Europhys. Lett.
Volume 47, Number 2, July 1999
Page(s) 240 - 246
Section Condensed matter: electronic structure, electrical, magnetic and optical properties
Published online 01 September 2002
DOI: 10.1209/epl/i1999-00378-5

Europhys. Lett, 47 (2), pp. 240-246 (1999)

Localization of fermions in an anisotropic random magnetic field

Y.-B. Kim

Department of Physics, The Pennsylvania State University
University Park, PA 16802, USA
Institute for Theoretical Physics, University of California
Santa Barbara, CA 93106, USA

(received 16 April 1999; accepted 25 May 1999)

PACS. 72.10Bg - General formulation of transport theory.
PACS. 72.15Rn - Localization effects (Anderson or weak localization).
PACS. 71.55Jv - Disordered structures; amorphous and glassy solids.


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 the 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 $N \rightarrow 0$ limit. We suggest that the fermionic state becomes critical in an anisotropic fashion.


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