Nearly 3 orders of magnitude enhancement in the Hall coefficient is observed in Cu x -͑SiO 2 ͒ 12x granular films. This large enhancement of the Hall coefficient not only is significantly larger than the prediction of the classical percolation theory, but also occurs at a metal concentration identified to be the quantum percolation threshold. Measurements of the electron dephasing length and magnetoresistance, plus the TEM characterization of microstructures, yield a physical picture consistent with the mechanism of the local quantum interference effect. DOI: 10.1103/PhysRevLett.86.5562 PACS numbers: 72.20.My, 71.30. +h, 72.80.Tm, 73.50.Jt As a basic material constant, the Hall coefficient is generally indicative of the density and sign of the charge carriers. Thus, in granular metals, as the metal concentration decreases, the lower carrier density is expected to yield an enhanced Hall coefficient which peaks at the percolations threshold with a factor of ϳ30 for ϳ1 mm thick films [1,2]. Recently, however, it was found that in the magnetic ͑NiFe͒-SiO 2 , and Fe-SiO 2 granular films [2-5], the extraordinary Hall coefficient was enhanced by a factor of 10 4 when the metal volume fraction is close to x 0.53 (the classical percolation threshold). An especially intriguing feature of this discovery is that, even after magnetic saturation, the ordinary Hall coefficient was still observed to increase by almost 3 orders of magnitude [4], suggesting a magnetic-independent mechanism could be operative.In this Letter, we focus on the origin of the ordinary giant Hall effect (GHE) by studying the nonmagnetic Cu-SiO 2 granular system. We find the same 3 orders of magnitude enhancement in the Hall coefficient. By carrying out measurements on the electron dephasing length and the magnetoresistance (MR), and by characterizing our samples by transmission electron microscope (TEM) pictures, we find the Hall coefficient to peak at the quantum percolation threshold. Based on the picture that inhomogeneities (due to the small substructures) inside a dephasing length would necessarily cause local quantum interference and thereby modify the effective local properties, we show that all experimental data can be quantitatively accounted for within this simple framework. In particular, when the small substructures are suppressed through annealing, the GHE is shown to disappear, in agreement with the theoretical prediction [6].Cu-SiO 2 granular films with different metal volume fractions were fabricated by using the cosputtering technique with a glass or Kapton substrate, at a temperature of 50 ± C. The base pressure of the chamber was kept below 2 3 10 27 Torr. The films deposited on the glass were used for transport measurements and the films on Kapton were for composition determination. The metal volume fraction x for all the films was obtained from energydispersive x-ray spectroscopy analysis. The dc resistance was measured by using the standard four-probe technique, and the Hall resistance was measured by using the five-contacts me...

The mixed quantum-classical Liouville equation is derived from a semiclassical perspective starting from the full quantum Schrödinger equation. An asymptotic numerical scheme for solving the equation is discussed which relies on propagating swarms of interacting “threads” which represent the density matrix or other observable. It is demonstrated that this “multithreads” method performs extremely well on simple one-dimensional model systems designed to test nonadiabatic molecular dynamic methods, yielding essentially exact results for a variety of models.

In this article, an exact surface-hopping procedure and an approximate asymptotic method for performing molecular dynamics based on a mixed quantum-classical Liouville equation ͓J. Chem. Phys. 110, 8919 ͑1999͔͒ for partially Wigner transformed dynamical variables of a coupled quantum subsystem and classical bath are elaborated. The methods are based upon writing the equations of motion in a basis set in which quantum transitions do not alter the classical trajectory, and therefore avoid ad-hoc momentum jump approximations and are free of singular kernels associated with sampling momenta. 2 Results obtained utilizing the new trajectory methods are presented for a model two-level system bilinearly coupled to a classical harmonic oscillator. These results are compared to results obtained from standard methods of performing mixed quantum-classical dynamics. The new methods perform well for the model system over a wide range of initial kinetic energies.

We show that in metallic percolating networks the wave nature of the charge carriers can significantly modify the classical picture of the Hall effect, especially in the metal concentration range xϷx q , where x denotes the metal volume, and x q the quantum-percolation threshold. Calculations based on the model of local quantum interference effect are shown to give a consistent and quantitative account of the recent experimental findings on the ͑ordinary͒ giant Hall effect. DOI: 10.1103/PhysRevB.66.075309 PACS number͑s͒: 72.20.My, 72.15.Rn, 73.50.Jt Percolation is a geometric concept basic to the study of physical properties of inhomogeneous materials. In metalinsulator composites, the assumption that the charge carriers are classical point particles leads directly to the prediction of a conductivity transition at the geometric percolation threshold x c , below which the metallic component can no longer form an infinite network. Consideration of the wave nature of the physical charge carriers ͑electrons͒, however, leads to a somewhat different picture at temperature Tϭ0, when inelastic scattering is absent. That is, multiple scattering of the electronic waves induced by the random percolating geometry of the conducting channels inevitably localizes the electronic wave functions at a metal concentration x q Ͼx c ͓x q ϭ1 in one-dimensional ͑1D͒ and 2D samples͔, denoted the quantum mobility edge. As a result, for x c ϽxϽx q the predictions of the classical-and the quantum-percolation models are at odds with each other: Whereas the metallic networks are connected and therefore the classical-percolation model predicts metallic behavior, the quantum-percolation model predicts a nonmetallic behavior. 1 Indeed, both types of behavior have been observed in thin ͑2D͒ metallic films. Whereas the nonmetallic temperature dependence observed at low temperatures is widely accepted as due to the weaklocalization effect arising from quantum wave interferences, 2,3 at higher temperatures inelastic scattering is seen to suppress wave effects and restore the metallic behavior predicted by classical percolation. Beyond the 2D samples and the weak localization at low temperatures, however, consideration of quantum wave interference effects has been lacking for Hall effect in 3D samples in the concentration range xϳx q , where wave effects could be potentially significant. In view of recent experimental findings on the giant Hall effect ͑GHE͒, 4 -7 a theory of Hall effect that takes into consideration the wave effects would be especially called for.As a basic material constant, the Hall coefficient is generally indicative of the density and sign of the charge carriers. Thus, in granular metals, as the metal concentration decreases, the lower carrier density is expected to yield an enhanced Hall coefficient that peaks at the percolation threshold with a factor of ϳ30 for ϳ1 m thick films. 4 Recently, however, it was found that in the magnetic (NiFe)SiO 2 and FeSiO 2 granular films, 4 -7 the extraordinary Hall coefficient was enhan...