Excited cooper pairs

Excited Cooper pairs formed in a many-fermion system are those with nonzero total center-of-mass momentum (CMM). They are normally neglected in the st andard Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity for bein g too few compared with zero CMM pairs. However, a Bose-Einstein condensati on picture requires both zero and nonzero CMM pairs. Assuming a BCS model i nteraction between fermions we determine the populations for all CMM values of Cooper pairs by actually calculating the number of nonzero-CMM pairs re lative to that of zero-CMM ones in bath 2D and 3D. Although this ratio decr eases rapidly with CMM, the number of Cooper pairs for any specific CMM les s than the maximum (depairing or breakup) momentum turns out to be typicall y larger than about 95% of those with zero-CMM at zero temperature T. Even at T similar to 100 K this fraction in 2D is still as large as about 70% fo r typical quasi-2D cuprate superconductor parameters.