, is of considerable interest for its excellent applications in novel devices, such as polarization-sensitive photodetectors and integrated polarization-controllers. However, great challenges to date in the controllable synthesis of high-quality ReSe₂ have hindered its in-depth investigations and practical applications. Herein, we report a feasible synthesis of monolayer single-crystal ReSe₂ flakes on the Au foil substrate by using a chemical vapor deposition route. Particularly, we focus on the temperature-dependent Raman spectroscopy investigations of monolayer ReSe₂ grown on Au foils, which present concurrent red shifts of E_g-like and A_g-like modes with increasing measurement temperature from 77-290 K. Linear temperature dependences of both modes are revealed and explained from the anharmonic vibration of the ReSe₂ lattice. More importantly, the strong interaction of ReSe₂ with Au, with respect to that with SiO₂/Si, is further confirmed by temperature-dependent Raman characterization. This work is thus proposed to shed light on the optical and thermal properties of such anisotropic two-dimensional three-atom-thick materials.

Chemical synthesis of two-dimensional atomic crystals, heterostructures and superlattices

Two-dimensional atomic crystals (2DACs) have attracted intense recent interest. With a nearly perfect crystalline structure and dangling-bond free surface, these atomically thin materials have emerged as a new material platform for fundamental materials science and diverse technology opportunities at the limit of single atom thickness. Over the past decade, a wide range of 2DACs has been prepared by mechanically exfoliating bulk layered crystals, which has fueled the rapid progress of the entire field in terms of fundamental physics and basic device demonstrations. However, studies to date are largely limited to mechanically exfoliated flakes, which are clearly not scalable for practical applications. The chemical synthesis of these materials has been lagging far behind fundamental property investigations or novel device demonstrations, which limits further progress of the field. To explore the full potential of 2DACs requires a robust synthesis of these atomically thin materials and scalable construction of complex heterostructures with designed spatial modulation of chemical compositions and electronic structures. The extreme aspect ratio and highly delicate nature of the atomically thin crystals pose a significant synthetic challenge beyond traditional bulk crystals and have motivated considerable efforts worldwide. Here we will review the recent advances, challenges and future perspective of the chemical synthesis of 2DACs, heterostructures and superlattices.

Dissociation of two-dimensional excitons in monolayer WSe2

Two-dimensional (2D) semiconducting materials are promising building blocks for optoelectronic applications, many of which require efficient dissociation of excitons into free electrons and holes. However, the strongly bound excitons arising from the enhanced Coulomb interaction in these monolayers suppresses the creation of free carriers. Here, we identify the main exciton dissociation mechanism through time and spectrally resolved photocurrent measurements in a monolayer WSe₂p–n junction. We find that under static in-plane electric field, excitons dissociate at a rate corresponding to the one predicted for tunnel ionization of 2D Wannier–Mott excitons. This study is essential for understanding the photoresponse of 2D semiconductors and offers design rules for the realization of efficient photodetectors, valley dependent optoelectronics, and novel quantum coherent phases.

In two-dimensional semiconductors excitons are strongly bound, suppressing the creation of free carriers. Here, the authors investigate the main exciton dissociation pathway in p-n junctions of monolayer WSe₂ by means of time and spectrally resolved photocurrent measurements.

Nanoscale chiral valley-photon interface through optical spin-orbit coupling

The emergence of two-dimensional transition metal dichalcogenide materials has sparked intense activity in valleytronics, as their valley information can be encoded and detected with the spin angular momentum of light. We demonstrate the valley-dependent directional coupling of light using a plasmonic nanowire-tungsten disulfide (WS₂) layers system. We show that the valley pseudospin in WS₂ couples to transverse optical spin of the same handedness with a directional coupling efficiency of 90 ± 1%. Our results provide a platform for controlling, detecting, and processing valley and spin information with precise optical control at the nanoscale.

High-Performance All 2D-Layered Tin Disulfide: Graphene Photodetecting Transistors with Thickness-Controlled Interface Dynamics

Tin disulfide crystals with layered two-dimensional (2D) sheets are grown by chemical vapor deposition using a novel precursor approach and integrated into all 2D transistors with graphene (Gr) electrodes. The Gr:SnS₂:Gr transistors exhibit excellent photodetector response with high detectivity and photoresponsivity. We show that the response of the all 2D photodetectors depends upon charge trapping at the interface and the Schottky barrier modulation. The thickness-dependent SnS₂ measurements in devices reveal a transition from the interface-dominated response for thin crystals to bulklike response for the thicker SnS₂ crystals, showing the sensitivity of devices fabricated using layered materials on the number of layers. These results show that SnS₂ has photosensing performance when combined with Gr electrodes that is comparable to other 2D transition metal dichalcogenides of MoS₂ and WS₂.

Two-Dimensionally Layered p-Black Phosphorus/n-MoS2/p-Black Phosphorus Heterojunctions

Layered heterojunctions are widely applied as fundamental building blocks for semiconductor devices. For the construction of nanoelectronic and nanophotonic devices, the implementation of two-dimensional materials (2DMs) is essential. However, studies of junction devices composed of 2DMs are still largely focused on single p-n junction devices. In this study, we demonstrate a novel pnp double heterojunction fabricated by the vertical stacking of 2DMs (black phosphorus (BP) and MoS₂) using dry-transfer techniques and the formation of high-quality p-n heterojunctions between the BP and MoS₂ in the vertically stacked BP/MoS₂/BP structure. The pnp double heterojunctions allowed us to modulate the output currents by controlling the input current. These results can be applied for the fabrication of advanced heterojunction devices composed of 2DMs for nano(opto)electronics.

Hole Transport in Exfoliated Monolayer MoS2

Ideal monolayers of common semiconducting transition-metal dichalcogenides (TMDCs) such as MoS₂, WS₂, MoSe₂, and WSe₂ possess many similar electronic properties. As it is the case for all semiconductors, however, the physical response of these systems is strongly determined by defects in a way specific to each individual compound. Here we investigate the ability of exfoliated monolayers of these TMDCs to support high-quality, well-balanced ambipolar conduction, which has been demonstrated for WS₂, MoSe₂, and WSe₂, but not for MoS₂. Using ionic-liquid gated transistors, we show that, contrary to WS₂, MoSe₂, and WSe₂, hole transport in exfoliated MoS₂ monolayers is systematically anomalous, exhibiting a maximum in conductivity at negative gate voltage ( V _G) followed by a suppression of up to 100 times upon further increasing V _G. To understand the origin of this difference, we have performed a series of experiments including the comparison of hole transport in MoS₂ monolayers and thicker multilayers, in exfoliated and CVD-grown monolayers, as well as gate-dependent optical measurements (Raman and photoluminescence) and scanning tunneling imaging and spectroscopy. In agreement with existing ab initio calculations, the results of all these experiments are consistently explained in terms of defects associated with chalcogen vacancies that only in MoS₂ monolayers, but not in thicker MoS₂ multilayers nor in monolayers of the other common semiconducting TMDCs, create in-gap states near the top of the valence band that act as strong hole traps. Our results demonstrate the importance of studying systematically how defects determine the properties of 2D semiconducting materials and of developing methods to control them.

Large-area synthesis and photoelectric properties of few-layer MoSe2 on molybdenum foils

Compared with MoS₂ and WS₂, selenide analogs have narrower band gaps and higher electron mobilities, which make them more applicable to real electrical devices. In addition, few-layer metal selenides have higher electrical conductivity, carrier mobility and light absorption than the corresponding monolayers. However, the large-scale and high-quality growth of few-layer metal selenides remains a significant challenge. Here, we develop a facile method to grow large-area and highly crystalline few-layer MoSe₂ by directly selenizing the Mo foil surface at 550 °C within 60 min under ambient pressure. The atomic layers were controllably grown with thicknesses between 3.4 and 6 nm, which just met the thickness range required for high-performance electrical devices. Furthermore, we fabricated a vertical p-n junction photodetector composed of few-layer MoSe₂ and p-type silicon, achieving photoresponsivity higher by two orders of magnitude than that of the reported monolayer counterpart. This technique provides a feasible approach towards preparing other 2D transition metal dichalcogendes for device applications.

Valley Topological Phases in Bilayer Sonic Crystals

Recently, the topological physics in artificial crystals for classical waves has become an emerging research area. In this Letter, we propose a unique bilayer design of sonic crystals that are constructed by two layers of coupled hexagonal array of triangular scatterers. Assisted by the additional layer degree of freedom, a rich topological phase diagram is achieved by simply rotating scatterers in both layers. Under a unified theoretical framework, two kinds of valley-projected topological acoustic insulators are distinguished analytically, i.e., the layer-mixed and layer-polarized topological valley Hall phases, respectively. The theory is evidently confirmed by our numerical and experimental observations of the nontrivial edge states that propagate along the interfaces separating different topological phases. Various applications such as sound communications in integrated devices can be anticipated by the intriguing acoustic edge states enriched by the layer information.

Tunable Γ-K Valley Populations in Hole-Doped Trilayer WSe_{2}

We present a combined experimental and theoretical study of valley populations in the valence bands of trilayer WSe_{2}. Shubnikov-de Haas oscillations show that trilayer holes populate two distinct subbands associated with the K and Γ valleys, with effective masses 0.5m_{e} and 1.2m_{e}, respectively; m_{e} is the bare electron mass. At a fixed total hole density, an applied transverse electric field transfers holes from Γ orbitals to K orbitals. We are able to explain this behavior in terms of the larger layer polarizability of the K orbital subband.

Valley-selective directional emission from a transition-metal dichalcogenide monolayer mediated by a plasmonic nanoantenna

Background: Two-dimensional (2D) transition-metal dichalcogenides (TMDCs) with intrinsically crystal inversion-symmetry breaking have shown many advanced optical properties. In particular, the valley polarization in 2D TMDCs that can be addressed optically has inspired new physical phenomena and great potential applications in valleytronics. Results: Here, we propose a TMDC-nanoantenna system that could effectively enhance and direct emission from the two valleys in TMDCs into diametrically opposite directions. By mimicking the emission from each valley of the monolayer of WSe2 as a chiral point-dipole emitter, we demonstrate numerically that the emission from different valleys is directed into opposite directions when coupling to a double-bar plasmonic nanoantenna. The directionality derives from the interference between the dipole and quadrupole modes excited in the two bars, respectively. Thus, we could tune the emission direction from the proposed TMDC-nanoantenna system by tuning the pumping without changing the antenna structure. Furthermore, we discuss the general principles and the opportunities to improve the average performance of the nanoantenna structure. Conclusion: The scheme we propose here can potentially serve as an important component for valley-based applications, such as non-volatile information storage and processing.

Group 6 transition metal dichalcogenide nanomaterials: synthesis, applications and future perspectives

Group 6 transition metal dichalcogenides (G6-TMDs), most notably MoS₂, MoSe₂, MoTe₂, WS₂ and WSe₂, constitute an important class of materials with a layered crystal structure. Various types of G6-TMD nanomaterials, such as nanosheets, nanotubes and quantum dot nano-objects and flower-like nanostructures, have been synthesized. High thermodynamic stability under ambient conditions, even in atomically thin form, made nanosheets of these inorganic semiconductors a valuable asset in the existing library of two-dimensional (2D) materials, along with the well-known semimetallic graphene and insulating hexagonal boron nitride. G6-TMDs generally possess an appropriate bandgap (1-2 eV) which is tunable by size and dimensionality and changes from indirect to direct in monolayer nanosheets, intriguing for (opto)electronic, sensing, and solar energy harvesting applications. Moreover, rich intercalation chemistry and abundance of catalytically active edge sites make them promising for fabrication of novel energy storage devices and advanced catalysts. In this review, we provide an overview on all aspects of the basic science, physicochemical properties and characterization techniques as well as all existing production methods and applications of G6-TMD nanomaterials in a comprehensive yet concise treatment. Particular emphasis is placed on establishing a linkage between the features of production methods and the specific needs of rapidly growing applications of G6-TMDs to develop a production-application selection guide. Based on this selection guide, a framework is suggested for future research on how to bridge existing knowledge gaps and improve current production methods towards technological application of G6-TMD nanomaterials.

Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures

Transition metal dichalcogenides have valley degree of freedom, which features optical selection rule and spin-valley locking, making them promising for valleytronics devices and quantum computation. For either application, a long valley polarization lifetime is crucial. Previous results showed that it is around picosecond in monolayer excitons, nanosecond for local excitons and tens of nanosecond for interlayer excitons. Here we show that the dark excitons in two-dimensional heterostructures provide a microsecond valley polarization memory thanks to the magnetic field induced suppression of valley mixing. The lifetime of the dark excitons shows magnetic field and temperature dependence. The long lifetime and valley polarization lifetime of the dark exciton in two-dimensional heterostructures make them promising for long-distance exciton transport and macroscopic quantum state generations.

Few-layer Tellurium: one-dimensional-like layered elementary semiconductor with striking physical properties

Few-layer Tellurium, an elementary semiconductor, succeeds most of striking physical properties that black phosphorus (BP) offers and could be feasibly synthesized by simple solution-based methods. It is comprised of non-covalently bound parallel Te chains, among which covalent-like feature appears. This feature is, we believe, another demonstration of the previously found covalent-like quasi-bonding (CLQB) where wavefunction hybridization does occur. The strength of this inter-chain CLQB is comparable with that of intra-chain covalent bonding, leading to closed stability of several Te allotropes. It also introduces a tunable bandgap varying from nearly direct 0.31 eV (bulk) to indirect 1.17 eV (2L) and four (two) complex, highly anisotropic and layer-dependent hole (electron) pockets in the first Brillouin zone. It also exhibits an extraordinarily high hole mobility (∼10⁵ cm²/Vs) and strong optical absorption along the non-covalently bound direction, nearly isotropic and layer-dependent optical properties, large ideal strength over 20%, better environmental stability than BP and unusual crossover of force constants for interlayer shear and breathing modes. All these results manifest that the few-layer Te is an extraordinary-high-mobility, high optical absorption, intrinsic-anisotropy, low-cost-fabrication, tunable bandgap, better environmental stability and nearly direct bandgap semiconductor. This "one-dimension-like" few-layer Te, together with other geometrically similar layered materials, may promote the emergence of a new family of layered materials.