Bistability of electron temperature in atomically thin semiconductors in the presence of exciton photogeneration

Abstract

We study the dynamic equilibrium between trions and excitons in monolayers of transition metal dichalcogenides in the presence of resident charge carriers and continuous photogeneration of excitons. We show that heating of the system via Drude absorption of low-frequency radiation leads to bistability of the steady-state equilibrium. The first is a low-temperature state, in which almost all resident charge carriers are bound into trions. The second state occurs at high temperatures, where most trions are dissociated; in this regime, the heating is more efficient due to the higher Drude conductivity of unbound charge carriers compared to trions. Switching between these two states occurs on a timescale of tens to hundreds of picoseconds and is accompanied by a jump in various observables such as temperature, current, and the intensity of exciton or trion luminescence.

Figures (4)

• Figure 1: Diagram of the processes described by Eq. \ref{['syst']}: (a) Impact trion dissociation with the rate $\beta n_T n_e$ caused by electrons with an energy on the order of $E_T$; (b) Radiative recombination of an exciton within a trion ($n_T/\tau_T$), during which an optical photon is emitted and the outor electron remains in the conduction band; (c) Exciton energy relaxation via electron capture from the conduction band, accompanied by optical phonon emission )$\gamma n_e n_X$); (d) Exciton photogeneration $G_X$ and radiative recombination ($n_X/\tau_X$), see text for details. (f) The dependence of the density of unbound electrons $n_e$ and trion density $n_T$ on the temperature of the electron gas. The solid lines correspond to the solution of Eq. \ref{['qudeq']}, while the dashed lines correspond to the Saha equation Eq. \ref{['eq:Saha']}. Inset shows dependence of ratio $n_T/n_e$ on the temperature of the electron gas. The parameters of calculation are $G_X = 4.5\cdot 10^{10}$ cm$^{-2}$ps$^{-1}$, $\gamma = 0.1$ cm$^{2}$s$^{-1}$, $n_c = 10^{12}$ cm$^{-2}$, $\tau_X = \tau_T = 50$ ps, $\beta = w_0\frac{k_BT}{E_T}e^{-\frac{E_T}{k_BT}}$, with $w_0 = 1.16\cdot10^3$ cm$^{2}$s$^{-1}$, $E_T = 25~\text{meV}$venanzi2024ultrafastshentsev2025terahertzayari2020phonon.
• Figure 2: (a) Dependence of electron gas temperature on the heating intensity $I$. (b) Dependence of electric current density $j$ on the applied electromagnetic field strength $E$ in the sample. Arrows indicate the direction of traversal on the hysteresis loop. The parameters of calculation are $\tau_{e,tr} = 2~$ps, $\tau_{e,LA} = 30~$ps, $r_D = 0$, $r_{LA} = 10$, $D_e^{(0)} = D_h^{(0)} = D_T^{(0)} = 5.2\cdot 10^8~$eV$\cdot$cm$^{-1}$, $D_X^{(0)} = 0$, $\rho = 4.46\cdot10^{-7}~$g$\cdot$cm$^{-2}$, $E_T = 25~$meV, $\hbar\omega_O = 30.3~$ meV ayari2020phonon, other parameters are the same as ones used for the calculations for Fig. \ref{['fig1']}.
• Figure 3: (a) Bifurcation region in the ($G_X$,$I$) diagram for different values of $r_{LA}$, with $r_D = 0$ and $n_c = 10^{12}$ cm$^{-2}$. (b) Same for different values $r_D$, with $r_{LA} = 10$ and $n_c = 5\cdot 10^{11}$ cm$^{-2}$, (c) Same for different values $n_c$, with $r_D = 0.15$ and $r_{LA} = 10$. (d) Temporal evolution of temperature, corresponding to the right vertical line in Fig. \ref{['fig2']}, with an initial deviation from equilibrium of 0.1 K. The characteristic switching time is $\tau_s \sim 10...100$ ps.
• Figure 4: (a) Dependence of the thermal process power (a.u.) on electron gas temperature (K). Black arrows illustrate the temperature ranges where bistability exists. Green dashed lines correspond to switching between branches at the boundaries of the hysteresis loop, as indicated by the green vertical lines in Fig. \ref{['fig2']}. (b) Temporal evolution of temperature corresponding to the left green dotted arrow from (a), namely, to the switching process with decreasing temperature. The characteristic switching time is $\tau_s \lesssim 100$ ps. (c) Temporal evolution of temperature corresponding to the right green dotted arrow from (a), i.e., to the switching process with increasing temperature. The characteristic switching time is $\tau_s \sim 10$ ps, which is considerably shorter than that in (b). The parameters of calculation are $n_c = 2\cdot 10^{11}$ cm$^{-2}$, $G_X = 5\cdot 10^{10}$ cm$^{-2}$ps$^{-1}$ cm$^{-2}$, $r_{LA} = 10$, $r_D = 0$, initial deviation of temperature from equilibrium for (b,c) is $\Delta T \lesssim 1$ К, $D_X^{(0)} = 5.2\cdot 10^7~$eV$\cdot$cm$^{-1}$, other parameters are the same as ones used for the calculations for Fig. \ref{['fig1']} and Fig. \ref{['fig2']}.