A Quantum Percolation Model for Magnetoconductance of Granular Metal Films
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A QUANTUM PERCOLATION MODEL FOR MAGNETOCONDUCTANCE OF GRANULAR METAL FILMS ZHAO-QING ZHANG* AND PING SHENG Exxon Research & Engineering Co., Route 22 East, Annandale, NJ 08801 *Also at Bartol Research Institute, University of Delaware, Newark, 19716
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ABSTRACT A quantum percolation model is introduced to study the magnetoconductance of granular metal films. This model incorporates the granular property of the films and enables us to study the magnetoconductance in the strong scattering regime. Our calculations show a sign change in magnetoconductance as the temperature varies. There also exist oscillations in the magnetoconductance as the magnetic field is increased. Both observations are consistent with some recent experimental data. INTRODUCTION When a magnetic field is applied to a conducting sample in direction perpendicular to the electric field, measured resistance usually increases because the magnetic field bends the trajectories of charge carriers away from the electric field direction. Granular metals constitute one of the few material systems where the resistance is actually observed to decrease upon the application of a magnetic field [1]. In the metallic regime of granular metal samples, this anomalous effect may be qualitatively understood as the manifestation of incipient electron localization. The diffusive motion of an electron, resulting from multiple scattering, can be modified by a coherent backscattering effect [2,3] peculiar to the wave-nature of electrons. A simple physical picture of the coherent backscattering effect is as follows. Two parallel rays, one denoted by the solid line and one by the dashed line, are incident on a random medium as shown in Fig. 1. After undergoing random scatterings In the medium, what emerges in the backscattering direction is a sum of many different scattering path amplitudes. This is true for both the solid and the dashed rays. In the figure we have shown only one of such scattering paths for illustration. For those rays that emerge exactly 180° from the direction of the incident ray (as the one shown by the solid line), one can always find identical time-reversed paths (such as the one shown by the dashed line) that have identical phases. In other words, time reversal invariance guarantees that in the 1800 backscattering direction the waves are coherent, in spite of multiple scattering. This property,
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Fig. 1 - A schematic picture of 180° backscattering path (solid line) and its time-reversed path (dashed line). Mat. Res. Soc. Symp. Proc. Vol. 195. 01990 Materials Research Society
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not valid for scattering into other angles, insures that the resulting constructive interference would exactly double the probability density of scattering into the backward direction than into other directions. Such an effect has been demonstrated experimentally using electromagnetic waves [2,3]. Since the above effect is generic to waves, its demonstration using light also implies its validity for electrons. A direct physical consequence of coherent backscattering i
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