Honeycomb, square, and kagom\'e vortex lattices in superconducting   systems with multi-scale inter-vortex interactions
  The recent proposal of Romero-Isart {\em et al.}~\cite{romero-isart_superconducting_2013} 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 kagom\'e 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. 
Qingyou Meng, Christopher N. Varney, Hans Fangohr, and Egor Babaev
cond-mat.supr-con cond-mat.quant-gas