Magnetoconductivity of two-dimensional electrons on liquid helium:Experiments in the fluid phaseM. J. Lea, P. Fozooni, A. Kristensen, P. J. Richardson, and K. DjerfiDepartment of Physics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, EnglandM. I. Dykman and C. Fang-YenDepartment of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824A. BlackburnDepartment of Electronics and Computer Science, University of Southampton, SO17 1BJ, England~Received 16 May 1996; revised manuscript received 25 November 1996!The magnetoconductivitys(B) of two-dimensional electrons on liquid helium was measured from 0.25 to1.3 K in the electron fluid phase in magnetic fields up to 8 T. In low magnetic fields B,s(0)/s(B)511(mB)2as in the Drude model, wheremis the zero-field mobility due to scattering by4He vapor atoms andripplons, even formB@ 1. The values of mobility are in good agreement with previous measurements and withcalculations for a correlated electron fluid. At higher fields,s(0)/s(B) deviates from the Drude model andbecomes density dependent due to many-electron effects. Only at the highest fields, or the lowest densities,doess(B) approach the theoretical single-particle magnetoconductivity. For both vapor-atom and ripplonscattering the results are in good agreement with a microscopic many-electron theory in which the diffusion ofthe cyclotron orbits is controlled by the internal fluctuational electric fields. The density and temperaturedependence of these internal fields derived from the experiments are in excellent agreement with Monte Carlosimulations. @S0163-1829~97!06024-4#I. INTRODUCTIONTwo-dimensional electrons in surface states above super-fluid helium form the simplest conducting system knownexperimentally.1Below 1 K the electrons are in the quantumground state of the potential well formed by the helium sur-face and a vertical electric field. However, they are free tomove horizontally with very high mobilitiesm, limited byscattering from4He vapor atoms and by the thermal surfacevibrations, or ripplons. For vapor atoms the scattering maybe regarded as almost ideal, short-range, and quasielasticwhile ripplon scattering is also well understood. At the elec-tron densities which are stable on bulk helium, n,23 1013m22, the electrons in the fluid phase are dilute ~typi-cal separation 1mm!, classical, and nondegenerate. How-ever, the electrons are strongly interacting via long-rangeCoulomb forces, with a macroscopic screening length deter-mined by the distance to underlying metallic electrodes~'100mm in these experiments.! In most experiments, theplasma parameter ~the ratio of the characteristic unscreenedCoulomb energy to the kinetic energy!, G5 e2(pn)1/2/4p«0kT@1, while for G. 127 ~low T! the sys-tem forms a two-dimensional ~2D! electron crystal.2Giventhe experimental flexibility and control over the density, tem-perature, mobility, and magnetic field, this is an ideal systemfor investigating the influence of electron-electron interac-tions on fundamental transport properties.In particular, recent data clearly indicates that electron-electron interactions, and the internal electric fields whichthey produce, have a dramatic influence on themagnetoresistivity3and magnetoconductivity4,5in this sys-tem. A single-particle approach will not suffice. Experimen-tally, the low field magnetoconductivity and magnetoresistiv-ity follow the simple Drude model over a very wide range ofconditions, even formB5vct<500, well in the range ofclassically strong magnetic fields ~vc5 eB/m is the cyclo-tron frequency!. This is rather surprising, given that Landaulevel quantization should occur with energy levels at (N1 0.5) \vcformB. 1. The energy density of states willchange dramatically with magnetic field and would be ex-pected to enhance the elastic scattering rate, depending onthe width of the Landau levels. For independent electrons,the only contribution to this width is the collision broaden-ing, which can be found from the self-consistent Bornapproximation6~SCBA! or from the method of moments7which give similar results. This approach works well for lowmobility samples,8though with some residual quantitativediscrepancies, but at higher mobilities (20,m, 2000 m2/V s), the narrower collision width becomes lessthan the energy spread given by the product of the many-electron internal force eEfand characteristic lengths such asthe thermal de Broglie wavelength and the quantum mag-netic length. This essentially smears out the density of statesand leads back to the Drude model for magnetic fields lessthan some onset field B0, which is typically 0.5 T for elec-trons on helium. For B. B0,sxxbecomes density dependentand 1/sxxis then directly proportional to the internal electricfield strength. At higher fields the collision width of the Lan-dau levels increases again and the independent electrontheory ~SCBA! does become valid. Previous measurementsand interpretations of the magnetoconductivity only consid-ered single-particle theories.9The many-electron transporteffects have been studied theoretically in the extreme quan-tum limit of strong magnetic field10and interesting density-PHYSICAL REVIEW B 15 JUNE 1997-IIVOLUME 55, NUMBER 24550163-1829/97/55~24!/16280~13!/$10.00 16 280 © 1997 The American Physical Societydependent effects were observed in cyclotron resonance.11Recently, the damping of edge magnetoplasmons has beenused to determine the magnetoconductivitysxx,12both inthe vapor-atom and ripplon scattering regimes, in goodagreement with the direct measurements reportedpreviously3,4and in this paper and confirming the influenceof many-electron effects.Recently a comprehensive many-electron theory of trans-port phenomena in strongly correlated classical and semi-classical systems has been developed.13In parallel with thisincreased theoretical understanding we have also developedthe experimental techniques based on high-precision Corbinoelectrodes, fabricated using modern lithographic techniques.These new electrodes give improved experimental resolu-tion.This paper describes measurements ofsxxfrom 0.25 to1.3 K in the 2D electron fluid phase, at fields up to 8 T, inboth the vapor-atom and ripplon scattering regimes. The pa-per is organized as follows. In Sec. II we give an account ofthe basic theoretical concepts underlying many-electronmagnetoconductivity within the framework of the Einsteindiffusion relation. In Sec. III we describe the experimentalcell, the Corbino