Surface state electrons in a helium micro-channel

This thesis describes an experimental investigation into the conduction of two-dimensional (2D) surface state electrons (SSE) on the surface of liquid helium, confined within a microchannel, at temperatures from 2K to below 0.1 K. Novel devices were designed to produce a structured substrate with a microchannel. This supports a suspended, superfluid, helium film, which can be charged with surface state electrons. The substrate was fabricated in the Orsted laboratory, Niels Bohr Institute fAPG, University of Copenhagen, Denmark, and is built with 5 patterned lithographic layers evaporated on a GaAs wafer, using both optical and electron beam lithographic techniques. The microchannel is 1.8 μm deep and has a width W = 16 μm. Full details are given of the fabrication processes developed and the problems that were overcome. Electrons were generated by thermionic emission from a filament and trapped on the helium surface in the channel. The resistivity ρ(T) of the two-dimensional electron sheet in the microchannel was measured using Sommer-Tanner techniques via electrodes fabricated on the substrate that are capacitively coupled to the electrons at frequencies between 5-20 kHz. Experiments were performed in the temperature range 0.06 ≤ T ≤ 2 K, for rms drive amplitudes 1 ≤ Vd ≤ 100 mV and for electron densities 1012 ≤ n ≤ 1013 m-2. Results were obtained in both the electron fluid and the electron solid phases, above and below the Wigner crystal melting temperature Tm. The conducting electrons were confirmed to be in the channel by the successful and repeatable cutting off of the measured current via the biasing of a microchannel gate electrode, as in an FET (field-effect transistor). For temperatures above 1 K, the device is ohmic in that the a.c. current through the electrons scales linearly with the drive voltage amplitude, with a phase shift φ proportional to the resistivity ρ(T). The temperature dependence of the resistivity of the electrons is in good agreement with the theory for gas atom scattering, showing little or no substrate scattering, in contrast to SSE on thin van der Waals helium films. For temperatures below 1 K (in the region of the Wigner solid melting temperature) the effective resistivity ρ(T) diverges from the theory and increases to a maximum as the temperature decreases. Within this region, T < 1 K, the resistivity is non-linear and increases with the a.c. current amplitude. Experiments at different frequencies show that the effective resistance depends on the average electron drift velocity ν. These effects were measured for a range of electron densities from 3 to 15 x 1012 m-2. The non-linearity is interpreted as due to coherent Bragg-Cerenkov scattering of the electrons from the ripplons on the free helium surface, as observed for electrons on bulk helium in the 2D electron Wigner crystal. This gives rise to dynamic pinning of the electrons to the ripplons at the phase velocity vi of the ripplons with a wave-vector equal to the reciprocal lattice vector of the crystal. A linear, ohmic, region is only present at low velocities ν < 7 m/s ∼ ν1. Above a critical electron velocity, the resistive force, expressed as an in-plane electric field E(v) in the channel, becomes constant and independent of the mean electron drift velocity ν. This is interpreted as a non-equilibrium phase transition in which the central region of the electrons is locked to a velocity ν1, while edge currents move at a higher velocity. A simple model is presented in which the mean electron drift velocity is given by υ-bar = αυ1 + (1-α)υedge, where ν1 and νedge are the mean electron velocities of the central and edge current filaments respectively and α is the fraction of the current carried by the central region. Above the critical velocity, oscillations are observed in the electric field E(ν), close to the expected melting temperature Tm. It is suggested that these are due to spatial ordering in the edge currents, in the form of electron lines, as predicted by molecular dynamic simulations. Other explanations for the oscillations are discussed but do not match the observations. (author)