Can Warmer than Room Temperature Electrons Levitate Above a Liquid Helium Surface?
Résumé
We address the problem of overheating of electrons trapped on the liquid helium surface by cyclotron resonance excitation. Previous experiments, suggest that electrons can be heated to temperatures up to 1000K more than three order of magnitude higher than the temperature of the helium bath in the sub-Kelvin range. In this work we attempt to discriminate between a redistribution of thermal origin and other out-of equilibrium mechanisms that would not require so high temperatures like resonant photo-galvanic effects, or negative mobilities. We argue that for a heating scenario the direction of the electron flow under cyclotron resonance can be controlled by the shape of the initial electron density profile, with a dependence that can be modeled accurately within the Poisson-Boltzmann theory framework. This provides an self consistency-check to probe if the redistribution is indeed consistent with a thermal origin. We find that while our experimental results are consistent with the Poisson-Boltzmann theoretical dependence but some deviations suggest that other physical mechanisms can also provide a measurable contribution. Analyzing our results with the heating model we find that the electron temperatures increases with electron density under the same microwave irradiation conditions. This unexpected density dependence calls for a microscopic treatment of the energy relaxation of overheated electrons. Recently electrons on helium have emerged as a promising platform for the study of non-equilibrium physics in ultra high purity two dimensional materials [1-5]. They allowed to explore from a different perspective microwave-induced resistance oscillations and zero-resistance states under microwave irradiation that were discovered in ultra high purity GaAs heterostructures [6-20]. Electrons on helium provide a dilute electron system with well-understood disorder potential and weak screening effects thus comparison with theory is simplified compared to GaAs. For example MIRO on electrons on helium strongly depend on the direction of the circular polarisation as expected for non-interacting electrons [21]. In contrast almost no circular polarisation dependence is observed in GaAs [22-24], even if a dependence on the orientation of the linear polarization is present [25, 26]. This discrepancy stimulated investigations on the role of edges, contacts and electron-electron interactions [27-29] in GaAs without yet reaching a full understanding. Due to their low density electrons on helium can also display spectacular physical phenomena so far without equivalent in other systems. It has been shown for example, that zero-resistance states on electrons on helium can develop into incompressible phases where the density becomes pinned to a critical value independent of the external confinement [30]; in other cases the electron density can instead become unstable and exhibit time dpendent self-generated oscillations [31]. More generally, the study of non equilibrium phenomena in electrons on helium is strongly connected with the prospect of using Rydberg states [32, 33], created by the interaction of electrons with their image charge inside liquid helium, for quantum computing [34]. So the relaxation times for excited states and the absorption lineshapes have all been carefully investigated [35-40]. From this perspective the possibility of creating overheated electrons by excitation of cyclotron resonance that was reported in [41] is highly interesting since it challenges the view that energy relaxation rates are all relatively fast in the microsecond range [42] due to two riplon emission processes [43] which should prevent an overheating of the electrons. In [41] the temperature under cyclotron resonance driving was estimated from the horizontal spread of the electrons under excitation and from their vertical displacement, both measurements leading a similar temperature of hundreds of Kelvin. However these two redistribution measurements do not allow to characterise the energy distribution of the electrons and to know if it is well described by a hot thermal distribution function. A characterisation of the non equilibrium distribution function is however important as non-thermal phenomena, for example resonant photo-galvanic effects [44, 45] or negative mobilities [46, 47] can also lead to a redistribution of electronic charges. In [48] the density distribution of overheated electrons on helium was analyzed using Poisson-Boltzmann theory for different equilibrium density profiles predicting a change of direction of the electron flow under CR when the initial density profile of electrons was changed. Here we thus decided to compare these theoretical predictions with experimental results as a way to estimate if the electron energy distribution is indeed close to a thermal one. We find that although thermal excitation is not the only mechanism contributing to electron displacement reasonably good agreement with the theoretical dependence can still be obtained for moderate driving strengths leading to an estimation of electron temperature of several hundred Kelvin consistent with [41]. We then analyze the dependence of the out-of-equilibrium electron temperature on the electron density finding the surprising conclusion that it increases almost linearly with the electron density. While this
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