Non-linear thermoelectric transport: A class of nano-devices for high efficiency and large power output

Molecular junctions and similar devices described by an energy dependent transmission coefficient can have a high linear response thermoelectric figure of merit. Since such devices are inherently non-linear, the full thermodynamic efficiency valid for any temperature and chemical potential difference across the leads is calculated. The general features in the energy dependence of the tranmission function that lead to high efficiency and also high power output are determined. It is shown that the device with the highest efficiency does not necessarily lead to large power output. To illustrate this, we use a model called the t-stub model representing tunneling through an energy level connected to another energy level. Within this model both high efficiency and high power output are achievable. Futhermore, by connecting many nanodevices it is shown to be possible to scale up the power output without compromising efficiency in an (exactly solvable) n-channel model even with tunneling between the devices.

Scale-dependent correction to the dynamical conductivity of a disordered system at unitary symmetry

Anderson localization has been studied extensively for more than half a century. However, while our understanding has been greatly enhanced by calculations based on a small epsilon expansion in d = 2 + epsilon dimensions in the framework of non-linear sigma models, those results can not be safely extrapolated to d = 3. Here we calculate the leading scale-dependent correction to the frequency-dependent conductivity sigma(omega) in dimensions d <= 3. At d = 3 we find a leading correction Re{sigma(omega)} ~ |omega|, which at low frequency is much larger than the omega^2 correction deriving from the Drude law. We also determine the leading correction to the renormalization group beta-function in the metallic phase at d = 3.

Asymmetric metal-insulator transition in disordered ferromagnetic films

We present experimental data and a theoretical interpretation on the conductance near the metal-insulator transition in thin ferromagnetic Gd films of thickness b approximately 2-10 nm. A large phase relaxation rate caused by scattering of quasiparticles off spin wave excitations renders the dephasing length L_phi < b in the range of sheet resistances considered, so that the effective dimension is d = 3. The observed approximate fractional temperature power law of the conductivity is ascribed to the scaling regime near the transition. The conductivity data as a function of temperature and disorder strength collapse on to two scaling curves for the metallic and insulating regimes. The best fit is obtained for a dynamical exponent z approximately 2.5 and a correlation length critical exponent u approximately 1.4 on the metallic side and a localization length exponent u approximately 0.8 on the insulating side.

Solutions for correlations along the coexistence curve and at the critical point of a kagome lattice gas with three-particle interactions

We consider a two-dimensional (d=2) kagome lattice gas model with attractive three-particle interactions around each triangular face of the kagome lattice. Exact solutions are obtained for multiparticle correlations along the liquid and vapor branches of the coexistence curve and at criticality. The correlation solutions are also determined along the continuation of the curvilinear diameter of the coexistence region into the disordered fluid region. The method generates a linear algebraic system of correlation identities with coefficients dependent only upon the interaction parameter. Using a priori knowledge of pertinent solutions for the density and elementary triplet correlation, one finds a closed and linearly independent set of correlation identities defined upon a spatially compact nine-site cluster of the kagome lattice. Resulting exact solution curves of the correlations are plotted and discussed as functions of the temperature, and are compared with corresponding results in a traditional kagome lattice gas having nearest-neighbor pair interactions. An example of application for the multiparticle correlations is demonstrated in cavitation theory.

Disorder and temperature dependence of the Anomalous Hall Effect in thin ferromagnetic films: Microscopic model

We consider the Anomalous Hall Effect (AHE) in thin disordered ferromagnetic films. Using a microscopic model of electrons in a random potential of identical impurities including spin-orbit coupling, we develop a general formulation for strong, finite range impurity scattering. Explicit calculations are done within a short range but strong impurity scattering to obtain AH conductivities for both the skew scattering and side jump mechanisms. We also evaluate quantum corrections due to interactions and weak localization effects. We show that for arbitrary strength of the impurity scattering, the electron-electron interaction correction to the AH conductivity vanishes exactly due to general symmetry reasons. On the other hand, we find that our explicit evaluation of the weak localization corrections within the strong, short range impurity scattering model can explain the experimentally observed logarithmic temperature dependences in disordered ferromagnetic Fe films.

Power law eigenvalue density, scaling and critical random matrix ensembles

We consider a class of rotationally invariant unitary random matrix ensembles where the eigenvalue density falls off as an inverse power law. Under a new scaling appropriate for such power law densities (different from the scaling required in Gaussian random matrix ensembles), we calculate exactly the two-level kernel that determines all eigenvalue correlations. We show that such ensembles belong to the class of critical ensembles.