Fermion-pairing on a square lattice in extreme magnetic fields

Details Fermion-pairing on a square lattice in extreme magnetic fields Fermion-pairing on a square lattice in extreme magnetic fields

2001-11-15

arxiv.org/abs/cond-mat/0111279v1

Physics

Condensed Matter

Superconductivity

7 pages, 3 figures

Scientific paper

10.1016/S0921-4534(02)01345-X

We consider the Cooper-problem on a two-dimensional, square lattice with a uniform, perpendicular magnetic field. Only rational flux fractions are considered. An extended (real-space) Hubbard model including nearest and next nearest neighbor interactions is transformed to "k-space", or more precisely, to the space of eigenfunctions of Harper's equation, which constitute basis functions of the magnetic translation group for the lattice. A BCS-like truncation of the interaction term is performed. Expanding the interactions in the basis functions of the irreducible representations of the point group $C_{4\nu}$ of the square lattice simplify calculations. The numerical results indicate enhanced binding compared to zero magnetic field, and thus re-entrant superconducting pairing at extreme magnetic fields, well beyond the point where the usual semi-classical treatment of the magnetic field breaks down.

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