%0 Journal Article %T Honeycomb, square, and kagom¨¦ vortex lattices in superconducting systems with multi-scale inter-vortex interactions %A Qingyou Meng %A Christopher N. Varney %A Hans Fangohr %A Egor Babaev %J Physics %D 2014 %I arXiv %R 10.1103/PhysRevB.90.020509 %X 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. %U http://arxiv.org/abs/1404.4305v2