Critical points in the macroscopic magnetotransport of normal conductor/perfect insulator/perfect conductor disordered composites

Abstract

The magnetotransport in a disordered composite medium, made of normal conductor, perfect insulator, and perfect conductor constituents, exhibits singular or critical point behavior at certain compositions, in the limit where the Hall conductivity of the normal constituent is much greater than its transverse Ohmic conductivity, but much less than its longitudinal Ohmic conductivity, e.g., if that constituent is an isotropic conductor and ${\ensuremath{\omega}}_{c}\ensuremath{\tau}\ensuremath{\gg}1.$ At those compositions the asymptotic behavior of the macroscopic Ohmic resistivity changes abruptly from saturating to nonsaturating dependence upon ${\ensuremath{\omega}}_{c}\ensuremath{\tau}.$ Near those compositions, the magnetotransport exhibits a characteristic scaling behavior. A different critical behavior is exhibited near those same compositions even when the Hall conductivity is negligible, but the longitudinal transverse Ohmic conductivity (i.e., along the magnetic-field direction) is much greater than the transverse Ohmic conductivity. In three-dimensional microstructures, both types of critical points are related to the phenomenon of anisotropic percolation. In two-dimensional or columnar microstructures, the location and character of the critical point depend on the direction of the magnetic field with respect to the columnar axis. Self-consistent effective-medium approximations are employed to discuss these critical points for two-dimensional as well as for three-dimensional microstructures.