Honeycomb, Square, and Kagome Vortex Lattices in Superconducting Systems with Multi-Scale Inter-Vortex Interactions

The recent proposal of Romero-Isart et al. [1] to utilize the vortex lattice phases of superconducting materials to prepare a lattice for ultra-cold atoms-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 multi-scale inter-vortex interaction. Multiple scales of the inter-vortex interaction can be created and controlled in layered systems made of different superconducting material or with differing interlayer spacing