Cooper pairing and superconductivity on a spherical surface

TL;DR

This paper explores how electron-ripplon interactions in a spherical helium bubble can induce Cooper pairing, leading to a unique superconducting-like state detectable via spectroscopic methods.

Contribution

It derives a BCS Hamiltonian for electrons on a sphere coupled to ripplons and analyzes the resulting pairing correlations and density of states.

Findings

Pairing correlations can be enhanced despite small ripplon energies.

The density of states shows a step-like increase at the pair-breaking energy.

No true energy gap is observed, but pairing signatures are detectable.

Abstract

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.