Variational method is used to investigate, at zero temperature, the deformed-
Fermi-surfaces mechanism for solving the problem of superconducting pairing of two
species of fermions (i.e., spin-up and -down) of mismatched Fermi surfaces due to
the existence of a uniform exchange or Zeeman field. After analyzing the depairing
regions in the whole three-dimensional parameter space, we obtain a trial groundstate
wave-function as a function of the three variational parameters, one of which is
the gap function. Then within the frame work of the weak-coupling BCS theory, the
expectation value of the Hamiltonian of a conductor under an exchange or Zeeman
field is derived, from which a gap equation is derived by differentiation. The influence
of deformed Fermi surfaces on the chemical potential is then calculated. Computer
programing is finally used to solve the gap equation, and find the minimum-energy
state with respect to the remaining two variational parameters (δµ and z). These
two parameters are better than the original parameters used in the trial Hamiltonian
when compared with the FF state. And we also found if we keep the total number of
electrons fixed, the system prefers an unchanged chemical potential and the ground state energy of the deformed-Fermi-surfaces state, which is found to be an angle
dependent case of Sarma’s solution III, is no better than that of the unpolarized
BCS state.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2111 |
| Date | 15 May 2009 |
| Creators | Lu, Jianxu |
| Contributors | Hu, Chia-ren |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Thesis, text |
| Format | electronic, application/pdf, born digital |
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