Drift and diffusion of paraexcitons inCu2O: Deformation-potential scattering in the low-temperature regime

Abstract

The diffusion constant and drift mobility of paraexcitons in ${\mathrm{Cu}}_2$O have been determined by the use of time-resolved luminescence imaging. Extremely large diffusion constants (D≊1000 ${\mathrm{cm}}^2$/s) and drift mobilities (μ≊${10}^7$ ${\mathrm{cm}}^2$/eV s) are measured at 1.2 K. Both D and μ exhibit very rapid and unusual temperature dependences which vary with applied stress. Calculations described here show that these properties can be attributed to the novel character of paraexcitons in ${\mathrm{Cu}}_2$O. Under zero stress this exciton is expected to couple mainly to longitudinal-acoustic phonons, which have a rather large velocity (≊4.5×${10}^5$ cm/s). Due to the large excitonic mass ($m^{\mathrm{*}}$≃3$m_0$), the thermal ve- locity [(3$k_B$T/$m^{\mathrm{*}}$ ${)}^{1/2}$] of the paraexcitons at T≲3 K is slower than this sound velocity, causing a freeze-out of the phonon-emission process. A rapid increase in scattering time is expected as the temperature is lowered further, which is in agreement with the data at zero or low stress. As stress is applied, the paraexciton wave function is altered, allowing a coupling to the transverse-acoustic phonons, which have a velocity (≊1.2×${10}^5$ cm/s) smaller than the exciton thermal velocity. Transverse-phonon emission thus reduces the exciton mobility and produces a more nearly $T^{\mathrm{-}3/2}$ dependence, as predicted for deformation-potential scattering in the high-temperature limit. We believe that these are the first observations of the low-temperature regime of deformation-potential scattering.