Fermions in an anisotropic random magnetic field

We study the localization of fermions in an anisotropic random magnetic field in two dimensions. It is assumed that the randomness in a particular direction is stronger than those in the other directions. We consider a network model of zero field contours, where there are two types of randomness - the random tunneling matrix element at the saddle points and unidirectional random variation of the number of fermionic states following zero field contours. After averaging over the random complex tunneling amplitude, the problem is mapped to an SU(2N) random exchange quantum spin chain in the $N \to 0$ limit. We suggest that the fermionic state becomes critical in an anisotropic fashion.Comment: 5 pages, replaced by revised version, accepted for publication in Europhysics Letter

A Constraint on the Anomalous Green's Function

It is shown that the physical constraint of the Anomalous Green's function gives a natural pairing condition. The resulting self-consistency equation is directly related to the BCS gap equation. Both inhomogeneous and homogeneous systems are considered to illustrate the importance of the constraint. Especially we find weak localization correction to the phonon-mediated interaction.Comment: 14 pages, latex, no figure