This thesis presents results from numerical simulations of the Nernst effect dueto phase fluctuations in models of two-dimensional granular superconductors. Inaddition other transport properties, such as thermal conductivity and electrical re-sistivity are calculated. The models are based on a phase only description withLangevin or resistively and capacitively shunted Josephson junction (RCSJ) dy-namics, generalized to be valid for any type of two-dimensional lattice structure.All transport coefficients are evaluated from equilibrium correlation functions usingKubo formulas.

In Paper I, anomalous sign reversals of the Nernst signal eN , corresponding tovortex motion from colder to hotter regions, are observed. These are attributedto geometric frustration effects close to magnetic fields commensurate with theunderlying lattice structure. The effect is seen also in systems with moderategeometric disorder, and should thus be possible to observe in real two-dimensionalgranular superconductors or Josephson junction arrays.

Paper II presents two different derivations of an expression for the heat current inLangevin and RCSJ dynamics. The resulting expression is through our simulationsseen to obey the required Onsager relation, as well as giving consistent resultswhen calculating κ and eN via Kubo formulas and through the responses to anapplied temperature gradient. In zero magnetic field and at low-temperatures, thecontribution to the thermal conductivity κ in RCSJ dynamics is calculated usinga spin-wave approximation, and is shown to be independent of temperature anddiverge logarithmically with system size. At higher temperatures, κ shows a non-monotonic temperature dependence. In zero magnetic field κ has a anomalouslogarithmic size dependence also in this regime. The off-diagonal component ofthe thermoelectric tensor αxy is calculated and displays the very same ∼1/T dependence at low temperatures predicted from calculations based on Gaussiansuperconducting fluctuations.

We study the Nernst effect due to vortex motion in two-dimensional granular superconductors using simulations with Langevin or resistively shunted Josephson-junction dynamics. In particular, we show that the geometric frustration of both regular and irregular granular materials can lead to thermally driven transport of vortices from colder to hotter regions, resulting in a sign reversal of the Nernst signal. We discuss the underlying mechanisms of this anomalous behavior in terms of heat transport by mobile vacancies in an otherwise pinned vortex lattice.

We study heat transport and thermoelectric effects in two-dimensional superconductors in a magnetic field. These are modeled as granular Josephson-junction arrays, forming either regular or random lattices. We employ two different models for the dynamics: relaxational model-A dynamics or resistively and capacitively shunted Josephson junction dynamics. We derive expressions for the heat current in these models, which are then used in numerical simulations to calculate the heat conductivity and Nernst coefficient for different temperatures and magnetic fields. At low temperatures and zero magnetic field the heat conductivity in the RCSJ model is calculated analytically from a spin wave approximation, and is seen to have an anomalous logarithmic dependence on the system size, and also to diverge in the completely overdamped limit C -> 0. From our simulations we find at low magnetic fields that the Nernst signal displays a characteristic "tilted hill" profile similar to experiments and a nonmonotonic temperature dependence of the heat conductivity. We also investigate the effects of granularity and randomness, which become important for higher magnetic fields. In this regime geometric frustration strongly influences the results in both regular and random systems and leads to highly nontrivial magnetic field dependencies of the studied transport coefficients.

We study quantum phase slips (QPS) in ultrathin superconducting wires. Starting from an effective one-dimensional microscopic model, which includes electromagnetic fluctuations, we map the problem to a (1+1)-dimensional gas of interacting instantons. We introduce a method to calculate the tunneling amplitude of quantum phase slips directly from Monte Carlo simulations. This allows us to go beyond the dilute instanton gas approximation and study the problem without any limitations of the density of QPS. We find that the tunneling amplitude shows a characteristic scaling behavior near the superconductor-insulator transition. We also calculate the voltage-charge relation of the insulating state, which is the dual of the Josephson current-phase relation in ordinary superconducting weak links. This evolves from a sinusoidal form in the regime of dilute QPS to more exotic shapes for higher QPS densities, where interactions are important.

We revisit the scaling properties of the resistivity and the current-voltage characteristics at and below the Berezinskii-Kosterlitz-Thouless transition, both in zero and nonzero magnetic field. The scaling properties are derived by integrating the renormalization group flow equations up to a scale where they can be reliably matched to simple analytic expressions. The vortex fugacity turns out to be dangerously irrelevant for these quantities below $T_c$, thereby altering the scaling behavior. We derive the possible crossover effects as the current, magnetic field or system size is varied, and find a strong multiplicative logarithmic correction near $T_c$, all which is necessary to account for when interpreting experiments and simulation data. Our analysis clarifies a longstanding discrepancy between the finite size dependence found in many simulations and the current-voltage characteristics of experiments. We further show that the logarithmic correction can be avoided by approaching the transition in a magnetic field, thereby simplifying the scaling analysis. We confirm our results by large scale numerical simulations, and calculate the dynamic critical exponent $z$, for relaxational Langevin dynamics and for resistively and capacitively shunted Josephson junction dynamics.

8.

Andersson, Andreas

et al.

KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.

Lidmar, Jack

KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.

We revisit the scaling properties of the resistivity and the current-voltage characteristics at and below the Berezinskii-Kosterlitz-Thouless transition, both in zero and nonzero magnetic fields. The scaling properties are derived by integrating the renormalization group flow equations up to a scale where they can be reliably matched to simple analytic expressions. The vortex fugacity turns out to be dangerously irrelevant for these quantities below T-c, thereby altering the scaling behavior. We derive the possible crossover effects as the current, magnetic field, or system size is varied, and find a strong multiplicative logarithmic correction near T-c, all of which is necessary to account for when interpreting experiments and simulation data. Our analysis clarifies a longstanding discrepancy between the finite size dependence found in many simulations and the current-voltage characteristics of experiments. We further show that the logarithmic correction can be avoided by approaching the transition in a magnetic field, thereby simplifying the scaling analysis. We confirm our results by large-scale numerical simulations, and calculate the dynamic critical exponent z, for relaxational Langevin dynamics and for resistively and capacitively shunted Josephson junction dynamics.