Continuum elasticity theory of edge excitations in a two-dimensional electron liquid with finite range interactions

We make use of continuum elasticity theory to investigate the collective modes that propagate along the edge of a two-dimensional electron liquid or crystal in a magnetic field. An exact solution of the equations of motion is obtained with the following simplifying assumptions: (i) The system is {\it macroscopically} homogeneous and isotropic in the half-plane delimited by the edge (ii) The electron-electron interaction is of finite range due to screening by external electrodes (iii) The system is nearly incompressible. At sufficiently small wave vector $q$ we find a universal dispersion curve $\omega \sim q$ independent of the shear modulus. At larger wave vectors the dispersion can change its form in a manner dependent on the comparison of various length scales. We obtain analytical formulas for the dispersion and damping of the modes in various physical regimes.Comment: 3 figure

Plasma dispersion of multisubband electron systems over liquid helium

Density-density response functions are evaluated for nondegenerate multisubband electron systems in the random-phase approximation for arbitrary wave number and subband index. We consider both quasi-two-dimensional and quasi-one- dimensional systems for electrons confined to the surface of liquid helium. The dispersion relations of longitudinal intrasubband and transverse intersubband modes are calculated at low temperatures and for long wavelengths. We discuss the effects of screening and two-subband occupancy on the plasmon spectrum. The characteristic absorption edge of the intersubband modes is shifted relatively to the single-particle intersubband separation and the depolarization shift correction can be significant at high electron densities

Temperature-dependent energy levels of electrons on liquid helium

We present measurements of the resonant microwave absorption by the Rydberg energy levels of surface state electrons on the surface of superfluid liquid helium, in the frequency range 165 - 220 GHz. The resonant frequency was strongly temperature dependent from 0.1 to 2 K. The experiments are in agreement with recent theoretical calculations of the renormalisation of the electron energy levels due to zero-point and thermal ripplons, analogous to a condensed matter Lamb shift. The temperature-dependent contribution to the linewidth for excitation to the first excited state at 189.6 GHz is compared with other measurements and theoretical predictions.Comment: 24 pages, 9 figure

Nonequilibrium phenomena in high Landau levels

Developments in the physics of 2D electron systems during the last decade have revealed a new class of nonequilibrium phenomena in the presence of a moderately strong magnetic field. The hallmark of these phenomena is magnetoresistance oscillations generated by the external forces that drive the electron system out of equilibrium. The rich set of dramatic phenomena of this kind, discovered in high mobility semiconductor nanostructures, includes, in particular, microwave radiation-induced resistance oscillations and zero-resistance states, as well as Hall field-induced resistance oscillations and associated zero-differential resistance states. We review the experimental manifestations of these phenomena and the unified theoretical framework for describing them in terms of a quantum kinetic equation. The survey contains also a thorough discussion of the magnetotransport properties of 2D electrons in the linear response regime, as well as an outlook on future directions, including related nonequilibrium phenomena in other 2D electron systems.Comment: 60 pages, 41 figure

Decay of excited surface electron states in liquid helium and related relaxation phenomena induced by short-wavelength ripplons

Decay rates of excited surface electron states on liquid helium are theoretically studied for different electron confinement potentials and in the presence of quantizing magnetic field. Contributions of both one-ripplon and two-ripplon scattering processes are analyzed. Regarding the decay rate of the first excited surface level (l=2), two-ripplon emission of short wave-length capillary waves is shown to dominate the conventional one-ripplon scattering in two distinct cases: the ambient temperature is low enough, or the surface state excitation energy Δ₂–Δ₁ does not match an excitation energy of the in-plane motion quantized under a strong magnetic field or in a quantum dot. In these cases, magnetic field and confinement cannot essentially reduce the decay rate which is of order of 10⁶ s⁻¹ and does not depend on temperature. Importance of these findings for a microwave resonance experiment is discussed

Microwave absorption saturation and decay heating of surface electrons on liquid helium

The microwave (MW) resonance absorption and decay heating of surface electrons (SEs) on liquid ⁴He are theoretically studied for the vapor atom scattering regime. The decay heating is shown to be an essential occurrence of a MW resonance experiment appearing even at low excitation rates. It strongly affects the occupancies of surface levels and the broadening of resonance lines long before the absorption suturation condition is reached. Contrary to the model of cold SEs usually used for description of the MW resonance, the new theory leads to MW absorption saturation when only a very small fraction of electrons (less than 10%) is left on the ground and the first excited levels

Cyclotron resonance of a two-dimensional Wigner solid

Cyclotron resonance absorption from a two-dimensional electron solid formed on a free surface of liquid helium is analyzed by means of the memory function formalism. The presence of the low-frequency phonon mode of the Wigner solid in a strong magnetic field is shown to broaden significantly the electron dynamical structure factor (DSF) as a function of frequency, strengthening the contribution from multi-phonon emission terms of the high-frequency mode. Thus in most cases the linewidth is formed by nonlinear terms of the DSF expansion in the cyclotron motion factor exp (-iwct) rather than by the linear terms analyzed previously. The inclusion of all these multi-phonon terms changes the sign of the many-electron effect and agrees well with available experimental data, eliminating the discrepancy between theory and experiment. Cyclotron resonance absorption from a two-dimensional electron solid formed on a free surface of liquid helium is analyzed by means of the memory function formalism. The presence of the low-frequency phonon mode of the Wigner solid in a strong magnetic field is shown to broaden significantly the electron dynamical structure factor (DSF) as a function of frequency, strengthening the contribution from multiphonon emission terms of the high-frequency mode. Thus in most cases the linewidth is formed by nonlinear terms of the DSF expansion in the cyclotron motion factor exp(−iωct) rather than by the linear terms analyzed previously. The inclusion of all these multiphonon terms changes the sign of the many-electron effect and agrees well with available experimental data, eliminating the discrepancy between theory and experiment