M. J. Lea

Observation of dynamical ordering in a confined Wigner crystal.

We present measurements of the conduction of nondegenerate free electrons along a low-dimensional channel at low temperatures, using surface-state electrons on liquid helium in novel microelectronic devices. Above 1 K, the electrons form an ideal classical Drude conductor. Below 1 K, Coulomb interactions produce electronic spatial order, leading to strong non-Ohmic effects and negative differential conductivity. Evidence is presented for self-organized current filaments in the channel, created by a nonequilibrium phase transition. Periodic conductance oscillations suggest an anisotropic spatial order with lines of electrons along the channel edges.

The transverse acoustic impedance of He II

The complex shear acoustic impedance of liquid He II has been measured at frequenciesf(=ω/2π) of 20.5, 34.1, and 47.8 MHz from 30 mK to the λ-point Tλ (2.176 K). The impedanceZ was found from the temperature dependence of the quality factor and the resonant frequency of a thickness shear mode quartz crystal resonator immersed in the liquid. The relationship for a hydrodynamic viscous liquidZ(T)=(1−i)(πfηρn)1/2 was used to measure the temperature dependence of the viscosity η(T) using tabulated values of the normal fluid density ρn(T). Deviations from hydrodynamic behavior occurred when the viscous penetration depth was less than the superfluid healing length, the phonon mean free path, and the roton mean free path. Near the λ-point,Z(T)/Z(Tλ) was frequency dependent and a value for the superfluid healing lengtha=(0.10±0.01)ε−2/3 nm was found, where ε=(Tλ−T)/Tλ. The effects of van der Waals forces near the crystal surface were also observed and a layer model was used to interpret the measurements. Below 1.8 K only rotons contribute significantly toZ and we determined the roton relaxation time as τr=8.5×10−14T−1/3 exp (8.65/T) sec. Below 1.2 K, ωτr>1 and we investigated the breakdown of hydrodynamics in this region. ForT<0.6 K the resonant frequency of the crystals decreased by Δf/f=2×10−7, but the origin of this effect is not yet known.

Counting Individual Trapped Electrons on Liquid Helium

We show that small numbers of electrons, including a single isolated electron, can be held in an electrostatic trap above the surface of superfluid helium. A potential well is created using microfabricated electrodes in a 5 μm diameter pool of helium. Electrons are injected into the trap from an electron reservoir on a helium microchannel. They are individually detected using a superconducting single-electron transistor as an electrometer. A Coulomb staircase is observed as electrons leave the trap one–by–one until the trap is empty. A design for a scalable quantum information processor using an array of electron traps is presented.

Microwave saturation of the Rydberg States of electrons on helium.

We present measurements of the resonant microwave excitation of Rydberg energy levels for surface-state electrons on superfluid helium. The temperature-dependent contribution to the linewidth gamma(T) agrees with theoretical predictions and is very small below 700 mK, in the ripplon scattering regime. Absorption saturation and power broadening were observed as the fraction of electrons in the first excited state was increased to 0.49, close to the thermal excitation limit of 0.5. The Rabi frequency Omega was determined as a function of microwave power. High values of the ratio Omega/gamma confirm this system as an excellent candidate for creating qubits.

The ac response of a 2-D electron gas on liquid helium in a magnetic field

The low frequency ac response of a 2-D electron gas on liquid helium in a magnetic field is analysed in terms of ρxx and ρxy, the components of the magnetoresistivity tensor. The electrons are screened by parallel electrodes and the system forms a 2-D transmission line. The 2-D wave equation is solved numerically for a bounded electron sheet in a rectangular geometry which is excited by one of the electrodes. For ωτ≪ 1, where τ is a relaxation time, heavily damped voltage waves propagate along the transmission line. In a field these waves propagate along the edges of the electron sheet with characteristic decay lengths or 2-D skin depths, parallel and perpendicular to the edges, which depend on ρxx and ρxy. The effects of these skin depths on measurements of the magnetoresistance and ac Hall effect are demonstrated. The relationship to the dc Hall effect and to edge magnetoplasmons is shown. The effects of incomplete screening, density inhomogeneities and edge capacitance are also discussed.

Magnetoresistance of 2D electrons on helium at 0.5 K

Measurements have been made of the resistivity of 2D electrons on liquid helium at T=0.5 K in magnetic fields up to 4 T. Strong quantum magnetoresistance is observed for h(cross) omega dc/kT<or=10, where omega c is the cyclotron frequency, due to the formation of Landau levels.

Microelectronics on liquid helium

Abstract Microelectronic devices for surface state electrons on liquid helium are being developed using surface structures on quartz and GaAs substrates. Conduction occurs along suspended helium films, held by surface tension in channels, 1–2 μm deep and 16–30 μm wide. Low-frequency devices with source, drain and gate electrodes have been demonstrated. Preliminary measurements indicate that the electron mobility is similar to that on bulk helium.

The Statistical Distribution Function For An Anyon Liquid

Abstract The distribution function for fermions has been derived from collision theory by using the detailed balance hypothesis. Its form goes to the correct boson (n = 1) and fermion (n = 1) limits. Further the equations for the density matrix have been derived from the Hamiltonian. The zero order approximation gives a distribution having the same form as that derived by the detailed balance arguments.

Magnetoresistance and Many-Electron Effects in Two-Dimensional Electrons on Liquid Helium

The magnetoresistance ρxx of a two-dimensional electron gas on the surface of liquid helium below 1 K has been measured up to the extreme quantum limit ωc/kT ≤ 20, where ωc is the cyclotron frequency. The resistivity increases almost quadratically with magnetic field, and is compared with a theoretical calculation based on many-electron effects.

Resonant Correlation-Induced Optical Bistability in an Electron System on Liquid Helium

We show that electrons on liquid helium display intrinsic bistability of resonant intersubband absorption. The bistability occurs for comparatively weak microwave power. The underlying giant nonlinearity of the many-electron response results from the interplay of the strong short-range electron correlations, the long relaxation time, and the multisubband character of the electron energy spectrum.