Theory of coherent pump–probe spectroscopy in monolayer transition metal dichalcogenides

Abstract

A valley-selective circular dichroism and a pronounced spin-valley locking in monolayer transition metal dichalcogenides (TMDCs) enable the investigation of new many-body physics revealed in the ultrafast nonlinear optical response of these atomically thin materials. While this topic is experimentally well studied in pump-probe spectroscopy, only a fragmented theoretical understanding is available due to the complexity and multitude of occurring effects. Here, a microscopic approach is presented to describe the ultrafast pump-probe response of monolayer TMDCs in the coherent limit. We focus on close to band edge excitations dominated by strongly correlated, bound electron-hole pairs, namely excitonic excitations. The approach includes Hartree-Fock and correlation effects up to two excitonic excitations known from conventional semiconductors as well as TMDC typical Coulomb mechanisms such as intra-and intervalley excitation and charge transfer. The investigated coherent limit is able to explain different signatures observed in ultrafast pump-probe spectroscopy for temporal pump-probe overlap within one consistent formalism dominated by excitons, biexcitons, and exciton-exciton scattering states.

The ultrafast onset of exciton formation in 2D semiconductors

“…These resonances correspond to the lowest-energy (or ground state) excitons in the A and B manifolds (i.e., the A 1 s and B 1 s states, respectively), possess the largest oscillator strengths, and dominate the optical response over the corresponding higher-energy unbound states. Based on previous experimental studies 3 , 29 and refined theoretical models 18 , we estimate that the exciton binding energy (i.e., the energetic difference between the 1s exciton and the lowest energy state in the exciton continuum) is of the order of 350 meV. In our measurements the pump photon energies span from 2.29 eV to 2.75 eV (with bandwidths spanning from 70 meV to 140 meV) and thus, at all energies, photoexcitation predominantly creates an initial population of excitons at or well-into the exciton continuum for the A excitons (as well as for the B excitons at energies above ~2.4 eV).…”

“…The terms proportional to Γ λ +1→ λ characterize the phonon-mediated relaxation from energetically higher densities with effective rates adapted to density functional theory calculations 48 , 49 . The solution of the Schrdinger equation for two electrons and two holes accesses biexcitons as well as exciton–exciton scattering continua 18 , 50 , 51 . The Heisenberg equation of motion for bound biexcitons as well as continuous exciton–exciton scattering states B η characterize damped ( ) oscillations (energy ϵ xx, η ), which are driven by two excitons mediated by Coulomb interactions ( ): …”

“…The dynamical response of TMDs and, in general, all semiconductors can be divided into coherent and incoherent regimes 14 , 15 . While the incoherent exciton dynamics of TMDs, including processes, such as exciton thermalization 16 , radiative/non radiative recombination 17 , intra and intervalley scattering 18 – 22 , exciton dissociation 23 , and exciton–exciton annihilation 24 , have been extensively studied, the coherent exciton response and the corresponding early stage dynamics of the exciton formation process are still almost unexplored largely because the limited available temporal resolution (i.e., >100 fs for pump-probe optical spectroscopy and >1 ps for time-resolved photoluminescence) has prevented the study of the primary early stage dynamics of exciton photo-generation processes 17 , 25 , 26 .…”

Local field effects in ultrafast light–matter interaction measured by pump-probe spectroscopy of monolayer MoSe2

“…These findings of the influence of local field and EID depending on the excitation density are in agreement with Refs. [25,32].…”

“…A more detailed discussion of possible values for V and W is given in Ref. [13], where a connection to the parameters retrieved from microscopically derived models [25,32] is given.…”