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Relation between BCS Hamiltonian and Ginzburg–Landau equation

✍ Scribed by Shigeyuki Aono

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
194 KB
Volume
69
Category
Article
ISSN
0020-7608

No coin nor oath required. For personal study only.

✦ Synopsis

It is intended to derive the Ginzburg᎐Landau GL equation directly

Ž

. from the Bardeen᎐Cooper᎐Schrieffer BCS Hamiltonian. By the use of the Hubbard᎐Stratonovitch transformation, the electron᎐electron interaction composed of four fermion operators is eliminated to yield an auxiliary boson field. This is an effective field in which electrons behave as if they were free. In applying the path integral method, the electron field is integrated out to remain the Lagrangian for this boson field. The symmetry breaking and the phase transition of the system described by this field are discussed, and it is shown that this boson field turns out to be the GL order parameter.

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