We present here a formalism based on time-dependent density-functional theory (TDDFT) to describe characteristics of both intra- and inter-valley excitons in semiconductors, the latter of which had remained a challenge. Through the usage of an appropriate exchange-correlation kernel (nanoquanta), we trace the energy difference between the intra- and inter-valley dark excitons in monolayer (1L) WSe2 to the domination of the exchange part in the exchange-correlation energies of these states. Furthermore, our calculated transition contribution maps establish the momentum resolved weights of the electron-hole excitations in both bright and dark excitons thereby providing a comprehensive understanding of excitonic properties of 1L WSe2. We find that the states consist of hybridized excitations around the corresponding valleys which leads to brightening of the dark excitons, i.e., significantly decreasing their lifetime which is reflected in the PL spectrum. Using many-body perturbation theory, we calculate the phonon contribution to the energy bandgap and the linewidths of the excited electrons, holes and (bright) exciton to find that as the temperature increases the bandgap significantly decreases, while the linewidths increase. Our work paves for describing the ultrafast charge dynamics of transition metal dichalcogenide within an ab initio framework.
Monolayer materials are strongly affected by their potential fluctuations, which are induced by an intrinsic corrugation or the surface roughness of the substrate. We compare the effective exciton-exciton annihilation (EEA) rate constants of monolayer WS2 on substrates with different surface topographies. We show that monolayer WS2 on the substrate with atomically flat terraces displays small effective EEA rate constant deviating from the overall tendency and multiple exciton decay components, which cannot be accounted for by a conventional EEA model. To obtain a correct description, we use a …
We present photoluminescence measurements in monolayer WSe$_2$, which point to the importance of the interaction between charged particles and excitonic complexes. The theoretical analysis highlights the key role played by exchange scattering, referring to cases wherein the particle composition of the complex changes after the interaction. For example, exchange scattering renders bright excitonic complexes dark in monolayer WSe$_2$ on accounts of the unique valley-spin configuration in this material. In addition to the ultrafast energy relaxation of hot excitonic complexes following their inte…
First-principles density functional theory plus Bethe-Salpeter equation calculations are employed to investigate the electronic and excitonic properties of monolayer titanium trichalcogenide alloys TiS$_{3-x}$Se$_x$ ($x$=1 and 2). It is found that bandgap and exciton binding energy display asymmetric dependence on the substitution of Se for S. While the bandgap can be significantly decreased as compared to that of pristine TiS$_3$, the exciton binding energy just varies a little, regardless of position and concentration of the Se substitution. A negative exciton formation energy is found when …
We report on large exciton tuning in WSe$_2$ monolayers via substrate induced non-degenerate doping. We observe a redshift of $\sim$62 meV for the $A$ exciton together with a 1-2 orders of magnitude photoluminescence (PL) quenching when the monolayer WSe$_2$ is brought in contact with highly oriented pyrolytic graphite (HOPG) compared to the dielectric substrates such as hBN and SiO$_2$. As the evidence of doping from HOPG to WSe$_2$, a drastic increase of the trion emission intensity was observed. Using a systematic PL and Kelvin probe force microscopy (KPFM) investigation on WSe$_2$/HOPG, WS…
We study experimentally and theoretically the exciton-phonon interaction in MoSe2 monolayers encapsulated in hexagonal BN, which has an important impact on both optical absorption and emission processes. The exciton transition linewidth down to 1 meV at low temperatures makes it possible to observe high energy tails in absorption and emission extending over several meV, not masked by inhomogeneous broadening. We develop an analytical theory of the exciton-phonon interaction accounting for the deformation potential induced by the longitudinal acoustic phonons, which plays an important role in e…
We study the effect of point-defect chalcogen vacancies on the optical properties of monolayer transition metal dichalcogenides using ab initio GW and Bethe-Salpeter equation calculations. We find that chalcogen vacancies introduce unoccupied in-gap states and occupied resonant defect states within the quasiparticle continuum of the valence band. These defect states give rise to a number of strongly-bound defect excitons and hybridize with excitons of the pristine system, reducing the valley-selective circular dichroism. Our results suggest a pathway to tune spin-valley polarization and other …
Utilizing the excess energy of photoexcitation that is otherwise lost as thermal effects can improve the efficiency of next-generation light-harvesting devices. Multiple exciton generation (MEG) in semiconducting materials yields two or more excitons by absorbing a single high-energy photon, which can break the Shockley-Queisser limit for the conversion efficiency of photovoltaic devices. Recently, monolayer transition metal dichalcogenides (TMDs) have emerged as promising light-harvesting materials because of their high absorption coefficient. Here, we report efficient MEG with low threshold …
The photoluminescence (PL) in monolayer transition metal dichalcogenides (TMDs) is dominated by recombination of electrons in the conduction band with holes in the spin-orbit split valence bands, and there are two distinct emission features referred to as the A-peak (ground state exciton) and B-peak (higher spin-orbit split state). The intensity ratio of these two features varies widely and several contradictory interpretations have been reported. We analyze the room temperature PL from MoS2, MoSe2, WS2, and WSe2 monolayers and show that these variations arise from differences in the non-radia…
Interactions of quantum materials with strong-laser fields can induce exotic nonequilibrium electronic states. Monolayer transition-metal dichalcogenides, a new class of direct-gap semiconductors with prominent quantum confinement, offer exceptional opportunities toward Floquet engineering of quasiparticle electron-hole states, or excitons. Strong-field driving has a potential to achieve enhanced control of electronic band structure, thus a possibility to open a new realm of exciton light-matter interactions. However, experimental implementation of strongly-driven excitons has so far remained …
We investigate the diffusion process of negatively charged excitons (trions) in WSe2 transition metal dichalcogenide monolayer. We measure time-resolved photoluminescence spatial profiles of these excitonic complexes which exhibit a non-linear diffusion process with an effective negative diffusion behavior. Specifically, we examine the dynamics of the two negatively charged bright excitons (intervalley and intravalley trion) as well as the dark trion. The time evolution allows us to identify the interplay of different excitonic species: the trionic species appear after the neutral excitonic on…
MA2Z4 monolayers form a new class of hexagonal non-centrosymmetric materials hosting extraordinary spin-valley physics. While only two compounds (MoSi2N4 and WSi2N4) were recently synthesized, theory predicts interesting (opto)electronic properties of a whole new family of such two-dimensional materials. Here, the chemical trends of band gaps and spin-orbit splittings of bands in selected MSi2Z4 (M = Mo, W; Z = N, P, As, Sb) compounds are studied from first-principles. Effective Bethe-Salpeter-equation-based calculations reveal high exciton binding energies. Evolution of excitonic energies und…
Fundamental Limits of Exciton-Exciton Annihilation for Light Emission in Transition Metal Dichalcogenide Monolayers
我们定量地说明了激子-激子湮灭（EEA）可能对单层过渡金属二硫属化物（TMDC）材料的光发射的基本限制。TMDC单层中的EEA显示出与基底的相互作用的依赖性，因为其速率从0.1 cm 2/s（0.05 cm 2/s）增加到0.3 cm 2/s（0.1 cm 2/s），对于WS 2（MoS 2）单层，移除基底。当激子密度超过1010 cm-2或1011 cm-2时，它成为激子衰减的主要途径，并主导发光效率。这为实现最佳发光效率设置了发光器件中注入电荷密度的上限。强EEA速率还规定了单层中粒子数反转的泵浦阈值为12-18 MW/cm 2（光学）或2.5- 4 × 105 A/cm 2（电学）。
Momentum resolved electron energy-loss spectroscopy was used to measure the dispersions of excitons in a free-standing monolayer of WSe2. Besides the parabolically dispersed valley excitons, a sub-gap dispersive exciton was observed at specific q values for the first time. The simultaneous STEM-ADF imaging of the local probed areas suggests that this sub-gap exciton is attributed to the prolific Se vacancies.
The variety of excitonic states in tungsten-based dichalcogenide monolayers stems from unique interplay between the spin and valley degrees of freedom. One of the exciton species is the indirect exciton (momentum or valley dark), which is responsible to a series of resonances when the monolayer is charge neutral. We investigate the short-range electron-hole exchange interaction of the indirect exciton, as well as its recombination mechanism mediated by impurities. The analysis provides thorough understanding of the energy and polarization of the zero-phonon indirect exciton resonance in the em…
The multivalley band structure of monolayer transition metal dichalcogenides (TMDs) gives rise to intravalley and intervalley excitons. Much knowledge of these excitons has been gained, but fundamental questions remain, such as how to describe them all in a unified picture with their correlations, how are those from different valleys coupled to form the intervalley biexciton? To address the issues, we derive an exciton Hamiltonian from interpair correlations between the constituent carriers-fermions of two excitons. Identifying excitons by irreducible representations of their point symmetry gr…
Excitons with binding energies of a few hundreds of meV control the optical properties of transition metal dichalcogenide monolayers. Knowledge of the fine structure of these excitons is therefore essential to understand the optoelectronic properties of these 2D materials. Here we measure the exciton fine structure of MoS2 and MoSe2 monolayers encapsulated in boron nitride by magneto-photoluminescence spectroscopy in magnetic fields up to 30 T. The experiments performed in transverse magnetic field reveal a brightening of the spin-forbidden dark excitons in MoS2 monolayer: we find that the dar…
Monolayer transition metal dichalcogenide (TMD) semiconductors such as MoSe$_2$ host strongly bound excitons which are known to exhibit a strong resonant third-order nonlinear response. Although there have been numerous studies of the ultrafast nonlinear response of monolayer TMDs, a study of the steady-state nonlinear response is lacking. We report a comprehensive study of the steady-state two-color nonlinear response of excitons in hBN-encapsulated monolayer MoSe$_2$ at 7 K. We observe differential transmission (DT) signals associated with the neutral and charged exciton species, which is st…
The results of magneto-optical spectroscopy investigations of excitons in a CVD grown monolayer of WSe2 encapsulated in hexagonal boron nitride are presented. The emission linewidth for the 1s state is of 4:7 meV, close to the narrowest emissions observed in monolayers exfoliated from bulk material. The 2s excitonic state is also observed at higher energies in the photoluminescence spectrum. Magneto-optical spectroscopy allows for the determination of the g-factors and of the spatial extent of the excitonic wave functions associated with these emissions. Our work establishes CVD grown monolaye…
The optical properties of monolayer and bilayer transition metal dichalcogenide semiconductors are governed by excitons in different spin and valley configurations, providing versatile aspects for van der Waals heterostructures and devices. We present experimental and theoretical studies of exciton energy splittings in external magnetic field in neutral and charged WSe$_2$ monolayer and bilayer crystals embedded in a field effect device for active doping control. We develop theoretical methods to calculate the exciton $g$-factors from first principles and tight-binding for all possible spin-va…
The intricate interplay between optically dark and bright excitons governs the light-matter interaction in transition metal dichalcogenide monolayers. We have performed a detailed investigation of the "spin-forbidden" dark excitons in WSe2 monolayers by optical spectroscopy in an out-of-plane magnetic field Bz. In agreement with the theoretical predictions deduced from group theory analysis, magneto-photoluminescence experiments reveal a zero field splitting $δ=0.6 \pm 0.1$ meV between two dark exciton states. The low energy state being strictly dipole forbidden (perfectly dark) at Bz=0 while …
Atomically thin MoS2 layer is a direct bandgap semiconductor exhibiting strong electron-hole interaction due to the extreme quantum confinement and reduced screening of Coulomb interactions, which results in the formation of stable excitons at room temperature. Therefore, various excitonic properties of MoS2 monolayer are extremely important in determining the strength of light matter interactions including their radiative recombination lifetime and optoelectronic response. In this paper, we report a comprehensive study of the underlying annihilation mechanism of various types of exciton in Mo…
Calculations combining first-principles electron-phonon ($e$-ph) interactions with the Boltzmann equation enable studies of ultrafast carrier and phonon dynamics. However, in materials with weak Coulomb screening, electrons and holes form bound excitons and their scattering processes become correlated, posing additional challenges for modeling nonequilibrium physics. Here we show calculations of ultrafast exciton dynamics and related time-domain spectroscopies using $ab~initio$ exciton-phonon (ex-ph) interactions together with an excitonic Boltzmann equation. Starting from the nonequilibrium e…
Exciton intervalley scattering, annihilation and relaxation dynamics, and diffusive transport in a monolayer transition metal dichalcogenides are central to the functionality of devices based on them. This motivated us to investigate these properties in exfoliated high-quality monolayer MoSe2 using heterodyned nonlinear four-wave-mixing transient grating spectroscopy. While free exciton excitations are found to be long-lived (~230 ps), an extremely fast intervalley scattering ( less than 120 fs) is observed leading to a negligible valley polarization, consistent with steady state photoluminesc…
Transitions metal dichalcogenides (TMDs) are direct semiconductors in the atomic monolayer (ML) limit with fascinating optical and spin-valley properties. The strong optical absorption of up to 20 % for a single ML is governed by excitons, electron-hole pairs bound by Coulomb attraction. Excited exciton states in MoSe$_2$ and MoTe$_2$ monolayers have so far been elusive due to their low oscillator strength and strong inhomogeneous broadening. Here we show that encapsulation in hexagonal boron nitride results in emission line width of the A:1$s$ exciton below 1.5 meV and 3 meV in our MoSe$_2$ a…
Monolayer WSe$_2$ hosts a series of exciton Rydberg states denoted by the principal quantum number n = 1, 2, 3, etc. While most research focuses on their absorption properties, their optical emission is also important but much less studied. Here we measure the photoluminescence from the 1s - 5s exciton Rydberg states in ultraclean monolayer WSe$_2$ encapsulated by boron nitride under magnetic fields from -31 T to 31 T. The exciton Rydberg states exhibit similar Zeeman shifts but distinct diamagnetic shifts from each other. From their luminescence spectra, Zeeman and diamagnetic shifts, we dedu…
We investigate Landau-quantized excitonic absorption and luminescence of monolayer WSe$_2$ under magnetic field. We observe gate-dependent quantum oscillations in the bright exciton and trions (or exciton-polarons) as well as the dark trions and their phonon replicas. Our results reveal spin- and valley-polarized Landau levels (LLs) with filling factors $n = +0, +1$ in the bottom conduction band and $n = -0$ to $-6$ in the top valence band, including the Berry-curvature-induced $n = \pm0$ LLs of massive Dirac fermions. The LL filling produces periodic plateaus in the exciton energy shift accom…
Monolayer transition metal dichalcogenides are a promising platform to investigate many-body interactions of excitonic complexes. In monolayer tungsten diselenide, the ground-state exciton is dark (spin-indirect), and the valley degeneracy allows low-energy dark momentum-indirect excitons to form. Interactions between the dark exciton species and the optically accessible bright exciton (X) are likely to play significant roles in determining the optical properties of X at high power, as well as limiting the ultimate exciton densities that can be achieved, yet so far little is known about these …
The magneto-optical response of monolayer transition metal dichalcogenides (TMDs), including excitonic effects, is studied using a nanoribbon geometry. We compute the diagonal optical conductivity and the Hall conductivity. Comparing the excitonic optical Hall conductivity to results obtained in the independent particle approximation, we find an increase in the amplitude corresponding to one order of magnitude when excitonic effects are included. The Hall conductivities are used to calculate Faraday rotation spectra for MoS2 and WSe2. Finally, we have also calculated the diamagnetic shift of t…
Novel 2D material CrI3 reveals unique combination of 2D ferromagnetism and robust excitonic response. We demonstrate that the possibility of the formation of magnetic topological defects, such as Neel skyrmions, together with large excitonic Zeeman splitting, leads to giant scattering asymmetry, which is the necessary prerequisite for the excitonic anomalous Hall effect. In addition, the diamagnetic effect breaks the inversion symmetry, and in certain cases can result in exciton localization on the skyrmion. This enables the formation of magnetoexcitonic quantum dots with tunable parameters.
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 probe and identify the main exciton dissociation mechanism through time- and spectrally-resolved photocurrent measurements in a monolayer WSe2 p-n junction. We find that under static in-plane electric field, excitons dissociate at a rate correspondi…
We investigate the spin-nonconserving relaxation channel of excitons by their couplings with phonons in two-dimensional transition metal dichalcogenides using $\textit{ab initio}$ approaches. Combining $\text{GW}$-Bethe-Salpeter equation method and density functional perturbation theory, we calculate the electron-phonon and exciton-phonon coupling matrix elements for the spin-flip scattering in monolayer WSe$_{\text{2}}$, and further analyze the microscopic mechanisms influencing these scattering strengths. We find that phonons could produce effective in-plane magnetic fields which flip spin o…
Janus transition-metal dichalcogenide monolayers are fully artificial materials, where one plane of chalcogen atoms is replaced by chalcogen atoms of a different type. Theory predicts an in-built out-of-plane electric field, giving rise to long-lived, dipolar excitons, while preserving direct-bandgap optical transitions in a uniform potential landscape. Previous Janus studies had broad photoluminescence (>15 meV) spectra obfuscating their excitonic origin. Here, we identify the neutral, and negatively charged inter- and intravalley exciton transitions in Janus WSeS monolayer with $\sim 6$ meV …
Monolayer transition metal dichalcogenide semiconductors, with versatile experimentally accessible exciton species, offer an interesting platform for investigating the interaction between excitons and a Fermi sea of charges. Using hexagonal boron nitride encapsulated monolayer MoSe2, we study the impact of charge density tuning on the ground and excited Rydberg states in the atomic layer. Consistent excitonpolaron behavior is revealed in both photoluminescence and reflection spectra of the A exciton 1s (A:1s) Rydberg state, in contrast to previous studies. The A:2s Rydberg state provides an op…
In semiconductor physics, many essential optoelectronic material parameters can be experimentally revealed via optical spectroscopy in sufficiently large magnetic fields. For monolayer transition-metal dichalcogenide semiconductors, this field scale is substantial --tens of teslas or more-- due to heavy carrier masses and huge exciton binding energies. Here we report absorption spectroscopy of monolayer MoS$_2$, MoSe$_2$, MoTe$_2$, and WS$_2$ in very high magnetic fields to 91~T. We follow the diamagnetic shifts and valley Zeeman splittings of not only the exciton's $1s$ ground state but also …
Reduced dielectric screening in two-dimensional materials enables bound excitons, which modifies their optical absorption and optoelectronic response even at room temperature. Here, we demonstrate the existence of excitons in the bandgap of the monolayer family of the newly discovered synthetic MoSi$_2$Z$_4$ (Z = N, P, and As) series of materials. All three monolayers support several bright and strongly bound excitons with binding energies varying from 1 eV to 1.35 eV for the lowest energy exciton resonances. On increasing the pump fluence, the exciton binding energies get renormalized, leadin…
