Low-Temperature Mobility of Surface Electrons and Ripplon-Phonon Interaction in Liquid Helium

TL;DR

This paper investigates how surface electrons in superfluid helium move at very low temperatures, focusing on how ripplon-phonon interactions influence their mobility and identifying conditions for observing these effects.

Contribution

It provides a detailed analysis of the temperature dependence of electron mobility and establishes the specific electric field and frequency conditions for experimental observation.

Findings

Mobility decreases rapidly with temperature as T^{-20/3}

Electric field E_ot < 1 kV/cm corresponds to T < 70 mK for observable effects

Frequency of driving field should be below 30 Hz for effect detection

Abstract

The low-temperature dc mobility of the two-dimensional electron system localized above the surface of superfluid helium is determined by the slowest stage of the longitudinal momentum transfer to the bulk liquid, namely, by the interaction of surface and volume excitations of liquid helium, which rapidly decreases with temperature. Thus, the temperature dependence of the low-frequency mobility is \mu_{dc} = 8.4x10^{-11}n_e T^{-20/3} cm^4 K^{20/3}/(V s), where n_e is the surface electron density. The relation T^{20/3}E_\perp^{-3} << 2x10^{-7} between the pressing electric field (in kV/cm) and temperature (in K) and the value \omega < 10^8 T^5 K^{-5}s^{-1} of the driving-field frequency have been obtained, at which the above effect can be observed. In particular, E_\perp = 1 kV/cm corresponds to T < 70 mK and \omega/2\pi < 30 Hz.