Dimensional effects on the tunneling conductivity of gold-implanted nanocomposite films

We study the dependence of the electrical conductivity on the gold concentration of Au-implanted polymethylmethacrylate (PMMA) and alumina nanocomposite thin films. For Au contents larger than a critical concentration, the conductivity of Au-PMMA and Au-alumina is well described by percolation in two dimensions, indicating that the critical correlation length for percolation is larger than the thickness of the films. Below the critical loading, the conductivity is dominated by tunneling processes between isolated Au particles dispersed in PMMA or alumina continuous matrices. Using an effective medium analysis of the tunneling conductivity, we show that Au-PMMA behaves as a tunneling system in two dimensions, as the film thickness is comparable to the mean Au particle size. On the contrary, the conductivity of Au-alumina films is best described by tunneling in three dimensions, although the film thickness is only a few times larger than the particle size. We interpret the enhancement of the effective dimensionality of Au-alumina films in the tunneling regime as due to the larger film thickness as compared to the mean interparticle distances.Comment: 7 pages, 7 figure

The small polaron crossover: comparison between exact results and vertex correction approximation

We study the crossover from quasi free electron to small polaron in the Holstein model for a single electron by means of both exact and self-consistent calculations in one dimension and on an infinite coordination lattice. We show that the crossover occurs when both strong coupling and multiphonon conditions are fulfilled leading to different relevant coupling constants in adiabatic and anti-adiabatic region of the parameters space. We also show that the self-consistent calculations obtained by including the first electron-phonon vertex correction give accurate results in a sizeable region of the phase diagram well separated from the polaronic crossover.Comment: 6 pages, revtex (europhys.sty,euromacr.tex); 3 postscript figure

The physical origin of the electron-phonon vertex correction

The electron-phonon vertex correction has a complex structure both in momentum and frequency. We explain this structure on the basis of physical considerations and we show how the vertex correction can be decomposed into two terms with different physical origins. In particular, the first term describes the lattice polarization induced by the electrons and it is essentially a single-electron process whereas the second term is governed by the particle-hole excitations due to the exchange part of the phonon-mediated electron-electron interaction. We show that by weakening the influence of the exchange interaction the vertex takes mostly positive values giving rise to an enhanced effective coupling in the scattering with phonons. This weakening of the exchange interaction can be obtained by lowering the density of the electrons, or by considering only long-ranged (small q) electron-phonon couplings. These findings permit to understand why in the High-Tc materials the small carrier density and the long ranged electron-phonon interaction may play a positive role in enhancing Tc.Comment: 11 pages, 5 postscript figure

Anomalous impurity effects in nonadiabatic superconductors

We show that, in contrast with the usual electron-phonon Migdal-Eliashberg theory, the critical temperature Tc of an isotropic s-wave nonadiabatic superconductor is strongly reduced by the presence of diluted non-magnetic impurities. Our results suggest that the recently observed Tc-suppression driven by disorder in K3C60 [Phys. Rev. B vol.55, 3866 (1997)] and in Nd(2-x)CexCuO(4-delta) [Phys. Rev. B vol.58, 8800 (1998)] could be explained in terms of a nonadiabatic electron-phonon coupling. Moreover, we predict that the isotope effect on Tc has an impurity dependence qualitatively different from the one expected for anisotropic superconductors.Comment: 10 pages, euromacr.tex, europhys.sty, 6 figures. Replaced with accepted version (Europhysics Letters

Anisotropic random resistor networks: a model for piezoresistive response of thick-film resistors

A number of evidences suggests that thick-film resistors are close to a metal-insulator transition and that tunneling processes between metallic grains are the main source of resistance. We consider as a minimal model for description of transport properties in thick-film resistors a percolative resistor network, with conducting elements governed by tunneling. For both oriented and randomly oriented networks, we show that the piezoresistive response to an applied strain is model dependent when the system is far away from the percolation thresold, while in the critical region it acquires universal properties. In particular close to the metal-insulator transition, the piezoresistive anisotropy show a power law behavior. Within this region, there exists a simple and universal relation between the conductance and the piezoresistive anisotropy, which could be experimentally tested by common cantilever bar measurements of thick-film resistors.Comment: 7 pages, 2 eps figure

Pauli susceptibility of nonadiabatic Fermi liquids

The nonadiabatic regime of the electron-phonon interaction leads to behaviors of some physical measurable quantities qualitatively different from those expected from the Migdal-Eliashberg theory. Here we identify in the Pauli paramagnetic susceptibility $\chi$ one of such quantities and show that the nonadiabatic corrections reduce $\chi$ with respect to its adiabatic limit. We show also that the nonadiabatic regime induces an isotope dependence of $\chi$, which in principle could be measured.Comment: 7 pages, 3 figures, euromacr.tex, europhys.sty. Replaced with accepted version (Europhysics Letters

Isotope effects in the Hubbard-Holstein model within dynamical mean-field theory

We study the isotope effects arising from the coupling of correlated electrons with dispersionless phonons by considering the Hubbard-Holstein model at half-filling within the dynamical mean-field theory. In particular we calculate the isotope effects on the quasi-particle spectral weight $Z$, the renormalized phonon frequency, and the static charge and spin susceptibilities. In the weakly correlated regime $U/t \lesssim 1.5$, where $U$ is the Hubbard repulsion and $t$ is the bare electron half-bandwidth, the physical properties are qualitatively similar to those characterizing the Holstein model in the absence of Coulomb repulsion, where the bipolaronic binding takes place at large electron-phonon coupling, and it reflects in divergent isotope responses. On the contrary in the strongly correlated regime $U/t \gtrsim 1.5$, where the bipolaronic metal-insulator transition becomes of first order, the isotope effects are bounded, suggesting that the first order transition is likely driven by an electronic mechanism, rather then by a lattice instability. These results point out how the isotope responses are extremely sensitive to phase boundaries and they may be used to characterize the competition between the electron-phonon coupling and the Hubbard repulsion.Comment: 10 pages, 8 figures. The paper has been already accepted on Phys. Rev.

Longitudinal and transversal piezoresistive response of granular metals

In this paper, we study the piezoresistive response and its anisotropy for a bond percolation model of granular metals. Both effective medium results and numerical Monte Carlo calculations of finite simple cubic networks show that the piezoresistive anisotropy is a strongly dependent function of bond probability p and of bond conductance distribution width \Delta g. We find that piezoresistive anisotropy is strongly suppressed as p is reduced and/or \Delta g is enhanced and that it vanishes at the percolation thresold p=p_c. We argue that a measurement of the piezoresistive anisotropy could be a sensitive tool to estimate critical metallic concentrations in real granular metals.Comment: 14 pages, 7 eps figure