Direct Observation of Many-Electron Magnetoconductivity in a Nondegenerate 2D Electron Liquid

Abstract

The magnetoconductivity o (8) of two-dimensional electrons on liquid helium was measured above 1 K, using high-precision Corbino electrodes. In low magnetic fields 8, o(0)/o(8) = I + (tI, B)2 as in the Drude model, where p, is the zero-field mobility due to scattering by He vapor atoms, even for pB» , 1. At higher fields fr(0)/o(8) becomes density dependent due to ffiany-electron effects, in excellent agreement with the theory of Dykman. Only at the highest fields, or the lowest densities, does a(B) approach the theoretical single-particle magnetoconductivity. PACS numbers: 73.20.Dx, 67.90.+z, 73.50.Jt Electrons above the surface of superfluid helium form a nearly ideal two-dimensional electron system (2DES).At the electron densities, n & 2 X 10" m 2, which are stable on bulk liquid, the electrons are nondegenerate and are perhaps the best example of a classical 2D conducting system [1]. The electrons are held in a vertical potential well produced by the repulsion of the helium surface and an applied vertical electric pressing field.At low temperatures T they are in the quantum ground state for vertical motion but are free to move horizontally. The electrons are scattered by 4He vapor atoms above 1 K and by surface ripplon modes on the helium at lower temperatures where the zero-field mobility p, can be as high as 103 m2/Vs. The matrix elements for the scattering are well known [2] and give good agreement with the experimental values for p, (T) [3]. Vapor atoms act as almost ideal point-scattering centers with quasielastic scattering (due to the large mass ratio). The application of a vertical magnetic field 8 to this system is particularly interesting for pB) I, t, he region of classically strong magnetic fields. In the singleelectron approximation the energy spectrum becomes a series of discrete quantized Landau levels, energy separation liat"where ay, = eB/m is the cyclotron frequency.The extreme quantum limit, boy, /kT = 1.3448/T ) 1, in which only the lowest I uidau level is occupied, is easily reached. However, the Coulomb interaction between electrons gives a fluctuating many-electron electric field which changes the discrete Landau levels into a continuous spectrum and strongly influences the magnetotransport in the quantum region. This was first recognized by Dykman who gave theoretical expressions for ripplon [4,5] and vapor atom scattering [6]. The Drude model for the magnetoconductivity o (8) of a classical 2DES assumes classical cyclotron orbits [radius R, = (2mkT)'/~/eB] and a field-independent scattering rate and gives CFp 1 2 -,.(.) = -(. ) =''~"' where frp = o'""(0) = nehru, is the zero-field conductivity.It is equivalent to the Einstein relation fr"= ne~L2/kTr where L is the diffusion length (~orbit radius in high fields) and I/r is the scattering rate. The formation of Landau levels changes the energy density of states and hence the scattering rate becomes field dependent. The quantum cyclotron radius must also be used in quantizing magnetic fields. Both these effects are included in the orb...

Magnetoresistivity of a Weakly-Screened, Low-Density, Two-Dimensional Electron Liquid

“…We observe the effect of electronelectron interactions on altering the orbital paths of electrons in small magnetic fields, which results in Drude behavior. This crossover from Drude to SCBA behavior has been confirmed by earlier experiments in the quantum limit, 2,4,5,[7][8][9][10][11] h " ! c > kT, at high densities.…”

“…At a given temperature increases with density. The derivative of gamma with respect to density decreases with increasing temperature except for an anomalous data point at 1.67 K. The variation of the high-field SCBA behavior with electron density has been observed for scattering from vapor atoms 4) and from ripplons. 11) Figure 4 shows all of the data on a universal curve obtained by scaling the normalized resistivity by ðn 0 =nÞ 9=8 , n 0 ¼ 0:21 Â 10 10 m À2 , and scaling the field by a best fit parameter À1 .…”

“…Aside from the non-degeneracy, it differs from other 2D electron systems in the strength of the electron-electron interaction. [1][2][3][4][5][6][7] The Coulomb interaction is weakly screened by metallic plates that are separated from the electron layer by about 1 mm. It is an ideal system for testing the properties of strongly-interacting electrons.…”

“…We fit our results with the theory of Dykman and Lea. [2][3][4][5][6][7] Preliminary results without this analysis were presented elsewhere. 12) …”

The diagonal and off-diagonal AC conductivity of two-dimensional electron gases with contactless Corbino geometry in the quantum Hall regime

“…5,6 A two-dimensional distributed model for capacitive coupling to electrodes with Corbino geometry has been used for many years to analyze nondegenerate 2DEGs on cryogenic surfaces. 8,9 In the present work we shall adopt this so-called Sommer-Tanner model, 10 which, to our knowledge, has not previously been applied to degenerate semiconductor 2DEGs. There is a significant difference between the conductivity results obtained with the Stern and Sommer-Tanner models for certain sample geometries.…”