Excitons and trions (or exciton-polarons) in transition metal dichalcogenides (TMDs) are known to decay predominantly through intravalley transitions. Electron-hole recombination across different valleys can also play a significant role in the excitonic dynamics, but intervalley transitions are rarely observed in monolayer TMDs, because they violate the conservation of momentum. Here we reveal the intervalley recombination of dark excitons and trions through more than one path in monolayer WSe$_2$. We observe the intervalley dark excitons, which can recombine by the assistance of defect scattering or chiral-phonon emission. We also reveal that a trion can decay in two distinct paths - through intravalley or intervalley electron-hole recombination - into two different final valley states. Although these two paths are energy degenerate, we can distinguish them by lifting the valley degeneracy under a magnetic field. In addition, the intra- and inter-valley trion transitions are coupled to zone-center and zone-corner chiral phonons, respectively, to produce distinct phonon replicas. The observed multipath optical decays of dark excitons and trions provide much insight into the internal quantum structure of trions and the complex excitonic interactions with defects and chiral phonons in monolayer valley semiconductors.
We report the observation and gate manipulation of intrinsic dark trions in monolayer WSe$_2$. By using ultraclean WSe$_2$ devices encapsulated by boron nitride, we directly resolve the weak photoluminescence of dark trions. The dark trions can be tuned continuously between negative and positive charged trions with electrostatic gating. We also reveal their spin triplet configuration and distinct valley optical emission by their characteristic Zeeman splitting under magnetic field. The dark trions exhibit large binding energy (14-16 meV). Their lifetime (~1.3 ns) is two orders of magnitude lon…
We report magneto-photoluminescence spectroscopy of gated MoS$_2$ monolayers in high magnetic fields to 28 T. At B = 0T and electron density $n_s\sim 10^{12}cm^-2$, we observe three trion resonances that cannot be explained within a single-particle picture. Employing ab initio calculations that take into account three-particle correlation effects as well as local and non-local electron-hole exchange interaction, we identify those features as quantum superpositions of inter- and intravalley spin states. We experimentally investigate the mixed character of the trion wave function via the filling…
Monolayer 2D semiconductors provide an attractive option for valleytronics due to the valley-addressability by helicity-specific light beam. But the short valley lifetime for excitons have hindered potential valleytronic applications. In this paper, we demonstrate a strategy for prolonging the valley lifetime by converting excitons to trions through effective gate control and by taking advantage of much longer valley lifetime for trions than for excitons. In continuous-wave experiments, we found the valley polarization increases as gate voltage is tuned away from the charge neutrality, with th…
We present a detailed investigation of the exciton and trion dynamics in naturally doped MoSe2 and WSe2 single atomic layers as a function of temperature in the range 10-300K under above band-gap laser excitation. By combining time-integrated and time-resolved photoluminescence (PL) spectroscopy we show the importance of exciton and trion localization in both materials at low temperatures. We also reveal the transition to delocalized exciton complexes at higher temperatures where the exciton and trion thermal energy exceeds the typical localization energy. This is accompanied with strong chang…
Effect of spin-dependent tunneling and intervalley scattering in magnetic-semiconductor van der Waals heterostructures on exciton and trion polarization
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…
We investigate valley dynamics associated with trions in monolayer tungsten diselenide (WSe2) using polarization resolved two-color pump-probe spectroscopy. When tuning the pump and probe energy across the trion resonance, distinct trion valley polarization dynamics are observed as a function of energy and attributed to the intra-valley and inter-valley trions in monolayer WSe2. We observe no decay of a near-unity valley polarization associated with the intra-valley trions during ~ 25 ps, while the valley polarization of the inter-valley trions exhibits a fast decay of ~ 4 ps. Furthermore, we …
Strong Coulomb interactions in single-layer transition metal dichalcogenides (TMDs) result in the emergence of strongly bound excitons, trions and biexcitons. These excitonic complexes possess the valley degree of freedom, which can be exploited for quantum optoelectronics. However, in contrast to the good understanding of the exciton and trion properties, the binding energy of the biexciton remains elusive, with theoretical calculations and experimental studies reporting discrepant results. In this work, we resolve the conflict by employing low-temperature photoluminescence spectroscopy to id…
Monolayer transition metal dichalcogenides (TMDs) hold great promise for future information processing applications utilizing a combination of electron spin and valley pseudospin. This unique spin system has led to observation of the valley Zeeman effect in neutral and charged excitonic resonances under applied magnetic fields. However, reported values of the trion valley Zeeman splitting remain highly inconsistent across studies. Here, we utilize high quality hBN encapsulated monolayer WSe$_2$ to enable simultaneous measurement of both intervalley and intravalley trion photoluminescence. We f…
Spin-forbidden intravalley dark exciton in tungsten-based transition metal dichalcogenides (TMDCs), owing to its unique spin texture and long lifetime, has attracted intense research interest. Here, we show that we can control the dark exciton electrostatically by dressing it with one free electron or free hole, forming the dark trions. The existence of the dark trions is suggested by the unique magneto-photoluminescence spectroscopy pattern of the boron nitride (BN) encapsulated monolayer WSe2 device at low temperature. The unambiguous evidence of the dark trions is further obtained by direct…
We perform absorption and photoluminescence spectroscopy of trions in hBN-encapsulated WSe$_2$, WS$_2$, MoSe$_2$, and MoS$_2$ monolayers, depending on temperature. The different trends for W- and Mo-based materials are excellently reproduced considering a Fermi-Dirac distribution of bright and dark trions. We find a dark trion, $\rm{X_D^-}$ 19 meV $\textit{below}$ the lowest bright trion, $\rm{X}_1^-$ in WSe$_2$ and WS$_2$. In MoSe$_2$, $\rm{X_D^-}$ lies 6 meV $\textit{above}$ $\rm{X}_1^-$, while $\rm{X_D^-}$ and $\rm{X}_1^-$ almost coincide in MoS$_2$. Our results agree with GW-BSE $\textit{a…
We report the direct observation of intervalley exciton between the Q conduction valley and $Γ$ valence valley in bilayer WSe$_2$ by photoluminescence. The Q$Γ$ exciton lies at ~18 meV below the QK exciton and dominates the luminescence of bilayer WSe$_2$. By measuring the exciton spectra at gate-tunable electric field, we reveal different interlayer electric dipole moments and Stark shifts between Q$Γ$ and QK excitons. Notably, we can use the electric field to switch the energy order and dominant luminescence between Q$Γ$ and QK excitons. Both Q$Γ$ and QK excitons exhibit pronounced phonon re…
The newly developed two-dimensional layered materials provide perfect platform for valley-spintronics exploration. To determine the prospect of utilizing the valley degree of freedom, it is of great importance to directly detect and understand the valley dynamics in these materials. Here, the exciton valley dynamics in monolayer WSe$_2$ is investigated by the two-color pump-probe magneto-optical Kerr technique. By tuning the probe photon energy in resonance with the free excitons and trions, the valley relaxation time of different excitonic states in monolayer WSe$_2$ is determined. Valley rel…
Monolayer transition metal dichalcogenides offer the possibility of optical control of the valley degree of freedom. In order to asses the potential of these materials in applications, detailed knowledge of the valley dynamics is essential. In this work, we apply low temperature time-resolved photoluminescence (PL) measurements to investigate exciton valley relaxation dynamics and, in particular, its behavior under strong excitation. At the lowest excitation powers the inter valley scattering time is $\simeq 50$ ps, but shortens by more than a factor of two at the highest powers. We attribute …
Single layers of transition metal dichalcogenides (TMDs) are direct gap semiconductors with nondegenerate valley indices. An intriguing possibility for these materials is the use of their valley index as an alternate state variable. Several limitations to such a utility include strong, phonon-enabled intervalley scattering, as well as multiparticle interactions leading to multiple emission channels. We prepare single-layer WS$_{2}$ such that the photoluminescence is from either the neutral or charged exciton (trion). After excitation with circularly polarized light, the neutral exciton emissio…
The direct band gap character and large spin-orbit splitting of the valence band edges (at the K and K' valleys) in monolayer transition metal dichalcogenides have put these two-dimensional materials under the spot-light of intense experimental and theoretical studies. In particular, for Tungsten dichalcogenides it has been found that the sign of spin splitting of conduction band edges makes ground state excitons radiatively inactive (dark) due to spin and momentum mismatch between the constituent electron and hole. One might similarly assume that the ground states of charged excitons and biex…
Spatially indirect excitons with displaced wavefunctions of electrons and holes play a pivotal role in a large portfolio of fascinating physical phenomena and emerging optoelectronic applications, such as valleytronics, exciton spin Hall effect, excitonic integrated circuit and high-temperature superfluidity. Here, we uncover three types of spatially indirect excitons (including their phonon replicas) and their quantum-confined Stark effects in hexagonal boron nitride encapsulated bilayer WSe2, by performing electric field-tunable photoluminescence measurements. Because of different out-of-pla…
WSe$_2$ monolayers with variable doping are an ideal system to study two-dimensional excitonic complexes. Here, we find that the strongest photoluminescence from bright neutral excitons occurs at moderate $p$-doping levels, owing to a rapid decrease of signal from positive dark trions and a slow increase of signal from positive bright trions with growing $p$-concentrations. We explain our observations with a qualitative model, in which the scattering rate of bright excitons into dark complexes is enhanced by exciton localization, while the scattering rate into positive bright trions increases …
Coupling degrees of freedom of distinct nature plays a critical role in numerous physical phenomena. The recent emergence of layered materials provides a laboratory for studying the interplay between internal quantum degrees of freedom of electrons. Here, we report experimental signatures of new coupling phenomena connecting real spin with layer pseudospins in bilayer WSe2. In polarization-resolved photoluminescence measurements, we observe large spin orientation of neutral and charged excitons generated by both circularly and linearly polarized light, with a splitting of the trion spectrum in…
Transition metal dichalcogenide heterobilayers offer attractive opportunities to realize lattices of interacting bosons with several degrees of freedom. Such heterobilayers can feature moiré patterns that modulate their electronic band structure, leading to spatial confinement of single interlayer excitons (IXs) that act as quantum emitters with $C_3$ symmetry. However, the narrow emission linewidths of the quantum emitters contrast with a broad ensemble IX emission observed in nominally identical heterobilayers, opening a debate regarding the origin of IX emission. Here we report the continuo…
The large surface-to-volume ratio in atomically thin 2D materials allows to efficiently tune their properties through modifications of their environment. Artificial stacking of two monolayers into a bilayer leads to an overlap of layer-localized wave functions giving rise to a twist angle-dependent hybridization of excitonic states. In this joint theory-experiment study, we demonstrate the impact of interlayer hybridization on bright and momentum-dark excitons in twisted WSe$_2$ bilayers. In particular, we show that the strong hybridization of electrons at the $Λ$ point leads to a drastic reds…
Monolayers of transition metal dichalcogenides are ideal materials to control both spin and valley degrees of freedom either electrically or optically. Nevertheless, optical excitation mostly generates excitons species with inherently short lifetime and spin/valley relaxation time. Here we demonstrate a very efficient spin/valley optical pumping of resident electrons in n-doped WSe2 and WS2 monolayers. We observe that, using a continuous wave laser and appropriate doping and excitation densities, negative trion doublet lines exhibit circular polarization of opposite sign and the photoluminesce…
The rich optical properties of transition metal dichalcogenide monolayers (TMD-MLs) render these materials promising candidates for the design of new optoelectronic devices. Despite the large number of excitonic complexes in TMD-MLs, the main focus has been put on optically bright neutral excitons. Spin-forbidden dark excitonic complexes have been addressed for basic science purposes, but not for applications. We report on spin-forbidden dark excitonic complexes in ML WSe$_2$ as an ideal system for the facile generation of radially polarized light beams. Furthermore, the spatially resolved pol…
The coherent third-order nonlinear response of monolayer transition-metal dichalcogenide (TMD) semiconductors, such as MoSe$_2$ is dominated by the nonlinear exciton response, as well as biexciton and trion resonances. The fact that these resonances may be spectrally close together makes identification of the signatures, for example in differential transmission (DT), challenging. Instead of focusing on explaining a given set of experimental data, a systematic study aimed at elucidating the roles of intravalley and intervalley electron-hole (e-h) exchange on the DT spectra is presented. Previou…
We observe a set of three replica luminescent peaks at ~21.4 meV below the dark exciton, negative and positive dark trions (or exciton-polarons) in monolayer WSe2. The replica redshift energy matches the energy of the zone-center E"-mode optical phonons. The phonon replicas exhibit parallel gate dependence and same g-factors as the dark excitonic states, but follow the valley selection rules of the bright excitonic states. While the dark states exhibit out-of-plane transition dipole and valley-independent linearly polarized emission in the in-plane directions, their phonon replicas exhibit in-…
Indirect excitons (IX) in semiconductor heterostructures are bosons, which can cool below the temperature of quantum degeneracy and can be effectively controlled by voltage and light. IX quantum Bose gases and IX devices were explored in GaAs heterostructures where an IX range of existence is limited to low temperatures due to low IX binding energies. IXs in van der Waals transition-metal dichalcogenide (TMD) heterostructures are characterized by large binding energies giving the opportunity for exploring excitonic quantum gases and for creating excitonic devices at high temperatures. TMD hete…
Strong Coulomb interactions in atomically thin semiconductors like monolayer WSe$_2$ induce not only tightly bound excitons, but also make their optical properties very sensible to doping. By utilizing a microscopic theory based on the excitonic Heisenberg equations of motion, we systematically determine the influence of doping on the excitonic linewidth, lineshift, and oscillator strength. We calculate trion resonances and demonstrate that the Coulomb coupling of excitons to the trionic continuum generates a non-Markovian interference, which, due to a time retardation, builds up a phase respo…
Exciton optical transitions in transition-metal dichalcogenides offer unique opportunities to study rich many-body physics. Recent experiments in monolayer WSe$_2$ and WS$_2$ have shown that while the low-temperature photoluminescence from neutral excitons and three-body complexes is suppressed in the presence of elevated electron densities or strong photoexcitation, new dominant peaks emerge in the low-energy side of the spectrum. I present a theory that elucidates the nature of these optical transitions showing the role of the intervalley Coulomb interaction. After deriving a compact dynamic…
Optical interband transitions in monolayer transition metal dichalcogenides such as WSe2 and MoS2 are governed by chiral selection rules. This allows efficient optical initialization of an electron in a specific K-valley in momentum space. Here we probe the valley dynamics in monolayer WSe2 by monitoring the emission and polarization dynamics of the well separated neutral excitons (bound electron hole pairs) and charged excitons (trions) in photoluminescence. The neutral exciton photoluminescence intensity decay time is about 4ps, whereas the trion emission occurs over several tens of ps. The …
We investigate the hole spin relaxation due to the Rashba spin-orbit coupling induced by an external perpendicular electric field in bilayer WSe$_2$. The Rashba spin-orbit coupling coefficients in bilayer WSe$_2$ are constructed from the corresponding monolayer ones. In contrast to monolayer WSe$_2$, the out-of-plane component of the bilayer Rashba spin-orbit coupling acts as a Zeeman-like field with opposite directions but identical values in the two valleys. For in-plane spins, this Zeeman-like field, together with the intervalley hole-phonon scattering, opens an intervalley spin relaxation …
Charged excitons, or X$^{\pm}$-trions, in monolayer transition metal dichalcogenides have binding energies of several tens of meV. Together with the neutral exciton X$^0$ they dominate the emission spectrum at low and elevated temperatures. We use charge tunable devices based on WSe$_2$ monolayers encapsulated in hexagonal boron nitride, to investigate the difference in binding energy between X$^+$ and X$^-$ and the X$^-$ fine structure. We find in the charge neutral regime, the X$^0$ emission accompanied at lower energy by a strong peak close to the longitudinal optical (LO) phonon energy. Th…
We have systematically examined the circular polarization of monolayer WSe2 at different temperature, excitation energy and exciton density. The valley depolarization in WSe2 is experimentally confirmed to be governed by the intervalley electron-hole exchange interaction. More importantly, a non-monotonic dependence of valley circular polarization on the excitation power density has been observed, providing the experimental evidence for the non-monotonic dependence of exciton intervalley scattering rate on the excited exciton density. The physical origination of our experimental observations h…
We investigate the steady-state out-of-plane spin diffusion in p-type bilayer WSe2 in the presence of the Rashba spin-orbit coupling and Hartree-Fock effective magnetic field. The out-of-plane components of the Rashba spin-orbit coupling serve as the opposite Zeeman-like fields in the two valleys. Together with the identical Hartree-Fock effective magnetic fields, different total effective magnetic field strengths in the two valleys are obtained. It is further revealed that due to the valley-dependent total effective magnetic field strength, similar (different) spin-diffusion lengths in the tw…
Identifying quantum numbers to label elementary excitations is essential for the correct description of light-matter interaction in solids. In monolayer semiconducting transition metal dichalcogenides (TMDs) such as MoSe$_2$ or WSe$_2$, most optoelectronic phenomena are described well by labelling electron and hole states with the spin projection along the normal to the layer (S$_z$). In contrast, for WSe$_2$/MoSe$_2$ interfaces recent experiments show that taking S$_z$ as quantum number is not a good approximation, and spin mixing needs to be always considered. Here we argue that the correct …
The presence of two spin-split valleys in monolayer (1L) transition metal dichalcogenide (TMD) semiconductors supports versatile exciton species classified by their spin and valley quantum numbers. While the spin-0 intravalley exciton, known as the "bright" exciton, is readily observable, other types of excitons, such as the spin-1 intravalley (spin-dark) and spin-0 intervalley (momentum-dark) excitons, are more difficult to access. Here we develop a waveguide coupled 1L tungsten diselenide (WSe2) device to probe these exciton species. In particular, TM coupling to the atomic layer's out-of-pl…
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 MoS$_2$ are studied with the aid of photoluminescence, photoluminescence excitation, and reflectance contrast experiments. We demonstrate that carrier concentration in MoS$_2$ monolayers, arising from charge transfer from impurities in the substrate, can be significantly tuned …
Vertically stacked van der Waals heterostructures constitute a promising platform for providing tailored band alignment with enhanced excitonic systems. Here we report observations of neutral and charged interlayer excitons in trilayer WSe2-MoSe2-WSe2 van der Waals heterostructures and their dynamics. The addition of a WSe2 layer in the trilayer leads to significantly higher photoluminescence quantum yields and tunable spectral resonance compared to its bilayer heterostructures at cryogenic temperatures. The observed enhancement in the photoluminescence quantum yield is due to significantly la…
Monolayer transition metal dichalcogenides, known for exhibiting strong excitonic resonances, constitute a very interesting and versatile platform for investigation of light-matter interactions. In this work we report on a strong coupling regime between excitons in monolayer WSe2 and photons confined in an open, voltage-tunable dielectric microcavity. The tunability of our system allows us to extend the exciton-polariton state over a wide energy range and, in particular, to bring the excitonic component of the lower polariton mode into resonance with other excitonic transitions in monolayer WS…
Due to degeneracies arising from crystal symmetries, it is possible for electron states at band edges ("valleys") to have additional spin-like quantum numbers. An important question is whether coherent manipulation can be performed on such valley pseudospins, analogous to that routinely implemented using true spin, in the quest for quantum technologies. Here we show for the first time that SU(2) valley coherence can indeed be generated and detected. Using monolayer semiconductor WSe2 devices, we first establish the circularly polarized optical selection rules for addressing individual valley e…
A monolayer of a transition metal dichalcogenide (TMD) such as WSe$_2$ is a two-dimensional (2D) direct band-gap valley-semiconductor having an effective Honeycomb lattice structure with broken inversion symmetry. The inequivalent valleys in the Brillouin zone could be selectively addressed using circularly-polarized light fields, suggesting the possibility for magneto-optical measurement and manipulation of the valley pseudospin degree of freedom. Here we report such experiments that demonstrate the valley Zeeman effect -- strongly anisotropic lifting of the degeneracy of the valley pseudospi…
Embedding a WS$_2$ monolayer in flakes of hexagonal boron nitride allowed us to resolve and study the photoluminescence response due to both singlet and triplet states of negatively charged excitons (trions) in this atomically thin semiconductor. The energy separation between the singlet and triplet states has been found to be relatively small reflecting rather weak effects of the electron-electron exchange interaction for the trion triplet in a WS$_2$ monolayer, which involves two electrons with the same spin but from different valleys. Polarization-resolved experiments demonstrate that the h…
As hosts for tightly-bound electron-hole pairs carrying quantized angular momentum, atomically-thin semiconductors of transition metal dichalcogenides provide an appealing platform for optically addressing the valley degree of freedom. In particular, the valleytronic properties of neutral and charged excitons in these systems have been widely investigated. Meanwhile, correlated quantum states involving more particles are so far elusive and controversial. Here we present experimental evidence for valleytronic four-particle biexcitons and five-particle exciton-trions in high-quality monolayer tu…
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…
We report on nanosecond long, gate-dependent valley lifetimes of free charge carriers in monolayer WSe$_2$, unambiguously identified by the combination of time-resolved Kerr rotation and electrical transport measurements. While the valley polarization increases when tuning the Fermi level into the conduction or valence band, there is a strong decrease of the respective valley lifetime consistent with both electron-phonon and spin-orbit scattering. The longest lifetimes are seen for spin-polarized bound excitons in the band gap region. We explain our findings via two distinct, Fermi level-depen…
Low temperature and polarization resolved magneto-photoluminescence experiments are used to investigate the properties of dark excitons and dark trions in a monolayer of WS$_2$ encapsulated in hexagonal BN (hBN). We find that this system is an $n$-type doped semiconductor and that dark trions dominate the emission spectrum. In line with previous studies on WSe$_2$, we identify the Coulomb exchange interaction coupled neutral dark and grey excitons through their polarization properties, while an analogous effect is not observed for dark trions. Applying the magnetic field in both perpendicular …
One of the main tasks in the investigation of 2-dimensional transition metal dichalcogenides is the determination of valley lifetimes. In this work, we combine time-resolved Kerr rotation with electrical transport measurements to explore the gate-dependent valley lifetimes of free conduction band electrons of monolayer WSe$_2$. When tuning the Fermi energy into the conduction band we observe a strong decrease of the respective valley lifetimes which is consistent with both spin-orbit and electron-phonon scattering. We explain the formation of a valley polarization by the scattering of opticall…
