Quantum Correction to Conductivity Close to Ferromagnetic Quantum Critical Point in Two Dimensions

We study the temperature dependence of the conductivity due to quantum interference processes for a two-dimensional disordered itinerant electron system close to a ferromagnetic quantum critical point. Near the quantum critical point, the cross-over between diffusive and ballistic regimes of quantum interference effects occurs at a temperature $T^{\ast}=1/\tau \gamma (E_{F}\tau)^{2}$, where $\gamma$ is the parameter associated with the Landau damping of the spin fluctuations, $\tau$ is the impurity scattering time, and $E_{F}$ is the Fermi energy. For a generic choice of parameters, $T^{\ast}$ is smaller than the nominal crossover scale $1/\tau$. In the ballistic quantum critical regime, the conductivity behaves as $T^{1/3}$.Comment: 5 pages, 1 figur

Multi-scale fluctuations near a Kondo Breakdown Quantum Critical Point

We study the Kondo-Heisenberg model using a fermionic representation for the localized spins. The mean-field phase diagram exhibits a zero temperature quantum critical point separating a spin liquid phase where the f-conduction hybridization vanishes, and a Kondo phase where it does not. Two solutions can be stabilized in the Kondo phase, namely a uniform hybridization when the band masses of the conduction electrons and the f spinons have the same sign, and a modulated one when they have opposite sign. For the uniform case, we show that above a very small Fermi liquid temperature scale (~1 mK), the critical fluctuations associated with the vanishing hybridization have dynamical exponent z=3, giving rise to a specific heat coefficient that diverges logarithmically in temperature, as well as a conduction electron inverse lifetime that has a T log T behavior. Because the f spinons do not carry current, but act as an effective bath for the relaxation of the current carried by the conduction electrons, the latter result also gives rise to a T log T behavior in the resistivity. This behavior is consistent with observations in a number of heavy fermion metals.Comment: 17 pages, 10 figure

Violation of Wiedemann-Franz law at the Kondo breakdown quantum critical point

We study both the electrical and thermal transport near the heavy-fermion quantum critical point (QCP), identified with the breakdown of the Kondo effect as an orbital selective Mott transition. We show that the contribution to the electrical conductivity comes mainly from conduction electrons while the thermal conductivity is given by both conduction electrons and localized fermions (spinons), scattered with dynamical exponent $z = 3$. This scattering mechanism gives rise to a quasi-linear temperature dependence of the electrical and thermal resistivity. The characteristic feature of the Kondo breakdown scenario turns out to be emergence of additional entropy carriers, that is, spinon excitations. As a result, we find that the Wiedemann-Franz ratio should be larger than the standard value, a fact which enables to differentiate the Kondo breakdown scenario from the Hertz-Moriya-Millis framework

Selective Mott transition and heavy fermions

Starting with an extended version of the Anderson lattice where the f-electrons are allowed a weak dispersion, we examine the possibility of a Mott localization of the f-electrons, for a finite value of the hybridization $V$. We study the fluctuations at the quantum critical point (QCP) where the f-electrons localize. We find they are in the same universality class as for the Kondo breakdown QCP, with the following notable features. The quantum critical regime sees the appearance of an additional energy scale separating two universality classes. In the low energy regime, the fluctuations are dominated by massless gauge modes, while in the intermediate energy regime, the fluctuations of the modulus of the order parameter are the most relevant ones. In the latter regime, electric transport simplifies drastically, leading to a quasi-linear resistivity in 3D and anomalous exponents lower than T in 2 D. This rather unique feature of the quantum critical regime enables us to make experimentally testable predictions.Comment: 27 pages, 5 figure

Low energy excitations and singular contributions in the thermodynamics of clean Fermi liquids

Using a recently suggested method of bosonization in an arbitrary dimension, we study the anomalous contribution of the low energy spin and charge excitations to thermodynamic quantities of a two-dimensional (2D) Fermi liquid. The method is slightly modified for the present purpose such that the effective supersymmetric action no longer contains the high energy degrees of freedom but still accounts for effects of the finite curvature of the Fermi surface. Calculating the anomalous contribution $\delta c(T)$ to the specific heat, we show that the leading logarithmic in temperature corrections to $\delta c(T)/T^2$ can be obtained in a scheme combining a summation of ladder diagrams and renormalization group equations. The final result is represented as the sum of two separate terms that can be interpreted as coming from singlet and triplet superconducting excitations. The latter may diverge in certain regions of the coupling constants, which should correspond to the formation of triplet Cooper pairs.Comment: 29 pages, 13 figure

Density of states in d-wave superconductors disordered by extended impurities

The low-energy quasiparticle states of a disordered d-wave superconductor are investigated theoretically. A class of such states, formed via tunneling between the Andreev bound states that are localized around extended impurities (and result from scattering between pair-potential lobes that differ in sign) is identified. Its (divergent) contribution to the total density of states is determined by taking advantage of connections with certain one-dimensional random tight-binding models. The states under discussion should be distinguished from those associated with nodes in the pair potential.Comment: 5 pages, 1 figur

Temperature and ac Effects on Charge Transport in Metallic Arrays of Dots

We investigate the effects of finite temperature, dc pulse, and ac drives on the charge transport in metallic arrays using numerical simulations. For finite temperatures there is a finite conduction threshold which decreases linearly with temperature. Additionally we find a quadratic scaling of the current-voltage curves which is independent of temperature for finite thresholds. These results are in excellent agreement with recent experiments on 2D metallic dot arrays. We have also investigated the effects of an ac drive as well as a suddenly applied dc drive. With an ac drive the conduction threshold decreases for fixed frequency and increasing amplitude and saturates for fixed amplitude and increasing frequency. For sudden applied dc drives below threshold we observe a long time power law conduction decay.Comment: 6 pages, 7 postscript figure