Exciton-phonon relaxation bottleneck and radiative decay of thermal exciton reservoir in two-dimensional materials

We study exciton radiative decay in a two-dimensional material, taking into account large thermal population in the non-radiative states, from which excitons are scattered into the radiative states by acoustic phonons. We find an analytical solution of the kinetic equation for the non-equilibrium distribution function of excitons in the radiative states. Our estimates for bright excitons in transition metal dichalcogenides indicate a strong depletion of radiative state population due to insufficient exciton-phonon scattering rate at low temperatures.Comment: 8 pages, 4 figure

Fine structure of K\mathrm{K}-excitons in multilayers of transition metal dichalcogenides

Reflectance and magneto-reflectance experiments together with theoretical modelling based on the $\mathbf{k\cdot p}$ approach have been employed to study the evolution of direct bandgap excitons in MoS$_2$ layers with a thickness ranging from mono- to trilayer. The extra excitonic resonances observed in MoS$_2$ multilayers emerge as a result of the hybridization of Bloch states of each sub-layer due to the interlayer coupling. The properties of such excitons in bi- and trilayers are classified by the symmetry of corresponding crystals. The inter- and intralayer character of the reported excitonic resonances is fingerprinted with the magneto-optical measurements: the excitonic $g$-factors of opposite sign and of different amplitude are revealed for these two types of resonances. The parameters describing the strength of the spin-orbit interaction are estimated for bi- and trilayer MoS$_2$.Comment: 14 pages, 10 figure

Semiconductor Bloch equation analysis of optical Stark and Bloch-Siegert shifts in monolayers WSe2_2 and MoS2_2

We report on the theoretical and experimental investigation of valley-selective optical Stark and Bloch-Siegert shifts of exciton resonances in monolayers WSe$_2$ and MoS$_2$ induced by strong circularly polarized nonresonant optical fields. We predict and observe transient shifts of both 1sA and 1sB exciton transitions in the linear interaction regime. The theoretical description is based on semiconductor Bloch equations. The solutions of the equations are obtained with a modified perturbation technique, which takes into account many-body Coulomb interaction effects. These solutions allow to explain the polarization dependence of the shifts and calculate their values analytically. We found experimentally the limits of the applicability of the theoretical description by observing the transient exciton spectra change due to many-body effects at high field amplitudes of the driving wave.Comment: 20 pages, 9 figures, this manuscript is related to the "Giant valley-selective Stark and Bloch-Siegert shifts of exciton resonances in WSe$_2$ and MoS$_2$ monolayers" manuscrip

Giant valley-selective Stark and Bloch-Siegert shifts of exciton resonances in WSe2_2 and MoS2_2 monolayers

In this letter we demonstrate that the valley degeneracy of exciton states in monolayers of WSe$_2$ and MoS$_2$ can be lifted by the interaction with strong circularly-polarized infrared pulses with durations of only few periods of the electric field whose photon energy is much lower than the energy of the excitonic transition. The observed valley-sensitive blue shifts of excitonic absorption lines are consequences of optical Stark and Bloch-Siegert shifts acting exclusively on the opposite valleys of the monolayer. We measured the transient valley-selective changes of sample reflectivity for 1sA as well as for 1sB exciton transitions corresponding to the two most intensive resonances in the studied materials. For the studied phenomena we developed a theoretical description based on semiconductor Bloch equations, which goes beyond the simple two-level model used in previous investigations. The theoretical approach takes into account Coulomb many-body effects in the monolayer and provides a unified description of both types of shifts. The detected room-temperature excitonic energy shifts of up to 30\,meV pave the way for practical applications of these effects.Comment: 6 pages, 3 figures, the manuscript is related to the "Semiconductor Bloch equation analysis of optical Stark and Bloch-Siegert shifts in monolayers WSe$_2$ and MoS$_2$" manuscrip

Neutral and charged dark excitons in monolayer WS2_2

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 and parallel configurations with respect to the monolayer plane, we determine the g-factor of dark trions to be $g\sim$-8.6. Their decay rate is close to 0.5 ns, more than 2 orders of magnitude longer than that of bright excitons.Comment: 6 pages, 6 figures, supplemental materia