Superlattices and Microstructures, Vol. 23, No. 3/4, 1998 Magnetotransport in a periodic composite medium: New phenomena in a classical physics context David J. Bergman, Yakov M. Strelniker School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv 69978, Israel (Received 30 September 1997) The magnetotransport properties of a composite conductor with a periodic microstructure have recently been studied both theoretically and numerically using a local classical con- tinuum physics description of the transport at the microscale. Surprising new phenomena were discovered, including an induced magnetoresistance which oscillates strongly when the magnetic field is sufficiently strong and is rotated with respect to the microstructure. A surprising aspect of this phenomenon is that the effect is much stronger when the mi- crostructure is two dimensional than when it is three dimensional. The physical reasons for this are discussed. Briefly, this is concerned with the question of whether the current distribution saturates with increasing strength of the magnetic field. In two-dimensional metal-insulator microstructures, the magnetoresistance usually does not saturate. But when it does, some components of the local current distribution must exhibit a surprising degree of uniformity over the conducting constituent. c  1998 Academic Press Limited Key words: magnetotransport, magnetoresistance, composite medium. 1. Introduction It is often assumed that any interesting new phenomena in solid materials must have their origins in quantum behavior. The rationalization which underlies this prejudice is that such materials have been studied for so long that all the important phenomena which can arise in the context of a classical continuum physics picture have already been discovered. A recent example that belies this expectation are the surprising magnetotransport properties of composite conductors which have a periodic microstructure [1]. When different homogeneous conductors are mixed together to make a macroscopically inhomogeneous or composite medium, the bulk effective transport properties will usually include a non-vanishing magnetore- sistance, even when each component is either a simple free-electron conductor or a perfect insulator. This can be understood as follows. When a prescribed average (i.e., volume average) current density 〈J〉 is made to flow through the composite medium, the local current density J(r) is usually non-uniform, and its magnitude as well as its direction vary from point to point. Therefore, in the presence of an external magnetic field B, the local electric Hall field E H ∝ (B × J) usually has a non-vanishing component along 〈J〉. The bulk effective ohmic resistivity ρ e in the direction of 〈J〉 is found from ρ e ≡ 〈J〉·〈E〉 〈J〉 2 . (1.1) 0749–6036/98/030547 + 11 $25.00/0 sm970522 c  1998 Academic Press Limited