Exciton Mott Transition in Si Revealed by Terahertz Spectroscopy

We investigate the exciton Mott transition in Si by using optical pump and terahertz probe spectroscopy. The density-dependent exciton ionization ratio $\alpha$ is quantitatively evaluated from the analysis of dielectric function and conductivity spectra. The Mott density is clearly determined by the rapid increase in $\alpha$ as a function of electron-hole ($e\mathrm{\text{−}}h$) pair density, which agrees well with the value expected from the random phase approximation theory. However, exciton is sustained in the high-density metallic region above the Mott density as manifested by the $1s\mathrm{\text{−}}2p$ excitonic resonance that remains intact across the Mott density. Moreover, the charge carrier scattering rate is strongly enhanced slightly above the Mott density due to nonvanishing excitons, indicating the emergence of highly correlated metallic phase in the photoexcited $e\mathrm{\text{−}}h$ system. Concomitantly, the loss function spectra exhibit the signature of plasmon-exciton coupling, i.e., the existence of a new collective mode of charge density excitation combined with the excitonic polarization at the proximity of Mott density.

Figure 1

(a) Schematics of the optical-pump and THz-probe experiment and the band structure of Si. (b) Photoinduced change of dielectric function and (c) optical conductivity at the indicated $e\mathrm{\text{−}}h$ pair density expressed in terms of the $r_s$ parameter (mean interparticles distance normalized by the exciton Bohr radius). The sample temperature is kept at 30 K, and the pump-probe delay time $\Delta t$ is fixed to 4 ns. Solid lines represent Drude-Lorentz fits (see text for details).

Figure 2

(a)–(c) Parameters determined from the Drude-Lorentz fits in Figs. 1b, 1c. (a) Plasma frequency (closed triangles) and exciton $1s\mathrm{\text{−}}2p$ transition energy (open triangles); (b) density of unbound $e\mathrm{\text{−}}h$ pairs (closed diamonds), $1s$ exciton (open diamonds), and ionization ratio (closed circles); (c) damping of the Drude term (closed squares) and the Lorentz term (open squares). The vertical dotted line represents the RPA Mott density ($r_s=3.0$) at 30 K. (d) The loss function spectra at $T_L=30\mathrm{K}$ and $\Delta t=4\mathrm{ns}$ at the indicated $r_s$ parameter. Solid curves show the double Lorentz fits. (e) Density dependence of two peaks (${\omega }_{+}$ and ${\omega }_{-}$) identified in the loss function spectra. The shaded area indicates the width of the two modes obtained from the fitting in (d). Dashed lines illustrate the exciton $1s\mathrm{\text{−}}2p$ resonance (${\omega }_{\mathrm{ex}}^{\prime }$) and the screened plasma frequency (${\omega }_{\mathrm{pl}}^{\prime }$) determined from (a).

Figure 3

(a) Temperature dependence of the loss function spectra at $\Delta t=4\mathrm{ns}$ and $r_s=3.1$. (b) Loss function spectra at the indicated temperature. Solid curves show the fitting with a double Lorentz model. The peak positions are indicated by the closed and open circles. (c) Temperature dependence of the Drude scattering rate [Eq. (1)] for $r_s=3.1$ and $r_s=6$.