Anomalous Nernst effect and heat transport by vortex vacancies in granular superconductors

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.

Figure 1

(Color online) Nernst signal $e_N$ versus filling fraction $f$ for a $20\times 20$ square lattice at different temperatures $T$. Notice how the Nernst signal goes clearly negative in the region $0.4\lesssim f\lesssim 0.5$. Inset: zoom-in of $e_N$ at $T=0.19$ around $f=1/3$, where $e_N$ also becomes negative.

Figure 2

(Color online) Nernst signal $e_N$ versus filling fraction $f$ for a $20\times 20$ triangular lattice at different temperatures $T$. Here, $e_N$ shows more structure as a function of $f$, but again becomes clearly negative for $f$ between 0.4 and 0.5.

Figure 3

(Color online) Top: Nernst signal $e_N$ versus filling fraction $f$ at $T=1$ for $20\times 20$ random lattices with different values of the parameter $d_{\text{min}}$. Each curve is an average over 16 disorder realizations. Bottom: examples of lattice structure and size (diameter) distribution of the grains for different values of $d_{\text{min}}$. The grain-size standard deviation $\sigma$ is also given in each histogram.

Figure 4

(Color online) Comparison of the Nernst signal $e_N$ versus filling fraction $f$ between RSJ and Langevin dynamics, and between models with critical currents $I_{ij}^c=I^c$ and $I_{ij}^c\sim d_{ij}^{\perp }$ for a $20\times 20$ random lattice with $d_{\text{min}}=0.8$ at $T=1$. Each curve is an average over eight disorder realizations. (The RSJ data extend only up to $f=1$.)