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Superconductivity with strongly correlated electrons and an electron–phonon interaction

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posted on 2018-09-19, 11:39 authored by Thomas M. Hardy
The effect on the stability of the superconducting phase due the addition of an electron–phonon interaction to a repulsive Hubbard model is studied. Our Hubbard–Fröhlich Hamiltonian includes electron hoping, the on-site Coulomb repulsion, vibrating ions (phonons) and the electron–phonon interaction. A Lang–Firsov transformation is used to integrate out the phonon degrees of freedom. The transformation reduces the model to simple a Hubbard Hamiltonian with an additional long-range electron–electron attraction. A variational Monte Carlo technique, with a projected BCS trial function, is used to investigate the ground state energies of our transformed Hubbard–Fröhlich Hamiltonian. For various electron densities, with a d-wave superconducting order parameter, it is found that the inclusion of the electron-phonon interaction significantly enhances the condensation energy (the energy required to break paired electrons). We show that increasing the strength of the electron-phonon interaction increases the condensation energy. It is also found that even with an infinite on-site repulsion, where the resonating valence bond state cannot exist, the EPI does still lead to a d-wave superconducting state. In addition we examine, analytically, the coexistence of ferromagnetism and superconductivity. Allowing different masses for spin-up and spin-down electrons in a BCS-type Hamiltonian two new branches in the energy spectrum are found. Including a spatially varying order parameter a new expression for the pairing amplitude of finite momentum pairs is derived.

Funding

EPSRC. Loughborough University (scholarship).

History

School

  • Science

Department

  • Physics

Publisher

© Thomas M. Hardy

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2009

Notes

A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy at Loughborough University.

Language

  • en

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