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

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

Co-existence of the Meissner and vortex-state on a superconducting spherical shell

We show that on superconducting spherical nanoshells, the co-existence of the Meissner state with a variety of vortex patterns drives the phase transition to higher magnetic fields. The spherical geometry leads to a Magnus-Lorentz force pushing the nucleating vortices and antivortices towards the poles, overcoming local pinning centers, preventing vortex-antivortex recombination and leading to the appearance of a Meissner belt around the sphere's equator. In sufficiently small and thin spherical shells paramagnetic vortex states can be stable, enabling spatial separation of freely moving shells with different radii and vorticity in an inhomogeneous external magnetic field.Comment: 11 pages, 5 figures (higher res gif version of fig.5 included in archive