Band-gap structure and chiral discrete solitons in optical lattices with   artificial gauge fields
  We study three-leg-ladder optical lattices loaded with repulsive atomic Bose-Einstein condensates and subjected to artificial gauge fields. By employing the plane-wave analysis and variational approach, we analyze the band-gap structure of the energy spectrum and reveal the exotic swallow-tail loop structures in the energy-level anti-crossing regions due to an interplay between the atom-atom interaction and artificial gauge field. Also, we discover stable discrete solitons residing in a semi-infinite gap above the highest band, these discrete solitons are associated with the chiral edge currents. 
Qinzhou Ye, Xizhou Qin, Yongyao Li, Honghua Zhong, Yuri S. Kivshar,   Chaohong Lee
cond-mat.quant-gas