Properties of surface state electrons on liquid helium

Electrons on the surface of liquid helium form a two-dimensional system that is of great interest for its own unique properties as well as being a probe of the helium surface. The spectroscopic evidence for the hydrogenic nature of the surface state is compared with predictions. Measurements of the electron mobility parallel to the surface in low and high electric fields are compared with theory. The lifetime in the surface state is discussed as well as the effect of the electron on the liquid surface. The possibility that the electrons crystallize to form a two-dimensional lattice and the properties of this lattice are also analyzed.     

Escape rate of two-dimensional electrons on liquid helium surface

Escape rate of two-dimensional electrons on liquid helium surface is measured. A strong dependence of the escape rate on the surface electron density suggests that the surface electron system is in a “liquid” state.     

Statistical description of the system electrons on the liquid helium surface

System of electrons on the liquid helium surface is considered. General methods for obtaining free energy functional for the systems in mean field approximation are developed. These methods applied for treating systems with particles arranged in a lattice. Thus obtained functional of free energy is analyzed. The localization distance for electron and conditions for existing square or triangular lattices as well as phase transition between them are obtained.     

Preparation of cluster states with trapped electrons on a liquid helium surface

We present a scheme for the preparation of one-dimensional (1D) and two-dimensional (2D) cluster states with electrons trapped on a liquid helium surface and driven by a classical laser beam. The two lowest levels of the vertical motion of the electron act as a two-level system, and the quantized vibration of the electron along one of the parallel directions (the x direction) serves as the bosonic mode. The degrees of freedom of the vertical and parallel motions of the trapped electron can be coupled together by a classical laser field. With the proper frequency of the laser field, the cluster states can be realized.     

Self-trapping of electrons in vortex rings in liquid helium

A model according to which “fast” and “exotic” negative ions in superfluid helium are the localized states of electrons in vortex rings has been presented. The quantization of radial and longitudinal motions of electrons inside the vortex core and the quantization of the vortex motion of liquid helium lead to the existence of a whole family of excited states of electron vortices, in qualitative agreement with the experiments on the mobility of exotic ions. The possibility of the verification of conclusions of the model in optical experiments has been considered.     

Theory of the resonant properties of electrons localized on the surface of liquid helium

The problem of the shape of the line of optical transition of an electron between bound states on the surface of liquid helium is solved within the independent boson model. Such bound states are realized, for example, in the potential of a positively charged impurity located on a substrate or in the field of a He⁺ ion located beneath the surface. Reference is made to the importance of the relaxation processes of the dimple on the helium surface under the electron. The adiabatic approximation, in the case of which the dimple does not change during the time of electron transition, is not always valid. At low temperatures, two maxima may appear on the absorption line. It is demonstrated that the far tails of the optical absorption line feature a universal (Urbach rule) exponential dependence on the electron transition energy.     

The influence of ions and radiation on tunneling of electrons from the surface of liquid helium

In work previously reported by Saville et al. [1] and Saville [2], we found that electrons tunneling from their shallow potential well above the surface of liquid helium behave as an almost ideal 1D hydrogen atom. Computations [3], without approximation or adjustable parameters, using the time dependent Schrödinger equation are in excellent agreement with measured tunneling rates. The same computation method was used to compute the influence of AC fields on the tunneling rates [3] as preparation for planned experiments. In this paper I discuss phenomena which appear to set upper and lower limits on the observable tunneling rates. Lower limits were determined by photo assisted escape due to thermal radiation and by cosmic ray generation of ions in the bulk liquid helium. Upper limits were set by the creation of excitations in the superfluid film on the top of the sample chamber when electrons impacted with energy greater than 21.6 eV. Through its influence on the tunneling rate, we were also able to measure very small changes in the electron potential at the surface due to a sub-monolayer coverage of³He.     

Shift in cyclotron resonance of electrons on liquid helium surfaces

We calculate the increase in cyclotron resonance frequency for electrons trapped within dimples on a liquid helium surface, when a vertical electric field is applied in addition to the strong vertical magnetic field.     

Effective mass of surface electrons in helium under non-equilibrium conditions

The mass shift of surface electrons in helium has been investigated theoretically caused by electron-ripplon interaction as a function of electromagnetic field power absorbed by a system. It is shown that the mass shift is negative at weak powers of external field but it increases as the power increases and changes its sign. The results of calculation and comparison with the experimental data testify to the favourable role of two-ripplon scattering processes in energy relaxation of surface electrons above helium.     

Photon-induced vanishing of magnetoconductance in 2D electrons on liquid helium

We report on a novel transport phenomenon realized by optical pumping in surface state electrons on helium subjected to perpendicular magnetic fields. The electron dynamics is governed by the photon-induced excitation and scattering-mediated transitions between electric subbands. In a range of magnetic fields, we observe vanishing longitudinal conductivity σ(xx)→0. Our result suggests the existence of radiation-induced zero-resistance states in the nondegenerate 2D electron system.     

Point-contact transport properties of strongly correlated electrons on liquid helium

We present transport measurements of a nondegenerate two-dimensional electron system on the surface of liquid helium at a point constriction. The constriction is formed in a microchannel by a split gate beneath the helium surface. The electrostatic energy of the electron system, which depends in part on the electron density, determines the split-gate voltage threshold of current flow through the constriction. Steplike increases in conductance are observed as the confinement strength is reduced. As the Coulomb interaction between electrons is strong, we attribute this effect to the increase in the number of electrons that can pass simultaneously through the constriction. Close to the threshold, single-electron transport is observed.     

How the thickness of a liquid helium film influences the spectrum of electrons localized above its surface

We consider the problem of finding the energy spectrum of electrons localized above the surface of a liquid helium film under the electrostatic attraction of induced charges. We show that the forces of attraction to the charges induced on the surface of a conductor located beneath the film begin to additionally influence the forces of attraction of the electrons to the free liquid surface as the film thickness decreases. When the film thickness becomes less than 10μm, this influence causes a significant increase in the energy difference between the lower levels and a decrease in their depth. We suggest a numerical method for solving the problem and present the results of our calculations of the energy spectrum of electrons localized above the surfaces of liquid ³He, ⁴He, and neon films. The influence of the pressing electric field on the energy spectrum is considered.     

Transport properties of overheated electrons trapped on a helium surface

An ultra-strong photovoltaic effect has recently been reported for electrons trapped on a liquid helium surface under a microwave excitation tuned at intersubband resonance [D. Konstantinov, A.D. Chepelianskii, K. Kono, J. Phys. Soc. Jpn 81, 093601 (2012)]. In this article, we analyze theoretically the redistribution of the electron density induced by an overheating of the surface electrons under irradiation, and obtain quantitative predictions for the photocurrent dependence on the effective electron temperature and confinement voltages. We show that the photo-current can change sign as a function of the parameters of the electrostatic confinement potential on the surface, while the photocurrent measurements reported so far have been performed only at a fixed confinement potential. The experimental observation of this sign reversal could provide a reliable estimation of the electron effective temperature in this new out of equilibrium state. Finally, we have also considered the effect of the temperature on the outcome of capacitive transport measurement techniques. These investigations led us to develop, numerical and analytical methods for solving the Poisson-Boltzmann equation in the limit of very low temperatures which could be useful for other systems.     

Anticrossing phenomena in a resonator with 2D electrons on liquid helium

We have investigated the details of the eigenmode for a resonator containing a two-dimensional electron system (2DES) formed on the surface of liquid helium. We show that anticrossing phenomena occur near the crossing point ω₀=ω_c, where ω₀ is the eigenmode of the resonator and ω_c is the cyclotron frequency. The structure of the coupling constant is established. It is a flexible parameter, i.e., sensitive especially to magnetic field and electron density. A finite coupling leads to a perturbation, δω, of the eigenmode of the resonator in presence of the 2DES. Corresponding calculations and measurements of δω are presented. The theory fits the experimental data. The influence of anticrossing on the cyclotron resonance absorption line shape is demonstrated.