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Critical point for the strong field magnetoresistance of a normal conductor/perfect insulator/perfect conductor composite with a random columnar microstructure

David J. Bergman
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Abstract

A recently developed self-consistent effective medium approximation, for composites with a columnar microstructure, is applied to such a three-constituent mixture of isotropic normal conductor, perfect insulator, and perfect conductor, where a strong magnetic field {\bf B} is present in the plane perpendicular to the columnar axis. When the insulating and perfectly conducting constituents do not percolate in that plane, the microstructure-induced in-plane magnetoresistance is found to saturate for large {\bf B}, if the volume fraction of the perfect conductor $p_S$ is greater than that of the perfect insulator $p_I$. By contrast, if $p_S<p_I$, that magnetoresistance keeps increasing as ${\bf B}^2$ without ever saturating. This abrupt change in the macroscopic response, which occurs when $p_S=p_I$, is a critical point, with the associated critical exponents and scaling behavior that are characteristic of such points. The physical reasons for the singular behavior of the macroscopic response are discussed. A new type of percolation process is apparently involved in this phenomenon.

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David J. Bergman. 2000-06-23. Critical point for the strong field magnetoresistance of a normal conductor/perfect insulator/perfect conductor composite with a random columnar microstructure. https://doi.org/10.1103/physrevb.62.13820

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