Terahertz radiation induced attractive-repulsive Fermi polaron conversion in transition metal dichalcogenide monolayers

Abstract

We present a theoretical study of terahertz radiation-induced transitions between attractive and repulsive Fermi polaron states in monolayers of transition metal dichalcogenides. Going beyond the simple few-particle trion picture, we develop a many-body description that explicitly accounts for correlations with the Fermi sea of resident charge carriers. We calculate the rate of the direct optical conversion process which has a threshold where the terahertz photon energy equals to the Fermi polaron binding energy. This process features a characteristic frequency dependence near the threshold, due to final-state electron-exciton scattering related to the trion correlation with the Fermi sea hole. Furthermore, we demonstrate that intense terahertz pulses can significantly heat the electron gas via Drude absorption enabling an additional, indirect conversion mechanism through collisions between hot electrons and polarons, which exhibits a strong exponential dependence on the electron temperature. Our results reveal the important role of many-body correlations and thermal effects in the terahertz-driven dynamics of excitonic complexes in two-dimensional semiconductors.

Figures (5)

• Figure 1: Sketch of studied processes. (a) Transition between attractive and repulsive Fermi polarity due to absorption of THz radiation (Sec. \ref{['sec:ETconv']}). (b) Decay of the attractive Fermi polaron state due to interaction with a "hot" electron (Sec. \ref{['sec:HEG']}).
• Figure 2: (a) Dependence of the transition rate $W_{\rm dir}(\omega)$ on the frequency of terahertz radiation at different Fermi energies calculated disregarding the broadening. Inset shows asymptotic of $W_{\rm dir}(\omega)$ near the threshold $\hbar\omega - |E_{FP}| \ll E_F \propto (\hbar\omega - |E_{FP}|)^{3/2}$. (b) Solid lines show the transition rate $W_{\rm dir}(\omega)$ at $E_F = 0.1 E_T$, for different spectral broadening $\Gamma$. The parameters of calculation venanzi2024ultrafastnaftaly2011hexagonal: $E_T = 25$ meV, $I = 1.25$$\mu$J/(cm$^2$ps), $M_e = 0.5~M_0$, $M_x = 1.1~ M_0$, where $M_0$ is free electron mass. The dashed curve is calculated in the trion approach of venanzi2024ultrafast, with the exciton radius $a = 1$ nm and the trion radius $b = 3$ nm, the dotted curve is the same model with $a = 0.6$ nm, $b = 1.1$ nm.
• Figure 3: (a) Dependence the electron gas temperature $T$ right after THz irradiation pulse calculated from Eq. \ref{['heat:balance']} for different scattering time by static impurities $\tau$ as a function of the THz frequency. Inset shows dependence the electron gas temperature $T$ on the THz pulse fluence $\phi$ with $\tau = 2$ ps and $\hbar\omega = 0.5 E_T$. (b) Time dependence of the electron gas temperature calculated from Eq. \ref{['heat:balance']} for $\tau=2$ ps. Inset shows the conversion rate for the indirect process as a function of time, see text for details. Shaded area shows the duration of the THz pulse. The parameters of calculation: lattice temperature $T_l = 5$ K, pulse duration $\tau_{\rm THz} = 4$ ps, $E_F = 0.1E_T$, $\phi = I\tau_{\rm THz} = 5$$\mu$J/cm$^2$, $D_0 = 5.2\cdot 10^8$ eV/cm, $\Xi = 3.4$ eV, $\rho = 4.46\cdot 10^{-7}$ g/cm$^2$, $s = 4.1\cdot 10^5$ cm/s, $\tau_{LA} = 30$ ps, other parameters are the same as ones used for the calculations for Fig. \ref{['fig1']}. Here we approximate the electron gas heat capacity as $C(T) \approx C_F^{2D}(T)$ for $k_BT < 3E_F/\pi^2$ and $C(T) \approx C^{2D}_B$ for $T>3E_F/\pi^2$.
• Figure 4: (a) Dependence of collision-induced transition rate $W_{\rm indir}$, Eq. \ref{['W:ub']}, on the electron gas temperature. Blue dots correspond to the transition rate for a trion with $\bm K = 0$, green dots correspond the same temperatures of electrons and trions. Solid lines are plotted after the approximate Eq. \ref{['W:ub:approx']} with electron density $n_e = 5.8\times10^{11}$ cm$^{-2}$ ($E_F = 0.1E_T$) and prefactors $w_0 = 1.16\times 10^3$ cm$^{2}$s$^{-1}$ and $0.76\times 10^3$ cm$^{2}$s$^{-1}$ found from the best fit of the numerical calculation. (b) Dependence of effective probability $P$\ref{['P']} on the THz radiation frequency, with fluence $\phi = 5$$\mu$J/cm$^{2}$ and $\tau_{\rm THZ} = 4$ ps. The dependence of electron temperature $T(\omega)$ for $P_{indir}(T)$ corresponds to Fig. \ref{['fig2']} with $\tau = 2$ ps.
• Figure 5: (a) The diagrammatic series defining the $T$ matrix in the Fermi polaron approach cotlect2019transportkadanoff2018quantumPhysRevB.105.075311. The lower line $X$ on Fig. \ref{['fig4']} denotes the bare Green's function $G^0_X$ of the exciton, the upper $e$ is the bare Green's function of the electron $G^0_e$. The dotted line is the electron-exciton interaction $V$. The insert is the self-energy part $\Sigma_0$ defining the energy of the Fermi polaron. (b) $\Sigma_1$ is the contribution in self-energy determining the asymptotics of absorption spectra at $\hbar\omega - |E_{FP}| \gg E_F$, which does not take into account the Fermi-polar corrections in the matrix element Eq. \ref{['M:TX']}. The wavy line represents the interaction of the electron with the classical field \ref{['Hle']}. (c) $\Sigma_2$ is the Fermi-polaron correction to $\Sigma_1$.