Cooper pairing and superconductivity on a spherical surface

Electrons in a multielectron bubble in helium form a spherical, two-dimensional system coupled to the ripplons at the bubble surface. The electron-ripplon coupling, known to lead to polaronic effects, is shown to give rise also to Cooper pairing. A Bardeen-Cooper-Schrieffer (BCS) Hamiltonian arises from the analysis of the electron-ripplon interaction in the bubble, and values of the coupling strength are obtained for different bubble configurations. The BCS Hamiltonian on the sphere is analysed using the Richardson method. We find that although the typical ripplon energies are smaller than the splitting between electronic levels, a redistribution of the electron density over the electronic levels is energetically favourable as pairing correlations can be enhanced. The density of states of the system with pairing correlations is derived. No gap is present, but the density of states reveals a strong step-like increase at the pair-breaking energy. This feature of the density of states should enable the unambiguous detection of the proposed state with pairing correlations in the bubble, through either capacitance spectroscopy or tunneling experiments, and allow to map out the phase diagram of the electronic system in the bubble.Comment: 25 pages, 7 figures, 1 tabl

Wigner lattice of ripplopolarons in a multielectron bubble in helium

The properties of ripplonic polarons in a multielectron bubble in liquid helium are investigated on the basis of a path-integral variational method. We find that the two-dimensional electron gas can form deep dimples in the helium surface, or ripplopolarons, to solidify as a Wigner crystal. We derive the experimental conditions of temperature, pressure and number of electrons in the bubble for this phase to be realized. This predicted state is distinct from the usual Wigner lattice of electrons, in that it melts by the dissociation of the ripplopolarons, when the electrons shed their localizing dimple as the pressure on the multielectron bubble drops below a critical value.Comment: 19 pages, 4 figure

The effect of pressure on statics, dynamics and stability of multielectron bubbles

The effect of pressure and negative pressure on the modes of oscillation of a multi-electron bubble in liquid helium is calculated. Already at low pressures of the order of 10-100 mbar, these effects are found to significantly modify the frequencies of oscillation of the bubble. Stabilization of the bubble is shown to occur in the presence of a small negative pressure, which expands the bubble radius. Above a threshold negative pressure, the bubble is unstable.Comment: 4 pages, 2 figures, accepted for publication in Physical Review Letter

Cold Collision Frequency Shift in Two-Dimensional Atomic Hydrogen

We report a measurement of the cold collision frequency shift in atomic hydrogen gas adsorbed on the surface of superfluid 4He at T<=90 mK. Using two-photon electron and nuclear magnetic resonance in 4.6 T field we separate the resonance line shifts due to the dipolar and exchange interactions, both proportional to surface density sigma. We find the clock shift Delta v_c = -1.0(1)x10^-7 Hz cm^-2 x sigma, which is about 100 times smaller than the value predicted by the mean field theory and known scattering lengths in the 3D case.Comment: 4 pages, 3 figure

Vortices on a superconducting nanoshell: phase diagram and dynamics

In superconductors, the search for special vortex states such as giant vortices focuses on laterally confined or nanopatterned thin superconducting films, disks, rings, or polygons. We examine the possibility to realize giant vortex states and states with non-uniform vorticity on a superconducting spherical nanoshell, due to the interplay of the topology and the applied magnetic field. We derive the phase diagram and identify where, as a function of the applied magnetic field, the shell thickness and the shell radius, these different vortex phases occur. Moreover, the curved geometry allows these states (or a vortex lattice) to coexist with a Meissner state, on the same curved film. We have examined the dynamics of the decay of giant vortices or states with non-uniform vorticity into a vortex lattice, when the magnetic field is adapted so that a phase boundary is crossed.Comment: 21 pages, 9 figure

Atomic Deuterium Adsorbed on the Surface of Liquid Helium

We investigate deuterium atoms adsorbed on the surface of liquid helium in equilibrium with a vapor of atoms of the same species. These atoms are studied by a sensitive optical method based on spectroscopy at a wavelength of 122 nm, exciting the 1S-2P transition. We present a direct measurement of the adsorption energy of deuterium atoms on helium and show evidence for the existence of resonantly enhanced recombination of atoms residing on the surface to molecules.Comment: 6 pages 4 figure

Pathways to metallic hydrogen

The traditional pathway that researchers have used in the goal of producing atomic metallic hydrogen is to compress samples with megabar pressures at low temperature. A number of phases have been observed in solid hydrogen and its isotopes, but all are in the insulating phase. The results of experiment and theory for this pathway are reviewed. In recent years a new pathway has become the focus of this challenge of producing metallic hydrogen, namely a path along the melting line. It has been predicted that the hydrogen melt line will have a peak and with increasing pressure the melt line may descend to zero Kelvin so that high pressure metallic hydrogen may be a quantum liquid. Even at lower pressures hydrogen may melt from a molecular solid to an atomic liquid. Earlier attempts to observe the peak in the melting line were thwarted by diffusion of hydrogen into the pressure cell components and other problems. In the second part of this paper we present a detailed description of our recent successful demonstration of a peak in the melting line of hydrogen