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 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 {\it real} solutions: one describing moving (i.e., having nonzero total, or center-of-mass, momenta) Cooper pairs as resonances (or bound composite particles with a {\it finite} lifetime), and another exhibiting superconducting collective excitations sometimes known as Anderson-Bogoliubov-Higgs (ABH) modes. A Bose-Einstein-condensation-based picture of superconductivity is addressed.

5 pages in PS, including 3 figures. In press Physica C

Cited by in corpus (6)

• Bose-Einstein Condensation in the Relativistic Ideal Bose Gas
• The BCS-Bose Crossover Theory
• Novel results in STM, ARPES, HREELS, Nernst, neutron, Raman, and isotope substitution experiments and their relation to bosonic modes and charge inhomogeneity, from perspective of negative-Ueff boson-fermion modelling of HTSC
• Two-dimensional Bose-Einstein Condensation in Cuprate Superconductors
• Further evidence for linearly-dispersive Cooper pairs
• Pre-formed Cooper pairs and Bose-Einstein condensation in cuprate superconductors