Mid-infrared dielectric response of Fermi-degenerate electron-hole droplets in diamond

Abstract

Exploring the properties of a highly quantum-degenerate electron-hole (e-h) state as a many-body system is an interesting problem in solid-state physics. Electron-hole droplets (EHDs) offer a potential platform for investigating such a state of Fermi-degenerate carriers at an extremely high density. Herein we present dielectric response measurements of carriers in the mid-infrared (MIR) region for a definitive evaluation of the dynamic properties of the e-h state of EHDs in diamond. With photoexcitation across the band-gap energy by using the two-photon absorption process, we performed time-resolved differential transmission spectroscopy by using MIR probe light and time-resolved photoluminescence spectroscopy in the deep-ultraviolet region. By linking the two temporal profiles, we overcame the problem of previous ambiguous PL analyses and elucidated the MIR dielectric response that reveals the surface plasmon resonance (SPR) of EHDs and the effect of the e-h Coulomb interaction on the dynamic dielectric response. Thus, we found that the carrier density inside EHDs remained constant at $8\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ up to 2 ns, whereas a decay time of 1 ns of the condensed volume was found and the AC conductivity relaxation rate of $2\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ maintained during this nanosecond timescale was the highest among group-IV semiconductors. We predicted a strong dependence of the e-h scattering rate on the probe frequency in the high-frequency region in which SPR appeared, suggesting that---when probed in the low-frequency region---dynamical relaxation does not interfere with the order formation expected in quantum-degenerate e-h systems at ultralow temperatures.