Simulations of thermoelectric transport in granularsuperconductors

Sammanfattning: 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.