Brightening of a dark monolayer semiconductor via strong light-matter coupling in a cavity

Engineering the properties of quantum materials via strong light-matter coupling is a compelling research direction with a multiplicity of modern applications. Those range from modifying charge transport in organic molecules, steering particle correlation and interactions, and even controlling chemical reactions. Here, we study the modification of the material properties via strong coupling and demonstrate an effective inversion of the excitonic band-ordering in a monolayer of WSe2 with spin-forbidden, optically dark ground state. In our experiments, we harness the strong light-matter coupling between cavity photon and the high energy, spin-allowed bright exciton, and thus creating two bright polaritonic modes in the optical bandgap with the lower polariton mode pushed below the WSe2 dark state. We demonstrate that in this regime the commonly observed luminescence quenching stemming from the fast relaxation to the dark ground state is prevented, which results in the brightening of this intrinsically dark material. We probe this effective brightening by temperature-dependent photoluminescence, and we find an excellent agreement with a theoretical model accounting for the inversion of the band ordering and phonon-assisted polariton relaxation.

where P ef f defines the effective incoherent pumping of the bright excitons. We assume that as pumped incoherently, the excitons thermalize very quickly, and only the excitons lying within the light cone contribute to the PL signal.
For not very low temperature, the effective pumping P ef f is This approximation holds for T ≫ 0.6K. Scattering rates W correspond to the inelastic phonon-assisted process. Since dark excitonic states lie below the bright ones, the bright to dark exciton scattering occurs with the emission of a phonon, and a reverse process with an absorption of the phonon. Assuming the system is at thermal equilibrium at temperature T, the scattering rates can be expressed as: where ∆ BD is the bright-dark exciton splitting which is equal to the spin splitting in the conduction band and is equal to approximately 40 meV [S1, S2], and W 0 is the bare exciton-phonon scattering rate which is a fitting parameter. The radiative exciton lifetime of the excitons within the light cone is set to 4 ps which corresponds to previously reported theoretical and experimental values [S3, S4] and the non-radiative lifetime which is typically related to the defect trapping is set to τ N R = 5 ps [S5]. By fitting the experimental temperature dependence we obtain the value of W 0 ≈ 10 ps −1 .

Supplementary section 2:
Model of ground state brightening via strong light-matter coupling We consider a simplified picture, where there is a single exciton state, and two cavity modes, corresponding to the ground and excited exciton modes in the trap ( Supplementary Fig. S1). We can write down the coherent part of the Hamiltonian in the matrix form where b, a 1 , a 2 are the annihilation operators for the exciton and two cavity modes. The frequencies ω x , ω c1 , ω c2 can be extracted from the experimental data, and g 1 , g 2 are the fitting parameters in our model. This Hamiltonian can be diagonalized yielding lower, middle and upper polariton modes a L , a M , a U . Moreover, we obtain the polariton energies ǫ L , ǫ M , ǫ U and exciton fraction in each of the polaritonic modes (Hopfield coefficients): X U , X M , X L . The rate of the phonon assisted scattering between the polaritons and the spin-dark excitons D is proportional to the exciton fraction in the respective polariton, and the occupation number of the phonons at the energy corresponding to the energy difference between the dark exciton and respective polariton. If the scattering occurs with the emission of phonon, the rate is proportional to n ph + 1 and if the scattering is with the absorption of phonon, then the rate is proportional to n ph . The phonon scattering rates thus are: , (Eq. S10) , (Eq. S12) where W 0 is the bare rate of exciton-phonon scattering obtained via fitting of the bare exciton PL signal. We also need to account for the fact that at nonresonant pumping only the excitons with the wavevectors inside the light cone form the polaritons. The system of equation then readṡ , and τ D is the dark exciton lifetime which is set equal to the non-radiative exciton lifetime. The values of g 1 = 0.02 eV and g 2 = 0.016 eV are extracted from fitting the experimental temperature dependence of the polariton PL signal. Moreover, in fitting we accounted for the temperature dependence of the bare exciton energy ω x ≈ 1.73 − 0.06(T /300) eV. Air pressure can affect the energy of microcavity photons and LP. Supplementary Fig. S2a shows the polariton dispersion at ambient conditions (room temperature, standard pressure), which is reproduced from Fig. 2a in the main text. The cavity mode is at 1.614 eV, and the energy of ground state is 1.610 eV.
Weak emission detected above 1.66 eV is collected from areas without the monolayer-hBN stack, i.e. the barrier of the polariton trap (the collection area of PL is tens of microns). Since the optical length of the cavity is significantly reduced at those positions, it occurs at strongly elevated energy. In the barrier, there is no active material which can directly generate luminescence, however light, which is generated by the polaritons in the trap or which is generated by weakly coupled excitons on the lateral interface between trap and barrier, can scatter into these modes.
Before performing temperature-dependent measurements, the cryostat is pumped several hours to get a high vacuum. Supplementary Fig. S2b shows the dispersion relation after vacuum pump (room temperature, pressure of 3E-5 hPa). We observe an energy shift of LP, which originates from the alteration of cavity mode. The cavity photon energy is changed to 1.630 eV and the resulted LP is at 1.624 eV. This energy shift is reversible: the dispersion relation gets back after measurements, when the air pressure is recovered. . The exciton fraction of LP is 20.5% at 294 K, and it decreases to 6.4% as the temperature is 10 K.  Fig. 3a in the main text. The white box represents the integration region that ranges from 1.52 to 1.74 eV (including all emission features). b Temperature dependent emission intensity of pristine WSe 2 monolayer, with the integration region shown in a. c The integration region ranges from 1.623 to 1.636 eV, corresponding to energies of ground state and first excited state of polaritons. d Temperature dependent emission intensity of pristine WSe 2 monolayer, with the integration region shown in c.