We demonstrate that the temperature and doping dependencies of the photoluminescence (PL) spectra of a doped MoS2 monolayer have several peculiar characteristics defined by trion radiative decay. While only zero-momentum exciton states are coupled to light, radiative recombination of non-zero momentum trions is also allowed. This leads to an asymmetric broadening of the trion spectral peak and redshift of the emitted light with increasing temperature. The lowest energy trion state is dark, which is manifested by the sharply non-monotonic temperature dependence of the PL intensity. Our calculations combine the Dirac model for the single-particle states, the parameters for which are obtained from the first principle calculations, and the direct solution of the three-particle problem within the Tamm-Dancoff approximation. The numerical results are well captured by a simple model that yields analytical expressions for the temperature dependencies of the PL spectra.
Monolayer molybdenum disulfide (MoS$_2$) has emerged as an excellent 2D model system because of its two inequivalent, direct-gap valleys that lead to exotic bound and excited states. Here we focus on one such bound state, the negatively charged trion. Unlike excitons, trions can radiatively decay with non-zero momentum by kicking out an electron, resulting in an asymmetric trion photoluminescence (PL) peak with a long low-energy tail. As a consequence, the peak position does not correspond to the zero momentum trion energy. By including the trion's long tail in our analysis we are able to accu…
Single-layer WS$_2$ is a direct-gap semiconductor showing strong excitonic photoluminescence features in the visible spectral range. Here, we present temperature-dependent photoluminescence measurements on mechanically exfoliated single-layer WS$_2$, revealing the existence of neutral and charged excitons at low temperatures as well as at room temperature. By applying a gate voltage, we can electrically control the ratio of excitons and trions and assert a residual n-type doping of our samples. At high excitation densities and low temperatures, an additional peak at energies below the trion do…
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 studied the excitation density dependence of photoluminescence (PL) spectra of excitons and trions (charged excitons) in hole-doped single-walled carbon nanotubes. We found that the PL intensity of trions exhibited a strong nonlinear saturation behavior as the excitation density increased, whereas that of excitons exhibited a weak sublinear behavior. The strong PL saturation of trions is attributed to depletion of doped holes that are captured by excitons in the formation processes. Moreover, the effective radiative lifetime of a trion was evaluated to be approximately 20 ns.
We present a full configuration interaction study of the spontaneous recombination of neutral and singly charged excitons (trions) in semiconductor quantum dots, from weak to strong coupling regimes. We find that the enhancement of the recombination rate of neutral excitons with increasing dot size is suppressed for negative trions, and even reversed for positive trions. Our findings agree with recent comprehensive photoluminescence experiments in self-assembled quantum dots [P. Dalgarno et al. Phys. Rev. B {\bf 77}, 245311 (2008)] and confirm the major role played by correlations in the valen…
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 scatte…
We present results on the radiative lifetimes of excitons and trions in a monolayer of metal dichalcogenide MoS2. The small exciton radius and the large exciton optical oscillator strength result in radiative lifetimes in the 0.18-0.30 ps range for excitons that have small in-plane momenta and couple to radiation. Average lifetimes of thermally distributed excitons depend linearly on the exciton temperature and can be in the few picoseconds range at small temperatures and more than a nanosecond near room temperature. Localized excitons exhibit lifetimes in the same range and the lifetime incre…
We report charged exciton (trion) formation dynamics in doped monolayer transition metal dichalcogenides (TMDs), specifically molybdenum diselenide (MoSe2), using resonant two-color pump-probe spectroscopy. When resonantly pumping the exciton transition, trions are generated on a picosecond timescale through exciton-electron interaction. As the pump energy is tuned from the high energy to low energy side of the inhomogeneously broadened exciton resonance, the trion formation time increases by ~ 50%. This feature can be explained by the existence of both localized and delocalized excitons in a …
We measure the optical absorption spectra and optical conductivities of excitons and trions in monolayers of metal dichalcogenide MoS$_{2}$ and compare the results with theoretical models. Our results show that the Wannier-Mott model for excitons, with modifications to account for small exciton radii and large exciton relative wavefunction spread in momentum space, phase space blocking due to Pauli exclusion in doped materials, and wavevector dependent dielectric constant, gives results that agree well with experiments. The measured exciton optical absorption spectra are used to obtain experim…
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…
Charged excitons (trions) are essential for the optical spectra in low dimensional doped monolayers (ML) of transitional metal dichalcogenides (TMDC). Using a direct diagonalization of the three-body Hamiltonian, we explore the low-lying trion states in four types of TMDC MLs. We show that the trions fine structure results from the interplay between the spin-valley fine structure of the single-particle bands and the exchange interaction between the composing particles. We demonstrate that by variations of the doping and dielectric environment, trion energy fine structure can be tuned, leading …
We present experimental and theoretical results on the high-quality single-layer MoS$_{2}$ which reveal the fine structure of charged excitons, i.e., trions. In the emission spectra we resolve and identify two trion peaks, T$_{1}$ and T$_{2}$, resembling the pair of singlet and triplet trion peaks (T$_S$ and T$_{T}$) in tungsten-based materials. However, in polarization-dependent photoluminescence measurements we identify these peaks as novel intra- and inter-valley singlet trions, constituting the trion fine structure distinct from that already known in bright and dark 2D materials with large…
The possibility of electrical manipulation and detection of charged exciton (trion) before its radiative recombination makes it promising for excitonic devices. Using a few-layer graphene/monolayer WS$_{2}$/monolayer graphene vertical heterojunction, we report inter-layer charge transport from top few-layer graphene to bottom monolayer graphene, mediated by coherently formed trion state. This is achieved by using a resonant excitation and varying the sample temperature, the resulting change in the WS$_{2}$ bandgap allows us to scan the excitation around the exciton-trion spectral overlap with …
Strong Coulomb interaction in monolayer transition metal dichalcogenides can facilitate nontrivial many-body effects among excitonic complexes. Many-body effects like exciton-exciton annihilation (EEA) have been widely explored in this material system. However, a similar effect for charged excitons (or trions), that is, trion-trion annihilation (TTA), is expected to be relatively suppressed due to repulsive like-charges, and has not been hitherto observed in such layered semiconductors. By a gate-dependent tuning of the spectral overlap between the trion and the charged biexciton through an "a…
We study the trion and biexciton in transition metal dichalcogenides monolayers within the framework of a nonrelativistic potential model using the method of hyperspherical harmonics (HH). We solve the three- and four-body Schrödinger equations with the Keldysh potential by expanding the wave functions of a trion and biexciton in terms of the antisymmetrized HH. Results of the calculations for the ground state energies are in good agreement with similar calculations for the Keldysh potential and in reasonable agreement with experimental measurements of trion and biexciton binding energies.
We report the first observation of trions (charged excitons), three-particle bound states consisting of one electron and two holes, in hole-doped carbon nanotubes at room temperature. When p-type dopants are added to carbon nanotube solutions, the photoluminescence and absorption peaks of the trions appear far below the E11 bright exciton peak, regardless of the dopant species. The unexpectedly large energy separation between the bright excitons and the trions is attributed to the strong electron-hole exchange interaction in carbon nanotubes.
Charged excitons called trions play an important role in the fundamental valley dynamics in the newly emerging 2D semiconductor materials. We used ultrafast pump- probe spectroscopy to study the valley trion dynamics in a MoSe$_2$ monolayer grown by using chemical vapor deposition. The dynamics display an ultrafast trion formation followed by a non-exponential decay. The measurements at different pump fluences show that the trion decay dynamics become slower as the excitation density increases. The observed trion dynamics and the associated density dependence are a result of the trapping by tw…
The optical spectra of transition metal dichalcogenide (TMDC) monolayers are dominated by excitons and trions. Here we establish the dependences of these optical transitions on disorder from hyperspectral imaging of h-BN encapsulated monolayer MoSe2. While both exciton and trion energies vary spatially, these two quantities are almost perfectly correlated, with spatial variation in the trion binding energy of only ~0.18 meV. In contrast, variation in the energy splitting between the two lowest energy exciton states is one order of magnitude larger at ~1.7 meV. Statistical analysis and theoreti…
We present a many-body formalism for the simulation of time-resolved nonlinear spectroscopy and apply it to study the coherent interaction between excitons and trions in doped transition-metal dichalcogenides. Although the formalism can be straightforwardly applied in a first-principles manner, for simplicity we use a parameterized band structure and a static model dielectric function, both of which can be obtained from a calculation using the $GW$ approximation. Our simulation results shed light on the interplay between singlet and triplet trions in molybdenum- and tungsten-based compounds. O…
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 …
Transition metal dichalcogenide (TMD) monolayers are two-dimensional semiconductors with two valleys in their band structure that can be selectively addressed using circularly polarized light. Their photoluminescence spectrum is characterized by neutral and charged excitons (trions) that form a chemical equilibrium governed by the net charge density. Here, we use chemical doping to drive the conversion of excitons into trions in $\text{WS}_{2}$ monolayers at room temperature, and study the resulting valley polarization via photoluminescence measurements under valley-selective optical excitatio…
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…
We study spatial photoluminescence characteristics of neutral and charged excitons across extended monolayer MoS$_2$ synthesized by chemical vapor deposition. Using two-dimensional hyperspectral photoluminescence mapping at cryogenic temperatures we identify regions with increased emission from charged excitons associated with both spin-orbit split valence subbands. Such regions are attributed to unintentional doping at defect sites with excess charge that bind neutral excitons to form defect-pinned trions. Our findings imply comparable timescales for the formation, relaxation, and radiative d…
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…
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 …
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…
Recently, the celebrated Keldysh potential has been widely used to describe the Coulomb interaction of few-body complexes in monolayer transition-metal dichalcogenides. Using this potential to model charged excitons (trions), one finds a strong dependence of the binding energy on whether the monolayer is suspended in air, supported on SiO$_2$, or encapsulated in hexagonal boron-nitride. However, empirical values of the trion binding energies show weak dependence on the monolayer configuration. This deficiency indicates that the description of the Coulomb potential is still lacking in this impo…
We study the impact of a free carrier reservoir on the optical properties of excitonic and trionic complexes in a MoSe$_2$ monolayer at cryogenic temperatures. By applying photodoping via a non-resonant pump laser the electron density can be controlled in our sample and in turn the exciton and trion densities can be tuned. We find a significant increase of the trion binding energy in the presence of an induced electron gas both in power- and in time-resolved photoluminescence spectra. This behaviour is reproduced within the original variational approach that takes into account both screening a…
Charge doping in transition metal dichalcogenide is currently a subject of high importance for future electronic and optoelectronic applications. Here we demonstrate chemical doping in CVD grown monolayer (1L) of WS2 by a few commonly used laboratory solvents by investigating the room temperature photoluminescence (PL). The appearance of distinct trionic emission in the PL spectra and quenched PL intensities suggest n-type doping in WS2. The temperature-dependent PL spectra of the doped 1L-WS2 reveal significant enhancement of trion emission intensity over the excitonic emission at low tempera…
Monolayers of transition metal dichalcogenides present an intriguing platform to investigate the interplay of excitonic complexes in two dimensional semiconductors. Here, we use optical spectroscopy to study light-matter coupling and non-equilibrium relaxation dynamics of three-particle exciton states, commonly known as trions. We identify the consequences of the exchange interaction for the trion finestructure in tungsten-based monolayer materials from variational calculations and experimentally determine the resulting characteristic differences in their oscillator strength. It allows us to q…
We study a 2D system of trion-polaritons at the quantum level and demonstrate that for monolayer semiconductors they can exhibit a strongly nonlinear optical response. The effect is due to the composite nature of trion-based excitations resulting in their nontrivial quantum statistical properties, and enhanced phase space filling effects. We present the full quantum theory to describe the statistics of trion-polaritons, and demonstrate that the associated nonlinearity persists at the level of few quanta, where two qualitatively different regimes of photon antibunching are present for weak and …
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 $\textit{a…
The possibility of almost linear tuning of the band gap and of the electrical and optical properties in monolayers (MLs) of semiconducting transition metal dichalcogenide (S-TMD) alloys opens up the way to fabricate materials with on-demand characteristics. By making use of photoluminescence spectroscopy, we investigate optical properties of WSSe MLs with a S/Se ratio of 57/43 deposited on SiO$_2$/Si substrate and encapsulated in hexagonal BN flakes. Similarly to the $"parent"$ WS$_2$ and WSe$_2$ MLs, we assign the WSSe MLs to the ML family with the dark ground exciton state. We find that, in …
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 emerging field of valleytronics aims to exploit the valley pseudospin of electrons residing near Bloch band extrema as an information carrier. Recent experiments demonstrating optical generation and manipulation of exciton valley coherence (the superposition of electron-hole pairs at opposite valleys) in monolayer transition metal dichalcogenides (TMDs) provide a critical step towards control of this quantum degree of freedom. The charged exciton (trion) in TMDs is an intriguing alternative to the neutral exciton for control of valley pseudospin because of its long spontaneous recombinatio…
Recently in [Phys. Rev. B 99, 241301(R) (2019)] tensor networks build upon logical circuits were briefly introduced to retrieve exciton and biexciton states. Compared to a conventional approach the tensor network methods scales logarithmic instead of linear in the grid points of the Brioullin zone and linear instead of exponential in the number of electrons and holes. This enables calculations with higher precision on the full Brioullin zone than previously possible. In this paper extensive details for an efficient implementation and the corresponding mathematical background are presented. In …
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…
Optical excitation typically enhances electrical conduction and low-frequency radiation absorption in semiconductors. We have, however, observed a pronounced transient decrease of conductivity in doped monolayer molybdenum disulfide (MoS2), a two-dimensional (2D) semiconductor, under femtosecond laser excitation. In particular, the conductivity is reduced dramatically down to only 30% of its equilibrium value with high pump fluence. This anomalous phenomenon arises from the strong many-body interactions in the system, where photoexcited electron-hole pairs join the doping-induced charges to fo…
We have successfully confined trions into a one-dimensional restricted space of a MoSe2 device with CNT gate electrodes. The dry transfer process, including deterministic dry transfer of aligned CNTs, has led to an hBN-encapsulated MoSe2 device with CNT back gate electrodes. In contrast to a location without CNT gate electrodes, applying voltage via CNT gate electrodes significantly alters PL spectra at a location with CNT gate electrodes. PL imaging has revealed that image contrast from trions is linear along the CNT electrode underneath, consistent with 1D confinement of trions in response t…
Photoluminescence (PL) of transition metal dichalcogenide (TMD) monolayers is strongly influenced by the dielectric environment. The defect states present in the substrate induces uncontrollable doping in the TMD monolayer and thereby modifies the PL spectra. There have been enormous efforts to tune and overcome the effect of inevitable subtract defects in PL spectra, but a proper understanding and a convenient way are still lacking. Here, we systematically studied the effect of surface defects by gradually increasing the separation between WS2 monolayer and substrate. Hence, we could precisel…
Monolayer transition metal dichalcogenide (TMDC) semiconductors exhibit strong excitonic optical resonances which serve as a microscopic, non-invasive probe into their fundamental properties. Like the hydrogen atom, such excitons can exhibit an entire Rydberg series of resonances. Excitons have been extensively studied in most TMDCs (MoS$_2$, MoSe$_2$, WS$_2$ and WSe$_2$), but detailed exploration of excitonic phenomena has been lacking in the important TMDC material molybdenum ditelluride (MoTe$_2$). Here, we report an experimental investigation of excitonic luminescence properties of monolay…
The ultrathin transition metal dichalcogenides (TMDs) have emerged as promising materials for various applications using two dimensional (2D) semiconductors. They have attracted increasing attention due to their unique optical properties originate from neutral and charged excitons. Here, we report negatively charged exciton formation in monolayer TMDs, notably tungsten disulfide WS2. Our theory is based on an effective mass model of neutral and charged excitons, parameterized by ab-initio calculations. Taking into the account the strong correlation between the monolayer WS2 and the surrounding…
We report an out-of-plane magnetic field induced large photoluminescence enhancement in WS${}_2$ flakes at $4$ K, in contrast to the photoluminescence enhancement provided by in-plane field in general. Two mechanisms for the enhancement are proposed. One is a larger overlap of electron and hole caused by the magnetic field induced confinement. The other is that the energy difference between $Λ$ and K valleys is reduced by magnetic field, and thus enhancing the corresponding indirect-transition trions. Meanwhile, the Landé g factor of the trion is measured as $-0.8$, whose absolute value is muc…
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…
We report a photoluminescence (PL) and transient reflection spectroscopy study of exciton dynamics in monolayer transition transition-metal dichalcogenides (TMDs). PL saturation in monolayer MoSe2 occurs an excitation intensity more than two orders of magnitude lower than in monolayer MoS2. Transient reflection shows that the nonlinear exciton-exciton annihilation is the dominant exciton decay process in monolayer MoSe2 in contrast to the previously reported linear exciton decay in monolayer MoS2. In addition, the exciton lifetime in MoSe2, > 125 ps, is more than an order of magnitude longer t…
We investigate with polarized microphotoluminescence the optical pumping of the valley degree of freedom in charge-tunable MoS2 monolayers encapsulated with hexagonal boron nitride at cryogenic temperatures. We report a large steady state valley polarization of the different excitonic complexes following circularly-polarized laser excitation 25 meV above the neutral exciton transition. For the first time in this material we reveal efficient valley pumping of positively-charged trions, which were so far elusive in non-encapsulated monolayers due to defect and laser-induced large electron doping…
The spectral signatures associated with different negatively charged exciton complexes (trions) in a WS$_2$ monolayer encapsulated in hBN, are analyzed from low temperature and polarization resolved reflectance contrast (RC) and photoluminescence (PL) experiments, with an applied magnetic field. Based on results obtained from the RC experiment, we show that the valley Zeeman effect affects the optical response of both the singlet and the triplet trion species through the evolution of their energy and of their relative intensity, when applying an external magnetic field. Our analysis allows us …
A fully microscopic model of the doping-dependent exciton and trion line widths in the absorption spectra of monolayer transition metal dichalcogenides in the low temperature and low doping regime is explored. The approach is based on perturbation theory and avoids the use of phenomenological parameters. In the low-doping regime, we find that the trion line width is relatively insensitive to doping levels while the exciton line width increases monotonically with doping. On the other hand, we argue that the trion line width shows a somewhat stronger temperature dependence. The magnitudes of the…
The optical properties of semiconducting transition metal dichalcogenides are dominated by both neutral excitons (electron-hole pairs) and charged excitons (trions) that are stable even at room temperature. While trions directly influence charge transport properties in optoelectronic devices, excitons may be relevant through exciton-trion coupling and conversion phenomena. In this work, we reveal the coherent and incoherent nature of exciton-trion coupling and the relevant timescales in monolayer MoSe2 using optical two-dimensional coherent spectroscopy. Coherent interaction between excitons a…
