We present low temperature magneto-photoluminescence experiments which demonstrate the brightening of dark excitons by an in-plane magnetic field B applied to monolayers of different semiconducting transition metal dichalcogenides. For both WSe2 and WS2 monolayers, the dark exciton emission is observed at ∼50 meV below the bright exciton peak and displays a characteristic doublet structure which intensity is growing with B 2 , while no magnetic field induced emission peaks appear for MoSe2 monolayer. Our experiments also show that the MoS2 monolayer has a dark exciton ground state with a dark-bright exciton splitting energy of ∼100

Abstract:Recent results on the optical properties of monolayer and few layers of semiconducting transition metal dichalcogenides are reviewed. Experimental observations are presented and discussed in the frame of existing models, highlighting the limits of our understanding in this emerging field of research. We first introduce the representative band structure of these systems and their interband optical transitions. The effect of an external magnetic field is then considered to discuss Zeeman spectroscopy and optical pumping experiments, both revealing phenomena related to the valley degree of freedom. Finally, we discuss the observation of single photon emitters in different types of layered materials, including wide band gap hexagonal boron nitride. While going through these topics, we try to focus on open questions and on experimental observations, which do not yet have a clear explanation.

We present a comprehensive optical study of thin flakes of tungsten disulfide (WS) with thickness ranging from mono- to octalayer and in the bulk limit. It is shown that the optical band-gap absorption of monolayer WS is governed by competing resonances arising from one neutral and two distinct negatively charged excitons whose contributions to the overall absorption of light vary as a function of temperature and carrier concentration. The photoluminescence response of monolayer WS is found to be largely dominated by disorder/impurity- and/or phonon-assisted recombination processes. The indirect band-gap luminescence in multilayer WS turns out to be a phonon-mediated process whose energy evolution with the number of layers surprisingly follows a simple model of a two-dimensional confinement. The energy position of the direct band-gap response (A and B resonances) is only weakly dependent on the layer thickness, which underlines an approximate compensation of the effect of the reduction of the exciton binding energy by the shrinkage of the apparent band gap. The A-exciton absorption-type spectra in multilayer WS display a non-trivial fine structure which results from the specific hybridization of the electronic states in the vicinity of the K-point of the Brillouin zone. The effects of temperature on the absorption-like and photoluminescence spectra of various WS layers are also quantified.

We demonstrate that, in monolayers (MLs) of semiconducting transition metal dichalcogenides, the s-type Rydberg series of excitonic states follows a simple energy ladder: ǫn = −Ry * /(n + δ) 2 , n=1,2,. . . , in which Ry * is very close to the Rydberg energy scaled by the dielectric constant of the medium surrounding the ML and by the reduced effective electron-hole mass, whereas the ML polarizability is only accounted for by δ. This is justified by the analysis of experimental data on excitonic resonances, as extracted from magneto-optical measurements of a high-quality WSe2 ML encapsulated in hexagonal boron nitride (hBN), and well reproduced with an analytically solvable Schrödinger equation when approximating the electron-hole potential in the form of a modified Kratzer potential. Applying our convention to other, MoSe2, WS2, MoS2 MLs encapsulated in hBN, we estimate an apparent magnitude of δ for each of the studied structures. Intriguingly, δ is found to be close to zero for WSe2 as well as for MoS2 monolayers, what implies that the energy ladder of excitonic states in these two-dimensional structures resembles that of Rydberg states of a three-dimensional hydrogen atom.

We perform a theoretical study of radiative decay of dark intravalley excitons in transition metal dichalcogenide monolayers. This decay necessarily involves an electronic spin flip. The intrinsic decay mechanism due to interband spin-flip dipole moment perpendicular to the monolayer plane, gives a rate about 100-1000 times smaller than that of bright excitons. However, we find that this mechanism also introduces an energy splitting due to a local field effect, and the whole oscillator strength is contained in the higher-energy component, while the lowest-energy state remains dark and needs an extrinsic spin-flip mechanism for the decay. Rashba effect due to a perpendicular electric field or a dielectric substrate, gives a negligible radiative decay rate (about 10 7 times slower than that of bright excitons). Spin flip due to Zeeman effect in a sufficiently strong in-plane magnetic field can give a decay rate comparable to that due to the intrinsic interband spin-flip dipole.

Embedding a WS 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 monolayer, which involves two electrons with the same spin but from different valleys. Polarization-resolved experiments demonstrate that the helicity of the excitation light is better preserved in the emission spectrum of the triplet trion than in that of the singlet trion. Finally, the singlet (intravalley) trions are found to be observable even at ambient conditions whereas the emission due to the triplet (intervalley) trions is only efficient at low temperatures.

Ohmic contacts are crucial elements of electron optics that have not received a clear theoretical description yet. We propose a model of an Ohmic contact as a piece of metal of the finite capacitance C attached to a quantum Hall edge. It is shown that charged quantum Hall edge states may have weak coupling to neutral excitations in an Ohmic contact. Consequently, despite being a reservoir of neutral excitations, an Ohmic contact is not able to efficiently equilibrate edge states if its temperature is smaller thanh c , where c is the inverse RC time of the contact. This energy scale for a floating contact may become as large as the single-electron charging energy e 2 /C.

Monolayers of semiconducting transition metal dichalcogenides are two-dimensional direct-gap systems which host tightly-bound excitons with an internal degree of freedom corresponding to the valley of the constituting carriers. Strong spin-orbit interaction and the resulting ordering of the spin-split subbands in the valence and conduction bands makes the lowest-lying excitons in WX2 (X being S or Se) spin-forbidden and optically dark. With polarization-resolved photoluminescence experiments performed on a WSe2 monolayer encapsulated in a hexagonal boron nitride, we show how the intrinsic exchange interaction in combination with the applied in-plane and/or out-of-plane magnetic fields enables one to probe and manipulate the valley degree of freedom of the dark excitons.Monolayers of transition metal dichalcogenides (TMDs), such as MX 2 with M=Mo or W, and X=S, Se or Te, are two-dimensional direct-gap semiconductors 1 which attract a lot of interest due to their unique physical properties and potential applications in optoelectronics, photonics and the development of valleytronics 2-5,7,18 . The direct bandgap in semiconducting TMDs (S-TMDs) is located at the two inequivalent K ± points (valleys) of the first Brillouin zone, related by time reversal symmetry. In monolayers, the tightly bound and optically bright excitons 8-11 from K ± valley can efficiently couple to light with right/left circular polarization 12,13 , respectively.A unique feature of S-TMD monolayers is the so-called spin-valley locking 13 : strong spin-orbit interaction lifts the degeneracy between the two spin projections s =↑, ↓ in each valley, leaving only the Kramers degeneracy between the opposite valleys, K + , s ↔ K − , −s. While the valence band spin-orbit splitting ∆ v is very large (several hundred meV 13 ), its conduction band counterpart ∆ c is by an order of magnitude smaller 14-18 , thus allowing some degree of manipulation by an in-plane magnetic field. In tungsten-based S-TMDs, ∆ c has the same sign as ∆ v , leading to the spin subband ordering shown in Fig. 1(a). In each valley, the optically bright exciton has a higher energy than the dark exciton which is composed of the conduction and valence electronic states with opposite spin projections. This, among other things, results in a strong temperature dependence of the photoluminescence (PL) efficiency, as the bright states become more populated at higher temperatures 8,19,21 .Dark excitons can couple to light only via a residual spin-flip dipole matrix element d ⊥ , whose direction is perpendicular to the monolayer plane 22-24 . In consequence, the emission of dark excitons is directed predominantly along the monolayer plane, in contrast to the out-of-plane emission of bright excitons characterized by strong inplane optical dipoles, d , see Fig. 1(b). Notably, the valley degeneracy of dark excitons is lifted by the exchange interaction which mixes the valleys and produces two eigenstates with different energies. The higher energy component takes up the whole oscillator strength ...