Cooper pairs as resonances

Abstract

Using the Bethe-Salpeter (BS) equation, Cooper pairing can be generalized to include contributions from holes as well as particles from the ground state of either an ideal Fermi gas (IFG) or of a BCS many-fermion state. The BCS model interfermion interaction is employed throughout. In contrast to the better-known original Cooper pair (CP) problem for either two particles or two holes, the generalized Cooper equation in the IFG case has no real-energy solutions. Rather, it possesses two complex-conjugate solutions with purely imaginary energies. This implies that the IFG ground state is unstable when an attractive interaction is switched on. However, solving the BS equation for the BCS ground state reveals two types of real solutions: one describing moving (i.e., having nonzero total, or center-of-mass., momenta) CPs as resonances (or bound composite particles with a finite lifetime). and another exhibiting superconducting collective excitations analogous to Anderson-Bogoliubov-Higgs RPA modes. A Bose-Einstein-condensation-based picture of superconductivity is addressed, (C) 2001 Elsevier Science B.V. All rights reserved.