Optical spectra of two-dimensional transition-metal dichalcogenides (TMDC) are influenced by complex multi-particle excitonic states. Their theoretical analysis requires solving the many-body problem, which in most cases, is prohibitively complicated. In this work, we calculate the optical spectra by exact diagonalization of the three-particle Hamiltonian within the Tamm-Dancoff approximation where the doping effects are accounted for via the Pauli blocking mechanism, modelled by a discretized mesh in the momentum space. The single-particle basis is extracted from the {\it ab initio} calculations. Obtained three-particle eigenstates and the corresponding transition dipole matrix elements are used to calculate the linear absorption spectra as a function of the doping level. Results for negatively doped MoS$_2$ monolayer (ML) are in an excellent quantitative agreement with the available experimental data, validating our approach. The results predict additional spectral features due to the intervalley exciton that is optically dark in an undoped ML but is brightened by the doping. Our approach can be applied to a plethora of other atomically thin semiconductors, where the doping induced brightening of the many-particle states is also anticipated.
Single layers of MoS2 and MoSe2 were optically pumped with circularly polarized light and an appreciable polarization was initialized as the pump energy was varied. The circular polarization of the emitted photoluminescence was monitored as function of the difference between the excitation energy and the A-exciton emission at the K-point of the Brillouin zone. Our results show a threshold of twice the LA phonon energy, specific to the material, above which phonon-assisted intervalley scattering causes depolarization. In both materials this lead to almost complete depolarization within ~100 meV…
Interactions between two excitons can result in the formation of bound quasiparticles, known as biexcitons. Their properties are determined by the constituent excitons, with orbital and spin states resembling those of atoms. Monolayer transition metal dichalcogenides (TMDs) present a unique system where excitons acquire a new degree of freedom, the valley pseudospin, from which a novel intervalley biexciton can be created. These biexcitons comprise two excitons from different valleys, which are distinct from biexcitons in conventional semiconductors and have no direct analogue in atomic and mo…
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…
We investigate the in-plane spin relaxation of electrons due to the D'yakonov-Perel' and Elliot-Yafet mechanisms including the intra- and inter-valley processes in monolayer MoS$_2$. We construct the effective Hamiltonian for the conduction band using the Löwdin partition method from the anisotropic two-band Hamiltonian with the intrinsic spin-orbit coupling of the conduction band included. The spin-orbit coupling of the conduction band induces the intra- and inter-valley D'yakonov-Perel' spin relaxation. In addition, the Elliot-Yafet spin relaxation also takes place due to the interband spin …
Intrinsic electron spin relaxation due to the D'yakonov-Perel' mechanism is studied in monolayer Molybdenum Disulphide. An intervalley in-plane spin relaxation channel is revealed due to the opposite effective magnetic fields perpendicular to the monolayer Molybdenum Disulphide plane in the two valleys together with the intervalley electron-phonon scattering. The intervalley electron-phonon scattering is always in the weak scattering limit, which leads to a rapid decrease of the in-plane spin relaxation time with increasing temperature. A decrease of the in-plane spin relaxation time with the …
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…
It is known that carrier mobility in layered semiconductors generally increases from two-dimension (2D) to three-dimension due to suppressed scattering channels resulting from decreased densities of electron and phonon states. In this work, we find an abnormal decrease of electron mobility from monolayer to bulk MoS2. By carefully analyzing the scattering mechanisms, we can attribute such abnormality to the stronger intravalley scattering in the monolayer but weaker intervalley scattering caused by less intervalley scattering channels and weaker corresponding electron-phonon couplings compared…
Gated molybdenum disulphide (MoS2) exhibits a rich phase diagram upon increasing electron doping, including a superconducting phase, a polaronic reconstruction of the bandstructure, and structural transitions away from the 2H polytype. The average time between two charge-carrier scattering events - the scattering lifetime - is a key parameter to describe charge transport and obtain physical insight in the behavior of such a complex system. In this work, we combine the solution of the Boltzmann transport equation (based on ab-initio density functional theory calculations of the electronic bands…
Monolayer transition metal dichalcogenides (TMDs) have been in focus of current research, among others due to their remarkable exciton landscape consisting of bright and dark excitonic states. Although dark excitons are not directly visible in optical spectra, they have a large impact on exciton dynamics and hence their understanding is crucial for potential TMD-based applications. Here, we study brightening mechanisms of dark excitons via interaction with phonons and in-plane magnetic fields. We show clear signatures of momentum- and spin-dark excitons in WS$_2$, WSe$_2$ and MoS$_2$, while th…
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…
Exciton valley depolarization in monolayer MoS2: non-Markovian quantum dynamics, intervalley scattering, and the breakdown of the Dyakonov-Perel mechanism
Institute of Atomic and Molecular Sciences, Academia Sinica（中央研究院原子与分子科学研究所）；Department of Materials Science and Engineering, Stanford University（斯坦福大学材料科学与工程系）；Department of Physics, University of Texas at Austin（德克萨斯大学奥斯汀分校物理系）；Department of Materials Science, Yale University（耶鲁大学材料科学系）
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 …
Many-body interactions in monolayer transition-metal dichalcogenides are strongly affected by their unique band structure. We study these interactions by measuring the energy shift of neutral excitons (bound electron-hole pairs) in gated WSe$_2$ and MoSe$_2$. Surprisingly, while the blueshift of the neutral exciton, $X^0$, in electron-doped samples can be more than 10~meV, the blueshift in hole-doped samples is nearly absent. Taking into account dynamical screening and local-field effects, we present a transparent and analytical model that elucidates the crucial role played by intervalley plas…
We investigate the ground-state properties of monolayer MoS$_2$ incorporating the Coulomb interaction together with a short-range intervalley interaction between charged particles between two valleys within the Hartree-Fock approximation. We consider four variables as independent parameters, namely homogeneous charge (electron or hole) density, averaged dielectric constant, spin degree of freedom and finally the Hubbard repulsion coefficient which originates mostly from $4d$ orbits of Mo atoms. We find the electronic charge compressibility within the mean-field approximation and show that non-…
Valley pseudospin in two-dimensional (2D) transition-metal dichalcogenides (TMDs) allows optical control of spin-valley polarization and intervalley quantum coherence. Defect states in TMDs give rise to new exciton features and theoretically exhibit spin-valley polarization; however, experimental achievement of this phenomenon remains challenges. Here, we report unambiguous valley pseudospin of defect-bound localized excitons in CVD-grown monolayer MoS2; enhanced valley Zeeman splitting with an effective g-factor of -6.2 is observed. Our results reveal that all five d-orbitals and the increase…
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…
The recently-discovered monolayer transition metal dichalcogenides (TMDCs) provide a fertile playground to explore new coupled spin-valley physics. Although robust spin and valley degrees of freedom are inferred from polarized photoluminescence (PL) experiments, PL timescales are necessarily constrained by short-lived (3-100ps) electron-hole recombination. Direct probes of spin/valley polarization dynamics of resident carriers in electron (or hole) doped TMDCs, which may persist long after recombination ceases, are at an early stage. Here we directly measure the coupled spin-valley dynamics in…
The polarization analysis of optical transitions in monolayer and bilayer transition-metal dichalcogenides provides invaluable information on the spin and valley (pseudospin) degrees of freedom. To explain optical properties of a given monolayer transition-metal dichalcogenide, one should consider (i) the order of its spin-split conduction bands, (ii) whether intervalley scattering is prone to phonon bottleneck, (iii) and whether valley mixing by electron-hole exchange can take place. Using these principles, we present a consistent physical picture that elucidates a variety of features in the …
Atomically thin transition metal dichalcogenides (TMDs) are direct-gap semiconductors with strong light-matter and Coulomb interaction. The latter accounts for tightly bound excitons, which dominate the optical properties of these technologically promising materials. Besides the optically accessible bright excitons, these systems exhibit a variety of dark excitonic states. They are not visible in optical spectra, but can strongly influence the coherence lifetime and the linewidth of the emission from bright exciton states. In a recent study, an experimental evidence for the existence of such d…
We use density functional theory to explore the possibility of making the semiconducting transition-metal dichalcogenide MoS$_2$ ferromagnetic by introducing holes into the narrow Mo $d$ band that forms the top of the valence band. In the single impurity limit, the repulsive Coulomb potential of an acceptor atom and intervalley scattering lead to a twofold orbitally degenerate effective-mass like $e'$ state being formed from Mo $d_{x^2-y^2}$ and $d_{xy}$ states, bound to the K and K$'$ valence band maxima. It also leads to a singly degenerate $a'_1$ state with Mo $d_{3z^2-r^2}$ character bound…
Single layers of transition metal dichalcogenides are two-dimensional direct bandgap semiconductors with degenerate, but inequivalent, `valleys' in the electronic structure that can be selectively excited by polarized light. Coherent superpositions of light and matter, exciton-polaritons, have been observed when these materials are strongly coupled to photons, but these hybrid quasiparticles do not harness the valley-sensitive excitations of monolayer transition metal dichalcogenides. Here, we demonstrate evidence for valley polarized exciton-polaritons in monolayers of MoS$_2$ embedded in a d…
Several monolayer transition metal dichalcogenides (TMDs) are direct band gap semiconductors and potentially efficient emitters in light emitting devices. Photons are emitted when strongly bound excitons decay radiatively, and accurate models of such excitons are important for a full understanding of the emission. Importantly, photons are emitted in directions uniquely determined by the exciton center of mass momentum and with lifetimes determined by the exciton transition matrix element. The exciton band structures of two-dimensional hexagonal materials, including TMDs, are highly unusual wit…
