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The BCS Ground State

  • Shigeji Fujita
  • Kei Ito
  • Salvador Godoy
Chapter

We assume a generalized BCS Hamiltonian which contains the kinetic energies of “electrons” and “holes”, and the pairing Hamiltonian arising from the phonon-exchange attraction and the Coulomb repulsion. We follow the original BCS theory to construct a many-pairon ground state and find a ground state energy: \(W=(1/2)N_{0}(w_{1}+w_{2})\), where \(N_{0}\) is the total number of the pairons, and \(w_{1}\) and \(w_{2}\) are respectively the ground state energies of “electron” (\(j=1\)) and “hole” (\(j=2\)) pairons. Energy gaps \(\Delta_{j}\) are found in the quasi-electron excitation spectra: \(E_{k}^{(j)}\equiv (\epsilon_{k}^{2}+\Delta_{j}^{2})^{1/2}\).

Keywords

Fermi Surface Ground State Energy Cooper Pair Bulk Limit Section Section 
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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Dept. PhysicsState University of New YorkBuffaloUSA
  2. 2.National Center for University Entrance ExaminationTokyoJapan
  3. 3.Depto. FísicaUniversidad Nacional Autónoma de MéxicoMéxicoMéxico

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