Strong-field magnetotransport in a normal conductor/perfect conductor/insulator disordered composite material: Simulations of a discrete model

Abstract

We consider a two-dimensional disordered composite medium made of three constituents: a normal conductor, a perfect conductor, and an insulator, and we examine its macroscopic electrical response in cases where it is subject to a strong magnetic field applied perpendicular to its plane. To this end, we exploit a discrete network model and apply a Monte Carlo procedure for sampling ensembles of finite-size three-constituent networks of this kind. The simulations indicate that when the perfectly conducting and insulating constituents are below the percolation threshold, such that the material has a finite, nonvanishing conductivity tensor, two distinct behaviors of the macroscopic magnetoresistance appear, according to whether the normal conductor by itself is below or above the percolation threshold. When the area fraction of the normal conductor is below that threshold, the macroscopic induced magnetoresistance is found to keep increasing with the magnetic field, without any saturation, whereas when that area fraction is above the percolation threshold, the magnetoresistance is found to saturate. Thus, the percolation threshold of the normal conductor is identified as a critical point. This critical phenomenon is associated with both a geometrical percolation and the presence of a large Hall effect. Its origin can be qualitatively understood by noticing the surprising fact that, in the strong-field limit, a perfectly conducting inclusion surrounded by a normally conducting neighborhood tends to expel currents almost like an insulating inclusion. The simulations also provide insights into difficulties that arise when simulating finite-size conducting networks at strong magnetic fields.