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Critical temperature and specific heat for Cooper pairing on a spherical surface

V. N. Gladilin·J. Tempere·I. F. Silvera·J. T. Devreese
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Abstract

Based on an exact solution of the Bardeen-Cooper-Schrieffer type Hamiltonian on a spherical surface, we calculate the specific heat for the electron system with pair correlations on a sphere. We find that it is possible to extract from the specific heat a temperature above which many-body states with broken Cooper pairs get populated. Therefore, we define this temperature as the characteristic temperature signalling the onset of a BCS-type pair-correlated state for electrons on a spherical surface. Such spherical electron systems are realized in multielectron bubbles in liquid helium, for which the above-mentioned characteristic temperature is found to be of the order of 10-100 mK. Both the specific heat and the critical temperature show a pronounced (4-6%) odd-even parity effect that persists even for numbers of electrons as large as 10$^6$.

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V. N. Gladilin, J. Tempere, I. F. Silvera, J. T. Devreese. 2007-01-23. Critical temperature and specific heat for Cooper pairing on a spherical surface. https://doi.org/10.1103/physrevb.74.104512

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