Honeycomb, square, and kagome vortex lattices in superconducting systems with multiscale intervortex interactions

The recent proposal of Romero-Isart et al. [Phys. Rev. Lett. 111, 145304 (2013)] to utilize the vortex lattice phases of superconducting materials to prepare a lattice for ultracold-atom-based quantum emulators raises the need to create and control vortex lattices of different symmetries. Here we propose a mechanism by which honeycomb, hexagonal, square, and kagome vortex lattices could be created in superconducting systems with multiscale intervortex interactions. Multiple scales of the intervortex interaction can be created and controlled in layered systems made of different superconducting materials or with differing interlayer spacings.

Figure 1

Schematic picture of the magnetic field lines of a vortex in a layered superconductor. Shaded (white) areas are superconductor (insulator) layers with different thicknesses. The flux spreads in the nonsuperconducting regions.

Figure 2

Phenomenological potential that describes the multiscale intervortex interaction for straight rigid vortex lines in a layered system with different layer parameters. The solid red curve gives rise to a honeycomb lattice at density [46] $\rho =1.50$, a hexagonal lattice at $\rho =2.25$, and a square lattice at $\rho =2.50$, while for the dashed green line a kagome lattice is the ground state at a density of $\rho =2.50$ [47].

Figure 3

The final vortex configuration at zero temperature for (a) $N_v=3024$ and $\rho =1.50$ (honeycomb lattice), (b) $N_v=2958$ and $\rho =2.25$ (hexagonal lattice), (c) $N_v=2958$ and $\rho =2.50$ (square lattice), and (d) $N_v=1020$ and $\rho =2.50$ (kagome lattice). (a)–(c) correspond to the solid red curve of Fig. 2, while (d) corresponds to the dashed green curve.

Figure 4

Comparison of the radial distribution function $g\left(r\right)$ of the vortex configurations shown in Fig. 3 with those of the ideal geometry for (a) honeycomb, (b) hexagonal, (c) square, and (d) kagome lattices. The dashed blue line is the zero temperature result after simulated annealing, and the solid red line is the ideal result.

Figure 5

Number of nearest neighbors $n_i$ up to the fifth nearest neighbor for the (a) honeycomb (b) hexagonal, (c) square, and (d) kagome lattices of Fig. 3 with $N_v\approx 1000$ (squares) and 3000 (circles) vortices. Here, $n_i$ is normalized to the number of neighbors in a perfect lattice.