Absence of Cooper-type bound states in three- and few-electron systems
arXiv:cond-mat/9805235 · doi:10.1007/s100510050437
Abstract
It is shown that the appearance of a fixed-point singularity in the kernel of the two-electron Cooper problem is responsible for the formation of the Cooper pair for an arbitrarily weak attractive interaction between two electrons. This singularity is absent in the problem of three and few superconducting electrons at zero temperature on the full Fermi sea. Consequently, such three- and few-electron systems on the full Fermi sea do not form Cooper-type bound states for an arbitrarily weak attractive pair interaction.
arXiv comment10 pages. Accepted in European Physical Journal B