Diversity of trion states and substrate effects in the optical properties of an MoS2 monolayer

Probing Dark Excitons in Monolayer MoS_{2} by Nonlinear Two-Photon Spectroscopy

We report a new dark exciton in monolayer MoS_{2} using second harmonic generation spectroscopy. Hereby, the spectrally dependent second harmonic generation intensity splits into two branches, and an anticrossing is observed at ∼25  meV blue detuned from the bright neutral exciton. These observations are indicative of coherent quantum interference arising from strong two-photon light-matter interaction with an excitonic state that is dark for single photon interaction. The existence of the dark state is supported by engineering its relaxation to bright localized excitons, mediated by vibrational modes of a proximal nanobeam cavity. We show that two-photon light-matter interaction involving dark states has the potential to control relaxation pathways induced by nanostructuring the local environment. Moreover, our results indicate that dark excitons have significant potential for nonlinear quantum devices based on their nontrivial excitonic photophysics.

Exciton-Driven and Layer-Independent Linear and Nonlinear Optical Properties in NbOCl2

We investigate the electronic structure and linear and nonlinear [second-harmonic generation (SHG)] spectra of the NbOCl2 monolayer, bilayer, and bulk by using a real-time first-principles approach based on many-body theory. First, the interlayer couplings between NbOCl2 layers are very weak, due to the relatively large interlayer distance, saturation of the p orbital of Cl atoms, and high degree of localization of charge density around the Nb atom for both the lowest conduction band and the highest valence band. Second, the quasiparticle gaps and exciton binding energy for the three systems show layer-dependent features and decrease with an increase in layer thickness. Most importantly, the linear and SHG spectra of the NbOCl2 monolayer, bilayer, and bulk are dominated by strong excitonic resonances and exhibit layer-independent features due to the weak interlayer couplings. Our findings demonstrate that excitonic effects should be included in studying the optical properties of not only two-dimensional materials but also layered bulk materials with weak interlayer couplings.

Elucidating Solvatochromic Shifts in Two-Dimensional Photocatalysts by Solving the Bethe-Salpeter Equation Coupled with Implicit Solvation Method

Many studies have focused on tailoring the photophysical properties of two-dimensional (2D) materials for photocatalytic (PC) or photoelectrochemical (PEC) applications. To understand the optical properties of 2D materials in solution, we established a computational method that combined the Bethe-Salpeter equation (BSE) calculations with our GW-GPE method, allowing for GW/BSE-level calculations with implicit solvation described using the generalized Poisson equation (GPE). We applied this method to MoS2, phosphorene (PP), and g-C3N4 and found that when the solvent dielectric increased, it reduced the exciton binding energy and quasiparticle bandgap, resulting in almost no solvatochromic shift in the excitonic peaks of MoS2 and PP, which is consistent with previous experiments. However, our calculations predicted that the solvent dielectric had a significant impact on the excitonic properties of g-C3N4, exhibiting a large solvatochromic shift. We expect that our GW/BSE-GPE method will offer insights into the design of 2D materials for PC and PEC applications.

Giant Faraday rotation in atomically thin semiconductors

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

Two-Channel Indirect-Gap Photoluminescence and Competition between the Conduction Band Valleys in Few-Layer MoS2

MoS2 is a two-dimensional layered transition metal dichalcogenide with unique electronic and optical properties. The fabrication of ultrathin MoS2 is vitally important, since interlayer interactions in its ultrathin varieties will become thickness-dependent, providing thickness-governed tunability and diverse applications of those properties. Unlike with a number of studies that have reported detailed information on direct bandgap emission from MoS2 monolayers, reliable experimental evidence for thickness-induced evolution or transformation of the indirect bandgap remains scarce. Here, the sulfurization of MoO3 thin films with nominal thicknesses of 30 nm, 5 nm and 3 nm was performed. All sulfurized samples were examined at room temperature with spectroscopic ellipsometry and photoluminescence spectroscopy to obtain information about their dielectric function and edge emission spectra. This investigation unveiled an indirect-to-indirect crossover between the transitions, associated with two different Λ and K valleys of the MoS2 conduction band, by thinning its thickness down to a few layers.

Photoluminescence Enhancement of Monolayer WS2 by n-Doping with an Optically Excited Gold Disk

In nanophotonics and quantum optics, we aim to control and manipulate light with tailored nanoscale structures. Hybrid systems of nanostructures and atomically thin materials are of interest here, as they offer rich physics and versatility due to the interaction between photons, plasmons, phonons, and excitons. In this study, we explore the optical and electronic properties of a hybrid system, a naturally n-doped monolayer WS2 covering a gold disk. We demonstrate that the nonresonant excitation of the gold disk in the high absorption regime efficiently generates hot carriers via localized surface plasmon excitation, which n-dope the monolayer WS2 and enhance the photoluminescence emission by regulating the multiexciton population and stabilizing the neutral exciton emission. The results are relevant to the further development of nanotransistors in photonic circuits and optoelectronic applications.

Enhanced interactions of excitonic complexes in free-standing WS2

Excitonic complexes, bound states of electrons and holes, provide a promising platform in monolayer transition-metal dichalcogenide (TMDC) semiconductors for investigating diverse many-body interaction phenomena. The surrounding dielectric environment has been found to strongly influence the excitonic properties of the TMDC monolayers. While the impact of different dielectric surroundings on two-dimensional semiconductor materials and their strong correlations have been well studied, the effects on exciton formation and its properties resulting from a further reduction in dielectric screening remain elusive. In this study, we examined free-standing tungsten disulfide (WS2) monolayers, where the efficient generation of higher-order correlated excitonic complexes is readily observed. This phenomenon arises from the effective mutual interactions among excitons and internal carriers, attributed to the modulated exciton dynamics generated by the further reduced dielectric screening effect in the freestanding structure. The formation efficiency of excitonic complexes is enhanced and the multiple biexciton species (five particles such as charged biexcitons and acceptor/donor-bound biexcitons) are successfully induced under low excitation intensity and moderate temperature conditions. Our findings offer valuable insights into the influence of the dielectric environment on exciton interactions and enable a productive avenue for exploring fundamental many-body interactions, providing new possibilities for dielectric engineering of atomic thin semiconductors.

Biexciton and Singlet Trion Upconvert Exciton Photoluminescence in a MoSe2 Monolayer Supported by Acoustic and Optical K-Valley Phonons

Transition metal dichalcogenide monolayers represent unique platforms for studying both electronic and phononic interactions as well as intra- and intervalley exciton complexes. Here, we investigate the upconversion of exciton photoluminescence in MoSe2 monolayers. Within the nominal transparency window of MoSe2 the exciton emission is enhanced for resonantly addressing the spin-singlet negative trion and neutral biexciton at a few tens of meV below the neutral exciton transition. We identify that the A'1 optical phonon at the K valley provides the energy gain in the upconversion process at the trion resonance, while ZA(K) phonons with their spin- and valley-switching properties support the biexciton driven upconversion of the exciton emission. Interestingly, the latter upconversion process yields unpolarized exciton photoluminescence, while the former also leads to circularly polarized emission. Our study highlights high-order exciton complexes interacting with optical and acoustic K-valley phonons and upconverting light into the bright exciton.

Evaluation of the excitation spectra with diffusion Monte Carlo on an auxiliary bosonic ground state

We aim to improve upon the variational Monte Carlo (VMC) approach for excitations replacing the Jastrow factor by an auxiliary bosonic (AB) ground state and multiplying it by a fermionic component factor. The instantaneous change in imaginary time of an arbitrary excitation in the original interacting fermionic system is obtained by measuring observables via the ground-state distribution of walkers of an AB system that is subject to an auxiliary effective potential. The effective potential is used to (i) drive the AB system's ground-state configuration space toward the configuration space of the excitations of the original fermionic system and (ii) subtract from a diffusion Monte Carlo (DMC) calculation contributions that can be included in conventional approximations, such as mean-field and configuration interaction (CI) methods. In this novel approach, the AB ground state is treated statistically in DMC, whereas the fermionic component of the original system is expanded in a basis. The excitation energies of the fermionic eigenstates are obtained by sampling a fermion-boson coupling term on the AB ground state. We show that this approach can take advantage of and correct for approximate eigenstates obtained via mean-field calculations or truncated interactions. We demonstrate that the AB ground-state factor incorporates the correlations missed by standard Jastrow factors, further reducing basis truncation errors. Relevant parts of the theory have been tested in soluble model systems and exhibit excellent agreement with exact analytical data and CI and VMC approaches. In particular, for limited basis set expansions and sufficient statistics, AB approaches outperform CI and VMC in terms of basis size for the same systems. The implementation of this method in current codes, despite being demanding, will be facilitated by reusing procedures already developed for calculating ground-state properties with DMC and excitations with VMC.

Lattice Vacancy Induced Energy Renormalization of Photonic Quasiparticles in Two-Dimensional Semiconductors

Coulomb interactions among dense charges and quasiparticle energy renormalization are at the center of quantum science because they significantly reshape the fundamental electronic and photonic properties of materials. While lattice vacancies are ubiquitous in solid materials, their physical effect on the Coulomb interaction among quasiparticles is normally weak and negligible. Here we show that in atomically thin semiconductors the presence of lattice vacancies emerges as an important but unexplored origin for the nontrivial renormalization of quasiparticle binding energies, due to the subtle modification of overall dielectric functions at low dimensionality. Such a renormalization effect leads to unusual reduction in the energy scales of photonic quasiparticles and red shifts of photoluminescence as the density of lattice vacancies increases. With strict configurative form factors derived, a dielectric screening model is also established for the generalized trilayer systems to capture the fine modification in the energy scales of quasiparticles and to elucidate the dielectric functions versus realistic Bohr lengths. This finding highlights the essential but commonly neglected role of lattice vacancies and deciphers the longstanding enigma of unpredictable photoluminescent line shifts in low-dimensional systems.

Coulomb engineering of two-dimensional Mott materials

Two-dimensional materials can be strongly influenced by their surroundings. A dielectric environment screens and reduces the Coulomb interaction between electrons in the two-dimensional material. Since in Mott materials the Coulomb interaction is responsible for the insulating state, manipulating the dielectric screening provides direct control over Mottness. Our many-body calculations reveal the spectroscopic fingerprints of such Coulomb engineering: we demonstrate eV-scale changes to the position of the Hubbard bands and show a Coulomb engineered insulator-to-metal transition. Based on our proof-of-principle calculations, we discuss the (feasible) conditions under which our scenario of Coulomb engineering of Mott materials can be realized experimentally.

Interspecies exciton interactions lead to enhanced nonlinearity of dipolar excitons and polaritons in MoS2 homobilayers

Nonlinear interactions between excitons strongly coupled to light are key for accessing quantum many-body phenomena in polariton systems. Atomically-thin two-dimensional semiconductors provide an attractive platform for strong light-matter coupling owing to many controllable excitonic degrees of freedom. Among these, the recently emerged exciton hybridization opens access to unexplored excitonic species, with a promise of enhanced interactions. Here, we employ hybridized interlayer excitons (hIX) in bilayer MoS₂ to achieve highly nonlinear excitonic and polaritonic effects. Such interlayer excitons possess an out-of-plane electric dipole as well as an unusually large oscillator strength allowing observation of dipolar polaritons (dipolaritons) in bilayers in optical microcavities. Compared to excitons and polaritons in MoS₂ monolayers, both hIX and dipolaritons exhibit ≈ 8 times higher nonlinearity, which is further strongly enhanced when hIX and intralayer excitons, sharing the same valence band, are excited simultaneously. This provides access to an unusual nonlinear regime which we describe theoretically as a mixed effect of Pauli exclusion and exciton-exciton interactions enabled through charge tunnelling. The presented insight into many-body interactions provides new tools for accessing few-polariton quantum correlations.

The Key Role of Non-Local Screening in the Environment-Insensitive Exciton Fine Structures of Transition-Metal Dichalcogenide Monolayers

In this work, we present a comprehensive theoretical and computational investigation of exciton fine structures of WSe2-monolayers, one of the best-known two-dimensional (2D) transition-metal dichalcogenides (TMDs), in various dielectric-layered environments by solving the first-principles-based Bethe-Salpeter equation. While the physical and electronic properties of atomically thin nanomaterials are normally sensitive to the variation of the surrounding environment, our studies reveal that the influence of the dielectric environment on the exciton fine structures of TMD-MLs is surprisingly limited. We point out that the non-locality of Coulomb screening plays a key role in suppressing the dielectric environment factor and drastically shrinking the fine structure splittings between bright exciton (BX) states and various dark-exciton (DX) states of TMD-MLs. The intriguing non-locality of screening in 2D materials can be manifested by the measurable non-linear correlation between the BX-DX splittings and exciton-binding energies by varying the surrounding dielectric environments. The revealed environment-insensitive exciton fine structures of TMD-ML suggest the robustness of prospective dark-exciton-based optoelectronics against the inevitable variation of the inhomogeneous dielectric environment.

Untangling the intertwined: metallic to semiconducting phase transition of colloidal MoS2 nanoplatelets and nanosheets

2D semiconducting transition metal dichalcogenides (TMDCs) are highly promising materials for future spin- and valleytronic applications and exhibit an ultrafast response to external (optical) stimuli which is essential for optoelectronics. Colloidal nanochemistry on the other hand is an emerging alternative for the synthesis of 2D TMDC nanosheet (NS) ensembles, allowing for the control of the reaction via tunable precursor and ligand chemistry. Up to now, wet-chemical colloidal syntheses yielded intertwined/agglomerated NSs with a large lateral size. Here, we show a synthesis method for 2D mono- and bilayer MoS₂ nanoplatelets with a particularly small lateral size (NPLs, 7.4 nm ± 2.2 nm) and MoS₂ NSs (22 nm ± 9 nm) as a reference by adjusting the molybdenum precursor concentration in the reaction. We find that in colloidal 2D MoS₂ syntheses initially a mixture of the stable semiconducting and the metastable metallic crystal phase is formed. 2D MoS₂ NPLs and NSs then both undergo a full transformation to the semiconducting crystal phase by the end of the reaction, which we quantify by X-ray photoelectron spectroscopy. Phase pure semiconducting MoS₂ NPLs with a lateral size approaching the MoS₂ exciton Bohr radius exhibit strong additional lateral confinement, leading to a drastically shortened decay of the A and B exciton which is characterized by ultrafast transient absorption spectroscopy. Our findings represent an important step for utilizing colloidal TMDCs, for example small MoS₂ NPLs represent an excellent starting point for the growth of heterostructures for future colloidal photonics.

Direct Visualization of Subnanometer Variations in the Excitonic Spectra of 2D/3D Semiconductor/Metal Heterostructures

The integration of metallic contacts with two-dimensional (2D) semiconductors is routinely required for the fabrication of nanoscale devices. However, nanometer-scale variations in the 2D/metal interface can drastically alter the local optoelectronic properties. Here, we map local excitonic changes of the 2D semiconductor MoS₂ in contact with Au. We utilize a suspended and epitaxially grown 2D/metal platform that allows correlated electron energy-loss spectroscopy (EELS) and angle resolved photoelectron spectroscopy (nanoARPES) mapping. Spatial localization of MoS₂ excitons uncovers an additional EELS peak related to the MoS₂/Au interface. NanoARPES measurements indicate that Au-S hybridization decreases substantially with distance from the 2D/metal interface, suggesting that the observed EELS peak arises due to dielectric screening of the excitonic Coulomb interaction. Our results suggest that increasing the van der Waals distance could optimize excitonic spectra of mixed-dimensional 2D/3D interfaces and highlight opportunities for Coulomb engineering of exciton energies by the local dielectric environment or moiré engineering.

Cluster Formation Effect of Water on Pristine and Defective MoS2 Monolayers

The structure and electronic properties of the molybdenum disulfide (MoS₂) monolayer upon water cluster adsorption are studied using density functional theory and the optical properties are further analyzed with the Bethe-Salpeter equation (BSE). Our results reveal that the water clusters are electron acceptors, and the acceptor tendency tends to increase with the size of the water cluster. The electronic band gap of both pristine and defective MoS₂ is rather insensitive to water cluster adsorbates, as all the clusters are weakly bound to the MoS₂ surface. However, our calculations on the BSE level show that the adsorption of the water cluster can dramatically redshift the optical absorption for both pristine and defective MoS₂ monolayers. The binding energy of the excitons of MoS₂ is greatly enhanced with the increasing size of the water cluster and finally converges to a value of approximately 1.16 eV and 1.09 eV for the pristine and defective MoS₂ monolayers, respectively. This illustrates that the presence of the water cluster could localize the excitons of MoS₂, thereby greatly enhance the excitonic binding energy.

Electrostatic and Environmental Control of the Trion Fine Structure in Transition Metal Dichalcogenide Monolayers

Charged excitons or trions are essential for optical spectra in low-dimensional doped monolayers (ML) of transitional metal dichalcogenides (TMDC). Using a direct diagonalization of the three-body Hamiltonian, we calculate the low-lying trion states in four types of TMDC MLs as a function of doping and dielectric environment. We show that the fine structure of the trion is the result of the interplay between the spin-valley fine structure of the single-particle bands and the exchange interaction. We demonstrate that by variations of the doping and dielectric environment, the fine structure of the trion energy can be tuned, leading to anticrossing of the bright and dark states, with substantial implications for the optical spectra of the TMDC ML.

Nanocavity-induced trion emission from atomically thin WSe2

Exciton is a bosonic quasiparticle consisting of a pair of electron and hole, with promising potentials for optoelectronic device applications, such as exciton transistors, photodetectors and light emitting devices. However, the charge-neutral nature of excitons renders them challenging to manipulate using electronics. Here we present the generation of trions, a form of charged excitons, together with enhanced exciton resonance in monolayer WSe₂. The excitation of the trion quasiparticles is achieved by the hot carrier transport from the integrated gold plasmonic nanocavity, formed by embedding monolayer WSe₂ between gold nanoparticles and a gold film. The nanocavity-induced negatively charged trions provide a promising route for the manipulation of excitons, essential for the construction of all-exciton information processing circuits.

Stable and flexible photodetector based on liquid-phase exfoliated titanium disulfide nanosheets

Herein, the TiS₂nanosheets (NSs) are prepared from the TiS₂bulk by the liquid-phase exfoliation to fabricate photoelectrochemical-type (PEC) photodetector. SEM images and Raman spectra show the successful acquisition of the TiS₂NSs. The as-prepared TiS₂photodetector shows self-powered ability with an applicable photoresponsivity that is about 0.37μA W^-1under zero bias potential and 80 mW cm^-2visible light, and the response time of rise is 0.67 s and the decay time is 2.81 s. In this case, the photodetector is made of ITO-coated polyethylene terephthalate (PET), so it can maintain stable performance under the bending conditions. These results display that the as-prepared photodetector has excellent photoelectric properties, which facilitates the development of TiS₂NSs in optoelectronic devices.

Recent progress in 2D hybrid heterostructures from transition metal dichalcogenides and organic layers: properties and applications in energy and optoelectronics fields

Atomically thin transition metal dichalcogenides (TMDs) present extraordinary optoelectronic, electrochemical, and mechanical properties that have not been accessible in bulk semiconducting materials. Recently, a new research field, 2D hybrid heteromaterials, has emerged upon integrating TMDs with molecular systems, including organic molecules, polymers, metal-organic frameworks, and carbonaceous materials, that can tailor the TMD properties and exploit synergetic effects. TMD-based hybrid heterostructures can meet the demands of future optoelectronics, including supporting flexible, transparent, and ultrathin devices, and energy-based applications, offering high energy and power densities with long cycle lives. To realize such applications, it is necessary to understand the interactions between the hybrid components and to develop strategies for exploiting the distinct benefits of each component. Here, we provide an overview of the current understanding of the new phenomena and mechanisms involved in TMD/organic hybrids and potential applications harnessing such valuable materials in an insightful way. We highlight recent discoveries relating to multicomponent hybrid materials. Finally, we conclude this review by discussing challenges related to hybrid heteromaterials and presenting future directions and opportunities in this research field.

Mechanisms of Quasi van der Waals Epitaxy of Three-Dimensional Metallic Nanoislands on Suspended Two-Dimensional Materials

Understanding structure at the interface between two-dimensional (2D) materials and 3D metals is crucial for designing novel 2D/3D heterostructures and improving the performance of many 2D material devices. Here, we quantify and discuss the 2D/3D interface structure and the 3D morphology in several materials systems. We first deposit faceted Au nanoislands on graphene and transition metal dichalcogenides, using measurements of the equilibrium island shape to determine values for the 2D/Au interface energy and examining the role of surface reconstructions, chemical identity, and defects on the grown structures. We then deposit the technologically relevant metals Ti and Nb under conditions where kinetic rather than thermodynamic factors govern growth. We describe a transition from dendritic to faceted islands as a function of growth temperature and discuss the factors determining island shape in these materials systems. Finally, we show that suspended 2D materials enable the fabrication of a novel type of 3D/2D/3D heterostructure and discuss the growth mechanism. We suggest that emerging nanodevices will utilize versatile fabrication of 2D/3D heterostructures with well-characterized interfaces and morphologies.

Stabilization of Three-Particle Excitations in Monolayer MoS2 by Fluorinated Methacrylate Polymers

While extrinsic factors, such as substrates and chemical doping, are known to strongly influence visible photoemission from monolayer MoS₂, key fundamental knowledge for p-type polymeric dopants is lacking. We investigated perturbations to the electronic environment of 2D MoS₂ using fluorinated polymer coatings and specifically studied stabilization of three-particle states by monitoring changes in intensities and emission maxima of three-particle and two-particle emissions. We calculated changes in carrier density and trion binding energy, the latter having an additional contribution from MoS₂ polarization by the polymer. Polarization is further suggested by Kelvin probe force microscopy (KPFM) measurements of large Fermi level shifts. Changes similar in magnitude, but opposite in sign, were observed in 2D MoS₂ coated with an analogous nonfluorinated polymer. These findings highlight the important interplay between electron exchange and electrostatic interactions at the interface between polymers and transition metal dichalcogenides (TMDCs), which govern fundamental electronic properties relevant to next-generation devices.

Theory of Excitons in Atomically Thin Semiconductors: Tight-Binding Approach

Atomically thin semiconductors from the transition metal dichalcogenide family are materials in which the optical response is dominated by strongly bound excitonic complexes. Here, we present a theory of excitons in two-dimensional semiconductors using a tight-binding model of the electronic structure. In the first part, we review extensive literature on 2D van der Waals materials, with particular focus on their optical response from both experimental and theoretical points of view. In the second part, we discuss our ab initio calculations of the electronic structure of MoS2, representative of a wide class of materials, and review our minimal tight-binding model, which reproduces low-energy physics around the Fermi level and, at the same time, allows for the understanding of their electronic structure. Next, we describe how electron-hole pair excitations from the mean-field-level ground state are constructed. The electron-electron interactions mix the electron-hole pair excitations, resulting in excitonic wave functions and energies obtained by solving the Bethe-Salpeter equation. This is enabled by the efficient computation of the Coulomb matrix elements optimized for two-dimensional crystals. Next, we discuss non-local screening in various geometries usually used in experiments. We conclude with a discussion of the fine structure and excited excitonic spectra. In particular, we discuss the effect of band nesting on the exciton fine structure; Coulomb interactions; and the topology of the wave functions, screening and dielectric environment. Finally, we follow by adding another layer and discuss excitons in heterostructures built from two-dimensional semiconductors.

Control of trion-to-exciton conversion in monolayer WS2 by orbital angular momentum of light

Controlling the density of exciton and trion quasiparticles in monolayer two-dimensional (2D) materials at room temperature by nondestructive techniques is highly desired for the development of future optoelectronic devices. Here, the effects of different orbital angular momentum (OAM) lights on monolayer tungsten disulfide at both room temperature and low temperatures are investigated, which reveal simultaneously enhanced exciton intensity and suppressed trion intensity in the photoluminescence spectra with increasing topological charge of the OAM light. In addition, the trion-to-exciton conversion efficiency is found to increase rapidly with the OAM light at low laser power and decrease with increasing power. Moreover, the trion binding energy and the concentration of unbound electrons are estimated, which shed light on how these quantities depend on OAM. A phenomenological model is proposed to account for the experimental data. These findings pave a way toward manipulating the exciton emission in 2D materials with OAM light for optoelectronic applications.

Fragment-Based Excited-State Calculations Using the GW Approximation and the Bethe-Salpeter Equation

Herein, we present a fragment-based approach for calculating the charged and neutral excited states in molecular systems, based on the many-body Green's function method within the GW approximation and the Bethe-Salpeter equation (BSE). The implementation relies on the many-body expansion of the total irreducible polarizability on the basis of fragment molecular orbitals. The GW quasi-particle energies in complex molecular environments are obtained by the GW calculation for the target fragment plus induced polarization contributions of the surrounding fragments at the static Coulomb-hole plus screened exchange level. In addition, we develop a large-scale GW/BSE method for calculating the delocalized excited states of molecular aggregates, based on the fragment molecular orbital method and the exciton model. The accuracy of fragment-based GW and GW/BSE methods was evaluated on molecular clusters and molecular crystals. We found that the accuracy of the total irreducible polarizability can be improved systematically by including two-body correction terms, and the fragment-based calculations can reasonably reproduce the results of the corresponding unfragmented calculations with a relative error of less than 100 meV. The proposed approach enables efficient excited-state calculations for large molecular systems with reasonable accuracy.

Exposing the trion's fine structure by controlling the carrier concentration in hBN-encapsulated MoS2

Atomically thin materials, like semiconducting transition metal dichalcogenides, are highly sensitive to the environment. This opens up an opportunity to externally control their properties by changing their surroundings. In this work, high-quality van der Waals heterostructures assembled from hBN-encapsulated monolayer MoS₂ are studied with the aid of photoluminescence, photoluminescence excitation, and reflectance contrast experiments. We demonstrate that carrier concentration in MoS₂ monolayers, arising from charge transfer from impurities in the substrate, can be significantly tuned within one order of magnitude by the modification of the bottom hBN flake thickness. The studied structures, characterized by spectral lines with linewidths approaching the narrow homogeneously broadened limit enabled observations of subtle optical and spin-valley properties of excitonic complexes. Our results allowed us to resolve three optically-active negatively charged excitons in MoS₂ monolayers, which are assigned to the intravalley singlet, intervalley singlet, and intervalley triplet states.

Trion dynamics and charge photogeneration in MoS2 nanosheets prepared by liquid phase exfoliation

Since excitonic quasiparticles, including excitons, trions and charges, have a great influence on the photoelectric characteristics of two-dimensional (2D) transition metal dichalcogenides (TMDs), systematic explorations of the trion dynamics and charge photogeneration in 2D TMDs are important for their future optoelectronic applications. Here, broadband femtosecond transient absorption spectroscopic experiments are performed first to investigate the peak shifting and broadening kinetics in MoS₂ nanosheets in solution prepared by liquid phase exfoliation (LPE-MoS₂, ∼9 layers, 9L), which reveal that the binding energies for the A-, B-, and C-exciton states are ∼77 meV, ∼76 meV, and -70 meV (the energy difference between free charges and excitons; the negative sign for C-excitons means a spontaneous dissociation nature in band-nesting regions), respectively. Then, the trion dynamics and charge photogeneration in LPE-MoS₂ nanosheets have been studied in detail, demonstrating that they are comparable to those in chemical vapor deposition grown MoS₂ films (1L-, 3L- and 7L-MoS₂). These experimental results suggest that LPE-TMD nanosheets also have the potential for use in charge-related optoelectronic devices based on 2D TMDs.

Computational methods for 2D materials modelling

Materials with thickness ranging from a few nanometers to a single atomic layer present unprecedented opportunities to investigate new phases of matter constrained to the two-dimensional plane. Particle-particle Coulomb interaction is dramatically affected and shaped by the dimensionality reduction, driving well-established solid state theoretical approaches to their limit of applicability. Methodological developments in theoretical modelling and computational algorithms, in close interaction with experiments, led to the discovery of the extraordinary properties of two-dimensional materials, such as high carrier mobility, Dirac cone dispersion and bright exciton luminescence, and inspired new device design paradigms. This review aims to describe the computational techniques used to simulate and predict the optical, electronic and mechanical properties of two-dimensional materials, and to interpret experimental observations. In particular, we discuss in detail the particular challenges arising in the simulation of two-dimensional constrained fermions and quasiparticles, and we offer our perspective on the future directions in this field.

Electrical tuning of optically active interlayer excitons in bilayer MoS2

Interlayer (IL) excitons, comprising electrons and holes residing in different layers of van der Waals bonded two-dimensional semiconductors, have opened new opportunities for room-temperature excitonic devices. So far, two-dimensional IL excitons have been realized in heterobilayers with type-II band alignment. However, the small oscillator strength of the resulting IL excitons and difficulties with producing heterostructures with definite crystal orientation over large areas have challenged the practical applicability of this design. Here, following the theoretical prediction and recent experimental confirmation of the existence of IL excitons in bilayer MoS₂, we demonstrate the electrical control of such excitons up to room temperature. We find that the IL excitonic states preserve their large oscillator strength as their energies are manipulated by the electric field. We attribute this effect to the mixing of the pure IL excitons with intralayer excitons localized in a single layer. By applying an electric field perpendicular to the bilayer MoS₂ crystal plane, excitons with IL character split into two peaks with an X-shaped field dependence as a clear fingerprint of the shift of the monolayer bands with respect to each other. Finally, we demonstrate the full control of the energies of IL excitons distributed homogeneously over a large area of our device.

Variationally optimized orbital approach to trions in two-dimensional materials

In this work, trions in two-dimensional (2D) space are studied by the variational method with trial wavefunctions being constructed by 2D slater-type orbitals. Via this method, trion energy levels and wavefunctions can be calculated efficiently with fairly good accuracy. We first apply this method to study trion energy levels in a 2D hydrogen-like system with respect to a wide range of mass ratios and screening lengths. We find that the ground-state trion is bound for the whole parameter range, and an excited-state trion with antisymmetric permutation of electrons with finite angular momentum is bound for large electron-hole mass ratios or long screening lengths. The binding energies of ground-state trions calculated by the present method agree well with those calculated by more sophisticated but computationally demanding methods. We then calculate trion binding energies in various monolayer transition metal dichalcogenides (TMDCs) by using this method with the inclusion of electron-hole exchange (EHX) interaction. For TMDCs, we found that the effect of EHX can be significant in determining the trion binding energy and the possible existence of stable excited-state trions.

Temperature-Dependent Electronic Ground-State Charge Transfer in van der Waals Heterostructures

Electronic charge rearrangement between components of a heterostructure is the fundamental principle to reach the electronic ground state. It is acknowledged that the density of state distribution of the components governs the amount of charge transfer, but a notable dependence on temperature is not yet considered, particularly for weakly interacting systems. Here, it is experimentally observed that the amount of ground-state charge transfer in a van der Waals heterostructure formed by monolayer MoS2 sandwiched between graphite and a molecular electron acceptor layer increases by a factor of 3 when going from 7 K to room temperature. State-of-the-art electronic structure calculations of the full heterostructure that accounts for nuclear thermal fluctuations reveal intracomponent electron-phonon coupling and intercomponent electronic coupling as the key factors determining the amount of charge transfer. This conclusion is rationalized by a model applicable to multicomponent van der Waals heterostructures.

Valley-Dependent Interlayer Excitons in Magnetic WSe2/CrI3

Heterostructures of two-dimensional transition-metal dichalcogenides and ferromagnetic substrates are important candidates for the development of viable new spin- or valleytronic devices. For the prototypical bilayer of WSe₂ on top of a ferromagnetic layer of CrI₃, we find substantially different coupling of both WSe₂ K-valleys to the sublayer. Besides an energy splitting of a few meV, the corresponding excitons have significantly different interlayer character with charge transfer allowed at the K̅^- point but forbidden at K̅⁺. The different exciton wave functions result in a distinctly different response to magnetic fields with g factors of about -4.4 and -4.0, respectively. By means of ab initio GW/Bethe-Salpeter equation calculations, these findings establish g factors as tool for investigating the exciton character and shedding light on the detailed quantum-mechanical interplay of magnetic and optical properties which are essential for the targeted development of optoelectronic devices.

Theory and Ab Initio Calculation of Optically Excited States-Recent Advances in 2D Materials

Recent studies of the optical properties of 2D materials have reported unique phenomena and features that are absent in conventional bulk semiconductors. Many of these interesting properties, such as enhanced light-matter coupling, gate-tunable photoluminescence, and unusual excitonic optical selection rules arise from the nature of the two- and multi-particle excited states such as strongly bound Wannier excitons and charged excitons. The theory, modeling, and ab initio calculations of these optically excited states in 2D materials are reviewed. Several analytical and ab initio approaches are introduced. These methods are compared with each other, revealing their relative strength and limitations. Recent works that apply these methods to a variety of 2D materials and material-defect systems are then highlighted. Understanding of the optically excited states in these systems is relevant not only for fundamental scientific research of electronic excitations and correlations, but also plays an important role in the future development of quantum information science and nano-photonics.

Identifying Defect-Induced Trion in Monolayer WS2 via Carrier Screening Engineering

Unusually high exciton binding energies (BEs), as much as ∼1 eV in monolayer transition-metal dichalcogenides, provide opportunities for exploring exotic and stable excitonic many-body effects. These include many-body neutral excitons, trions, biexcitons, and defect-induced excitons at room temperature, rarely realized in bulk materials. Nevertheless, the defect-induced trions correlated with charge screening have never been observed, and the corresponding BEs remain unknown. Here we report defect-induced A-trions and B-trions in monolayer tungsten disulfide (WS₂) via carrier screening engineering with photogenerated carrier modulation, external doping, and substrate scattering. Defect-induced trions strongly couple with inherent SiO₂ hole traps under high photocarrier densities and become more prominent in rhenium-doped WS₂. The absence of defect-induced trion peaks was confirmed using a trap-free hexagonal boron nitride substrate, regardless of power density. Moreover, many-body excitonic charge states and their BEs were compared via carrier screening engineering at room temperature. The highest BE was observed in the defect-induced A-trion state (∼214 meV), comparably higher than the trion (209 meV) and neutral exciton (174 meV), and further tuned by external photoinduced carrier density control. This investigation allows us to demonstrate defect-induced trion BE localization via spatial BE mapping in the monolayer WS₂ midflake regions distinctive from the flake edges.

Giant nonlinear optical activity in two-dimensional palladium diselenide

Nonlinear optical effects in layered two-dimensional transition metal chalcogenides have been extensively explored recently because of the promising prospect of the nonlinear optical effects for various optoelectronic applications. However, these materials possess sizable bandgaps ranging from visible to ultraviolet region, so the investigation of narrow-bandgap materials remains deficient. Here, we report our comprehensive study on the nonlinear optical processes in palladium diselenide (PdSe₂) that has a near-infrared bandgap. Interestingly, this material exhibits a unique thickness-dependent second harmonic generation feature, which is in contrast to other transition metal chalcogenides. Furthermore, the two-photon absorption coefficients of 1–3 layer PdSe₂ (β ~ 4.16 × 10⁵, 2.58 × 10⁵, and 1.51 × 10⁵ cm GW⁻¹) are larger by two and three orders of magnitude than that of the conventional two-dimensional materials, and giant modulation depths (α_s ~ 32%, 27%, and 24%) were obtained in 1–3 layer PdSe₂. Such unique nonlinear optical characteristics make PdSe₂ a potential candidate for technological innovations in nonlinear optoelectronic devices.

Strong nonlinearities in 2D materials can lead to interesting applications in optoelectronics. Here the authors investigate the optical nonlinearity of palladium diselenide, determine the layer dependent two photon absorption efficiency and the saturable absorption modulation depth.

Probing negatively charged and neutral excitons in MoS2/hBN and hBN/MoS2/hBN van der Waals heterostructures

High-quality van der Waals heterostructures assembled from hBN-encapsulated monolayer transition metal dichalcogenides enable observations of subtle optical and spin-valley properties whose identification was beyond the reach of structures exfoliated directly on standard SiO2/Si substrates. Here, we describe different van der Waals heterostructures based on uncapped single-layer MoS2 stacked onto hBN layers of different thicknesses and hBN-encapsulated monolayers. Depending on the doping level, they reveal the fine structure of excitonic complexes, i.e. neutral and charged excitons. In the emission spectra of a particular MoS2/hBN heterostructure without an hBN cap we resolve two trion peaks, T1 and T2, energetically split by about 10 meV, resembling the pair of singlet and triplet trion peaks (T S and T T ) in tungsten-based materials. The existence of these trion features suggests that monolayer MoS2 has a dark excitonic ground state, despite having a 'bright' single-particle arrangement of spin-polarized conduction bands. In addition, we show that the effective excitonic g-factor significantly depends on the electron concentration and reaches the lowest value of -2.47 for hBN-encapsulated structures, which reveals a nearly neutral doping regime. In the uncapped MoS2 structures, the excitonic g-factor varies from -1.15 to -1.39 depending on the thickness of the bottom hBN layer and decreases as a function of rising temperature.

Controllable Magnetic Proximity Effect and Charge Transfer in 2D Semiconductor and Double-Layered Perovskite Manganese Oxide van der Waals Heterostructure

Optically generated excitonic states (excitons and trions) in transition metal dichalcogenides are highly sensitive to the electronic and magnetic properties of the materials underneath. Modulation and control of the excitonic states in a novel van der Waals (vdW) heterostructure of monolayer MoSe₂ on double-layered perovskite Mn oxide ((La_0.8 Nd_0.2 )_1.2 Sr_1.8 Mn₂ O₇ ) is demonstrated, wherein the Mn oxide transforms from a paramagnetic insulator to a ferromagnetic metal. A discontinuous change in the exciton photoluminescence intensity via dielectric screening is observed. Further, a relatively high trion intensity is discovered due to the charge transfer from metallic Mn oxide under the Curie temperature. Moreover, the vdW heterostructures with an ultrathin h-BN spacer layer demonstrate enhanced valley splitting and polarization of excitonic states due to the proximity effect of the ferromagnetic spins of Mn oxide. The controllable h-BN thickness in vdW heterostructures reveals a several-nanometer-long scale of charge transfer as well as a magnetic proximity effect. The vdW heterostructure allows modulation and control of the excitonic states via dielectric screening, charge carriers, and magnetic spins.

Interplay between spin proximity effect and charge-dependent exciton dynamics in MoSe2/CrBr3 van der Waals heterostructures

Semiconducting ferromagnet-nonmagnet interfaces in van der Waals heterostructures present a unique opportunity to investigate magnetic proximity interactions dependent upon a multitude of phenomena including valley and layer pseudospins, moiré periodicity, or exceptionally strong Coulomb binding. Here, we report a charge-state dependency of the magnetic proximity effects between MoSe2 and CrBr3 in photoluminescence, whereby the valley polarization of the MoSe2 trion state conforms closely to the local CrBr3 magnetization, while the neutral exciton state remains insensitive to the ferromagnet. We attribute this to spin-dependent interlayer charge transfer occurring on timescales between the exciton and trion radiative lifetimes. Going further, we uncover by both the magneto-optical Kerr effect and photoluminescence a domain-like spatial topography of contrasting valley polarization, which we infer to be labyrinthine or otherwise highly intricate, with features smaller than 400 nm corresponding to our optical resolution. Our findings offer a unique insight into the interplay between short-lived valley excitons and spin-dependent interlayer tunneling, while also highlighting MoSe2 as a promising candidate to optically interface with exotic spin textures in van der Waals structures.

Reconstructing Local Profile of Exciton-Emission Wavelengths across a WS2 Bubble beyond the Diffraction Limit

Air bubbles formed between layers of two-dimensional (2D) materials not only are unavoidable but also emerge as an important means of engineering their excitonic emission properties, especially as controllable quantum light sources. Measuring the actual spatially resolved optical properties across such bubbles is important for understanding excitonic physics and for device applications; however, such a measurement is challenging due to nanoscale features involved which require spatial resolution beyond the diffraction limit. Additional complexity is the involvement of multiple physical effects such as mechanical strain and dielectric environment that are difficult to disentangle. In this paper, we demonstrate an effective approach combining micro-photoluminescence measurement, atomic force microscope profile mapping, and a theoretical strain model. We succeeded in reconstructing the actual spatial profiles of the emission wavelengths beyond the diffraction limit for bubbles formed by a monolayer tungsten disulfide on boron nitride. The agreements and consistency among various approaches established the validity of our approach. In addition, our approach allows us to disentangle the effects of strain and dielectric environment and provides a general and reliable method to determine the true magnitude of wavelength changes due to the individual effects across bubbles. Importantly, we found that micro-optical measurement underestimates the red and blue shifts by almost 5 times. Our results provide important insights into strain and screening-dependent optical properties of 2D materials on the nanometer scale and contribute significantly to our understanding of excitonic emission physics as well as potential applications of bubbles in optoelectronic devices.

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

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

Light-matter interaction in van der Waals hetero-structures

Even if individual two-dimensional materials own various interesting and unexpected properties, the stacking of such layers leads to van der Waals solids which unite the characteristics of two dimensions with novel features originating from the interlayer interactions. In this topical review, we cover fabrication and characterization of van der Waals hetero-structures with a focus on hetero-bilayers made of monolayers of semiconducting transition metal dichalcogenides. Experimental and theoretical techniques to investigate those hetero-bilayers are introduced. Most recent findings focusing on different transition metal dichalcogenides hetero-structures are presented and possible optical transitions between different valleys, appearance of moiré patterns and signatures of moiré excitons are discussed. The fascinating and fast growing research on van der Waals hetero-bilayers provide promising insights required for their application as emerging quantum-nano materials.

Intrinsic and Extrinsic Defect-Related Excitons in TMDCs

We investigate the excitonic peak associated with defects and disorder in low-temperature photoluminescence of monolayer transition metal dichalcogenides (TMDCs). To uncover the intrinsic origin of defect-related (D) excitons, we study their dependence on gate voltage, excitation power, and temperature in a prototypical TMDC monolayer MoS₂. Our results suggest that D excitons are neutral excitons bound to ionized donor levels, likely related to sulfur vacancies, with a density of 7 × 10¹¹ cm^-2. To study the extrinsic contribution to D excitons, we controllably deposit oxygen molecules in situ onto the surface of MoS₂ kept at cryogenic temperature. We find that, in addition to trivial p-doping of 3 × 10¹² cm^-2, oxygen affects the D excitons, likely by functionalizing the defect sites. Combined, our results uncover the origin of D excitons, suggest an approach to track the functionalization of TMDCs, to benchmark device quality, and pave the way toward exciton engineering in hybrid organic-inorganic TMDC devices.

Thermochemical stability, and electronic and dielectric properties of Janus bismuth oxyhalide BiOX (X = Cl, Br, I) monolayers

Ultrathin monolayers of bismuth oxyhalide materials BiOX (X = Cl, Br, I) grown along 〈001〉 are studied using first-principles density functional theory. Both pristine BiOX and Janus (X, X' = Cl, Br, I) monolayers are investigated by analyzing their structural stability using formation enthalpy and phonon density of states. On the other hand, their thermochemical reactivity is understood from their surface energy trends in symmetric and asymmetric terminations. The theoretically measured optical band gaps and fundamental band gaps of these Janus monolayers are compared with their pristine counterparts BiOX and BiOX' as well as to the known experimental measurements. All of the possible Janus monolayers possess structural, electronic and optical properties intermediate to the corresponding properties of the two associated pristine BiOX and BiOX' monolayers. According to the formation enthalpy, stabilization is equally favorable for all the monolayers, whereas the lowest surface energy is found for BiOCl_0.5Br_0.5, leading to excellent thermochemical reactivity which is consistent with recent experimental measurements. The frequency dependent dielectric functions are simulated in the density functional perturbation theory limit, and the optical band gaps are estimated from the absorption and reflectance spectra, and are in excellent agreement with the known experimentally measured values. High frequency dielectric constants of these materials with 2D symmetry are estimated from G ₀ W ₀ calculations including local field and spin-orbit effects. The larger dielectric constants and wider differences in the charge carriers' effective masses also provide proof that this new class of 2D materials has potential in photo-electrochemical applications. Thus, fabricating Janus monolayers of these oxyhalide compounds would open up a rational design strategy for tailoring their optoelectronic properties, which may offer guidance for the design of highly efficient optoelectronic materials for catalysis, valleytronic, and sensing applications.

Excited-State Trions in Monolayer WS_{2}

We discover an excited bound three-particle state, the 2s trion, appearing energetically below the 2s exciton in monolayer WS_{2}, using absorption spectroscopy and ab initio GW and Bethe-Salpeter equation calculations. The measured binding energy of the 2s trion (22 meV) is smaller compared to the 1s intravalley and intervalley trions (37 and 31 meV). With increasing temperature, the 1s and 2s trions transfer their oscillator strengths to the respective neutral excitons, establishing an optical fingerprint of trion-exciton resonance pairs. Our discovery underlines the importance of trions for the entire excitation spectrum of two-dimensional semiconductors.

Quantum plasmonic control of trions in a picocavity with monolayer WS2

Monitoring and controlling the neutral and charged excitons (trions) in two-dimensional (2D) materials are essential for the development of high-performance devices. However, nanoscale control is challenging because of diffraction-limited spatial resolution of conventional far-field techniques. Here, we extend the classical tip-enhanced photoluminescence based on tip-substrate nanocavity to quantum regime and demonstrate controlled nano-optical imaging, namely, tip-enhanced quantum plasmonics. In addition to improving the spatial resolution, we use the scanning probe to control the optoelectronic response of monolayer WS2 by varying the neutral/charged exciton ratio via charge tunneling in Au-Ag picocavity. We observe trion "hot spots" generated by varying the picometer-scale probe-sample distance and show the effects of weak and strong coupling, which depend on the spatial location. Our experimental results are in agreement with simulations and open an unprecedented view of a new range of quantum plasmonic phenomena with 2D materials that will help to design new quantum optoelectronic devices.

Many-body simulation of two-dimensional electronic spectroscopy of excitons and trions in monolayer transition metal dichalcogenides

Indications of coherently interacting excitons and trions in doped transition metal dichalcogenides have been measured as quantum beats in two-dimensional electronic spectroscopy, but the microscopic principles underlying the optical signals of exciton-trion coherence remain to be clarified. Here we present calculations of two-dimensional spectra of such monolayers based on a microscopic many-body formalism. We use a parameterized band structure and a static model dielectric function, although a full ab initio implementation of our formalism is possible in principle. Our simulated spectra are in excellent agreement with experiments, including the quantum beats, while revealing the interplay between excitons and trions in molybdenum- and tungsten-based transition metal dichalcogenides. Quantum beats are confirmed to unambiguously reflect the exciton-trion coherence time in molybdenum compounds, but are shown to provide a lower bound to the coherence time for tungsten analogues due to a destructive interference from coexisting singlet and triplet trions.

2D electronic spectroscopy found experimental indications of coherently interacting excitons and trions in doped transition metal dichalcogenides (TMDCs). Here, the authors perform simulations of 2D spectra of monolayer TMDCs based on a many-body formalism, allowing to relate exciton-trion coherence to quantum beats based on microscopic principles.

Nanoscale mapping of quasiparticle band alignment

Control of atomic-scale interfaces between materials with distinct electronic structures is crucial for the design and fabrication of most electronic devices. In the case of two-dimensional materials, disparate electronic structures can be realized even within a single uniform sheet, merely by locally applying different vertical gate voltages. Here, we utilize the inherently nano-structured single layer and bilayer graphene on silicon carbide to investigate lateral electronic structure variations in an adjacent single layer of tungsten disulfide (WS₂). The electronic band alignments are mapped in energy and momentum space using angle-resolved photoemission with a spatial resolution on the order of 500 nm (nanoARPES). We find that the WS₂ band offsets track the work function of the underlying single layer and bilayer graphene, and we relate such changes to observed lateral patterns of exciton and trion luminescence from WS₂.

Sharp atomic interfaces between materials dictate the interface’s electronic properties. The authors use angle-resolved photoemission spectroscopy with a spatial resolution of ~500 nm to investigate the nanoscale electronic band structure and band alignment in a lateral heterostructure composed of WS₂ placed on alternating nano-stripes of monolayer and bilayer graphene.

Hysteresis and its impact on characterization of mechanical properties of suspended monolayer molybdenum-disulfide sheets

The hysteresis phenomenon frequently arises in two-dimensional (2D) material nanoindentation, which is generally expected to be excluded from characterizing the elastic properties due to the imperfect elastic behaviour. However, the underlying mechanism of hysteresis and its effect on the characterization of the mechanical properties of 2D materials remain unclear. Cyclic loadings are exerted on the suspended monolayer molybdenum-disulfide (MoS2) films in atomic force microscopy (AFM) nanoindentation experiments. The elastic hysteresis loops are observed for most of the force-displacement curves. The friction/wear between the AFM silicon tip and the MoS2 monolayer is deemed to be dominant compared to the friction between the monolayer and the silicon dioxide substrate after the analysis, as determined using the finite element method (FEM) simulation. The loading force-displacement curves instead of the unloading curves have been used to deduce the elastic mechanical properties using a modified regression equation. The mean value of the obtained Young's modulus of monolayer MoS2, E, is equal to 209 ± 18 GPa, which is close to the inherent stiffness value, predicted by first principles calculation. Our results have confirmed that it is not obligatory to exclude the sample data with hysteresis behaviour for characterizing the elastic properties of 2D materials. In addition, all sample sheets have finally been penetrated and the mean breaking stress value, σmax, is 36.6 ± 0.9 GPa, determined using the radius value of the worn tip. Furthermore, the effect of the loading force and the shape/size of the suspended monolayer MoS2 sheets on the hysteresis behaviour in the 2D nanoindentation have also been analyzed and discussed, exhibiting interesting trends. Our findings provide guidance for the characterization of the mechanical properties of 2D materials using the AFM nanoindentation and the experimental samples with elastic hysteresis behaviour.