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 experimental estimates for the exciton radii that fall in the $7-10Å$ range and agree well with theory. The measured trion optical absorption spectra are used to obtain values for the trion radii that also agree well with theory. The measured values of the exciton and trion radii correspond to binding energies that are in good agreement with values obtained from first principles calculations.
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 …
The effect of doping on the parameters of an electron-hole liquid (EHL) in heterostructures based on transition metal dichalcogenides is studied. The phase diagram of the EHL is constructed. It is shown that for the formation of a high-temperature tightly bound EHL, as well as for the transition from the semiconducting (exciton) state to the semimetallic one (electron-hole plasma/liquid), it is advantageous to dope the energy band with larger number of valleys. The transition from trion gas to electron-hole plasma is investigated using the modified Mott criterion and variational calculation wi…
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 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 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…
The influence of a perpendicular magnetic field on the binding energy and structural properties of excitons, trions, and biexcitons in monolayers of semiconducting transition metal dichalcogenides (TMDs) is investigated. The stochastic variational method (SVM) with a correlated Gaussian basis is used to calculate the different properties of these few-particle systems. In addition, we present a simplified variational approach which supports the SVM results for excitons as a function of magnetic field. The exciton diamagnetic shift is compared with recent experimental results and we extend this …
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…
Excitons, trions, biexcitons, and exciton-trion complexes in two-dimensional transition metal dichalcogenide sheets of MoS$_2$, MoSe$_2$, MoTe$_2$, WS$_2$ and WSe$_2$ are studied by means of density functional theory and path integral Monte Carlo method in order to accurately account for the particle-particle correlations. In addition, the effect of dielectric environment on the properties of these exciton complexes is studied by modifying the effective interaction potential between particles. Calculated exciton and trion binding energies are consistent with previous experimental and computati…
We examine the excitonic properties of layered configurations of low dimensional transition metal dichalcogenides (LTMDCs) using the fractional dimensional space approach. The binding energies of the exciton, trion and biexciton in LTMDCs of varying layers are analyzed, and linked to the dimensionality parameter $α$, which provides insight into critical electro-optical properties (relative oscillator strength, absorption spectrum, exciton-exciton interaction) of the material systems. The usefulness of $α$ is highlighted by its independence of the physical mechanisms underlying the confinement …
Photoluminescence spectra, shows that monolayer Transition-metal dichalcogenides (MLTMDCs), possess charged exciton binding energies, conspicuously similar to the energy of optical phonons. This enigmatic coincidence has offered opportunities to investigate many-body interactions between trion, exciton and phonon and led to efficient excitonic anti-Stokes processes with the potential for laser refrigeration and energy harvesting. In this study, we show that in WSe2 materials, the trion binding energy matches two phonon modes, the outofplane HP and the in-plane LO mode. In this respect, using t…
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…
We present a comprehensive theoretical analysis of composite excitonic states in doped transition-metal dichalcogenide monolayers. Making use of the pair distribution function, we introduce a method to include the effect of screening in the interaction between the excitonic state and Fermi-sea electrons. Employing the screened potential, we study tetrons and pexcitons in which a trion is bound to one and two holes in the conduction band, respectively. A conduction-band hole denotes the lack of electrons with certain quantum numbers at the vicinity of the trion. We then analyze the hexciton com…
The electronic and structural properties of excitons and trions in monolayer transition metal dichalcogenides are investigated using both a multiband and a single-band model. In the multiband model we construct the excitonic Hamiltonian in the product base of the single-particle states at the conduction and valence band edges. We decouple the corresponding energy eigenvalue equation and solve the resulting differential equation self-consistently, using the finite element method (FEM), to determine the energy eigenvalues and the wave functions. As a comparison, we also consider the simple singl…
Efficient calculation of trion energies in monolayer transition metal dichalcogenides
Monash University（莫纳什大学）；ARC Centre of Excellence in Future Low-Energy Electronics Technologies, Monash University（莫纳什大学未来低能耗电子技术卓越中心）；Universidad Autónoma de Madrid（马德里自治大学）；Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid（马德里自治大学凝聚态物理中心（IFIMAC））
Trion states of three correlated particles (e.g., two electrons and one hole) are essential to understand the optical spectra of doped or gated nanostructures, like carbon nanotubes or transition-metal dichalcogenides. We develop a theoretical many-body description for such correlated states using an ab-initio approach. It can be regarded as an extension of the widely used $GW$ method and Bethe-Salpeter equation, thus allowing for a direct comparison with excitons. We apply this method to a semiconducting (8,0) carbon nanotube, and find that the lowest optically active trions are red-shifted b…
The band structure of many semiconducting monolayer transition metal dichalcogenides (TMDs) possesses two degenerate valleys, with equal and opposite Berry curvature. It has been predicted that, when illuminated with circularly polarized light, interband transitions generate an unbalanced non-equilibrium population of electrons and holes in these valleys, resulting in a finite Hall voltage at zero magnetic field when a current flows through the system. This is the so-called valley Hall effect that has recently been observed experimentally. Here, we show that this effect is mediated by photo-ge…
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…
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…
ARPES signatures of trions in van der Waals materials
Philipps-Universität Marburg（马尔堡菲利普斯大学）；mar.quest | Marburg Center for Quantum Materials and Sustainable Technologies（mar.quest | 马尔堡量子材料与可持续技术中心）；Stockholm University（斯德哥尔摩大学）；Georg-August-Universität Göttingen（格奥尔格·奥古斯特哥廷根大学）
Highly nonlinear Moiré exciton and trion polaritons
Laboratory for Physical Sciences, University of Maryland（马里兰大学物理科学实验室）；University of Rochester（罗切斯特大学）；University of Notre Dame（圣母大学）；The Institute of Optics, University of Rochester（罗切斯特大学光学研究所）
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…
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…
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…
The anisotropic nature of the new two-dimensional (2D) material phosphorene, in contrast to other 2D materials such as graphene and transition metal dichalcogenide (TMD) semiconductors, allows excitons to be confined in a quasi-one-dimensional (1D) space predicted in theory, leading to remarkable phenomena arising from the reduced dimensionality and screening. Here, we report a trion (charged exciton) binding energy of 190 meV in few-layer phosphorene at room temperature, which is nearly one to two orders of magnitude larger than those in 2D TMD semiconductors (20-30 meV) and quasi-2D quantum …
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…
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…
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…
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…
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…
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…
Transition metal dichalcogenides (TMDs) are known to support complex excitonic states. Revealing the differences in relaxation dynamics among different excitonic species and elucidating the transition dynamics between them may provide important guidelines for designing TMD-based excitonic devices. Combining photoluminescence (PL) and reflectance contrast measurements with ultrafast pump-probe spectroscopy under cryogenic temperatures, we herein study the relaxation dynamics of neutral and charged excitons in a back-gate-controlled monolayer device. Pump-probe results reveal quite different rel…
We develop a theoretical description of Coulomb interactions between trions (charged excitons) that define a nonlinear optical response in doped two-dimensional semiconductors. First, we formulate a microscopic theory of trion-trion interactions based on composite nature of these particles, and account for all possible exchange processes. Next, we calculate numerically the trion binding energies and corresponding three-body wavefunctions using a basis set with high expressivity. Then, using the obtained wavefunctions we calculate the matrix elements of two-trion scattering, and compare the con…
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…
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…
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 analyze the lineshape of the quasiparticle photoluminescence of monolayer and bilayer molybdenum ditelluride in temperature- and excitation intensity-dependent experiments. We confirm the existence of a negatively charged trion in the bilayer based on its emission characteristics and find hints for a coexistence of intra- and interlayer trions with a few meV splitting in energy. From the lineshape analysis of exciton and trion emission we extract values for exciton and trion deformation potentials as well as acoustical and optical phonon-limited mobilities in MoTe2, with the mobilities show…
Excitonic effects play a particularly important role in the optoelectronic behavior of two-dimensional semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide (i) statistically exact diffusion quantum Monte Carlo binding-energy data for a Mott-Wannier model of (donor/acceptor-bound) excitons, trions, and biexcitons in two-dimensional semiconductors in which charges interact via the Keldysh potential, (ii) contact pair-distribution functions to allow a perturbative description of contact interactions between charge carriers, and …
Strong Coulomb interaction in atomically-thin transition metal dichalcogenides makes these systems particularly promising for studies of excitonic physics. Of special interest are the manifestations of the charged excitons, also known as trions, in the optical properties of two-dimensional semiconductors. In order to describe the optical response of such a system, the exciton interaction with resident electrons should be explicitly taken into account. In this paper we demonstrate that this can be done both in the trion (essentially, few-particle) and Fermi-polaron (many-body) approaches, which…
Recent experimental progresses have demonstrated the great potential of electronic and excitonic moiré superlattices in transition metal dichalcogenides (TMDs) for quantum many-body simulations and quantum optics applications. Here we reveal that the moiré potential landscapes in the TMDs heterostructures have an electrostatic origin from the spontaneous charge transfer across the heterointerfaces dependent on the atomic registry. This allows engineering tunable multi-chromatic superlattices through the interference of moiré potentials from independently configurable heterointerfaces in multil…
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…
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 …
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…
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…
