Eur. Phys. J. B 5, 219-222 (1998)
https://doi.org/10.1007/s100510050437

Absence of Cooper-type bound states in three- and few-electron systems

¹ Instituto de Física Teórica, Universidade Estadual Paulista, 01.405-900 São Paulo, São Paulo, Brazil
² Departamento de Física, Instituto Tecnológico Aeronautica, Centro Técnico Aeroespacial, 12228-900 São José dos Campos, São Paulo, Brazil

Corresponding author: ^a adhikari@axp.ift.unesp.br

Received: 9 February 1998
Accepted: 13 May 1998
Published online: 15 September 1998

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.