Fermi liquid theory sheds light on hot electron-hole liquid in $1L-\mathrm{Mo}{\mathrm{S}}_2$

Two-dimensional (2D) transition metal dichalcogenides (TMDCs) exhibit an electron-hole liquid (EHL) phase transition at unusually high temperatures. Because these materials are atomically thin, optical excitation leads to material expansion. As a result, during the EHL phase transition, the electronic band structure evolves due to both material thermal expansion and renormalization of the bands under high excitation densities. Specifically, these effects lead to indirect gap electronic band structure with a valence band maximum located at the $\mathrm{\Gamma }$ valley. In this paper, we developed a methodology for analyzing the spectral evolution of the photoluminescence of suspended $1\mathrm{L}\text{−}\mathrm{Mo}{\mathrm{S}}_2$ during the EHL phase transition by using Fermi liquid theory. The resulting analysis reveals a 23-fold increase in radiative recombination per carrier, as well as valley-specific carrier densities and intraband carrier relaxation kinetics in $1\mathrm{L}\text{−}\mathrm{Mo}{\mathrm{S}}_2$. More broadly, the results outline a methodology for predicting critical EHL parameters, shedding light onto the EHL phase transition in 2D TDMCs.

Figure 1

(a) Photoluminescence (PL) measurements showing excitonic to electron-hole liquid (EHL) transition in suspended $1\mathrm{L}\text{−}\mathrm{Mo}{\mathrm{S}}_2$ [10]. Increased fluence corresponds to increased strain and temperature, PL redshift, and peak intensity increase. (b) Calculated bandgap shifts due to sample strain (referenced to K-VB). Inset shows fit of strain vs temperature based on Raman spectroscopy measurements [10]. (c) Schematic of band structure evolution during lattice expansion. Dashed lines indicate quasi-Fermi levels for electrons-holes. Shaded area shows the bandgap before and after phase transition.

Figure 2

Distribution of carriers for holes (left) and electrons (right) referenced from $\mathrm{\Gamma }\text{−}VB$ and $K\text{−}CB$, respectively, shown with and without Lorentzian convolution. Red lines indicate quasi-Fermi levels after laser heating ($T \approx$ 600 K). Note: Bare densities of states (DOSs) for two-dimensional (2D) semiconductors are not energy dependent, so the unconvolved distribution of carriers for electrons-holes (dashed lines) have purely Fermi-Dirac lineshapes.

Figure 3

(a) Waterfall plot of model fits vs experimental spectra [10]. Fit shows good agreement with photoluminescence (PL) data beyond fluences of 2 kW ${\mathrm{cm}}^{-2}$. Fit of highest fluence spectra calculated with (b) no intraband transition effects included and (c) using distribution of carriers convolved with a Lorentzian to account for broadening due to intraband transitions.

Figure 4

(a) Hole charge carrier density per valley ($n_h$), (b) calculated temperature, and (c) photoluminescence (PL) intensity front factor plotted against continuous wave (CW) laser power density. Saturation occurs at roughly 3.5 kW ${\mathrm{cm}}^{-2}$, beyond which the system maintains a constant density electron-hole liquid (EHL) phase. Error bars indicate $2\sigma$ calculated via Monte Carlo error estimation techniques (see Supplemental Material [11].)