Eur. Phys. J. B 32, 145-155 (2003)
https://doi.org/10.1140/epjb/e2003-00083-9

Electron-electron bound states in Maxwell-Chern-Simons-Proca QED₃

¹ Grupo de Física Teórica José Leite Lopes Petrópolis, RJ, Brazil
² Centro Brasileiro de Pesquisas Físicas (CBPF), Coordenação de Teoria de Campos e Partículas (CCP), Rua Dr. Xavier Sigaud 150, Rio de Janeiro, RJ 22290-180, Brazil
³ Universidade Federal do Maranhão (UFMA), Departamento de Física, Campus Universitário do Bacanga, São Luiz, MA, 65085-580, Brazil

Corresponding authors: ^a belich@cbpf.br - ^b delcima@cbpf.br - ^c manojr@cbpf.br - ^d helayel@cbpf.br

Received: 24 September 2002
Revised: 15 January 2003
Published online: 1 April 2003

Abstract

We start from a parity-breaking MCS QED₃ model with spontaneous breaking of the gauge symmetry as a framework for evaluation of the electron-electron interaction potential and for attainment of numerical values for the bound state. Three expressions (, , are obtained according to the polarization state of the scattered electrons. In an energy scale compatible with condensed matter electronic excitations, these three potentials become degenerated. The resulting potential is implemented in the Schrödinger equation and the variational method is applied to carry out the electronic binding energy. The resulting binding energies in the scale of  meV and a correlation length in the scale of  Å are possible indications that the MCS-QED₃ model adopted may be suitable to address an eventual case of pairing in the presence of parity-symmetry breakdown. The data analyzed here suggest an energy scale of  meV to fix the breaking of the U(1)-symmetry.