Pairing in spherical nanograins

Conditions are ascertained when the pairing and other thermodynamic properties of spherical nanograins with numbers of delocalized electrons N<105 can be investigated by using the Single Shell Model (SSM) that gives the eigenvalues of the pairing Hamiltonian for a solitary shell. In the frame of SSM the exact canonical and grand canonical descriptions are employed first to analyze the absence of the abrupt superconducting-normal phase transition in finite systems in which an increase of the pairing and BCS critical temperature can be observed and secondly to study such new phenomena as the temperature re-entrance of the pairing in postcritical magnetic fields and also low temperature oscillations of the magnetic susceptibility and electronic heat capacity in an increasing uniform magnetic field.