Asymmetric quantum transport in a double-stranded Kronig-Penney model
  We introduce a double-stranded Kronig-Penney model and analyze its transport properties. The asymmetric fluxes between two strands with suddenly alternating localization patterns are found as the energy is varied. The zero-size limit of the internal lines connecting two strands is examined using quantum graph vertices with four edges. We also consider a two-dimensional Kronig-Penney lattice with two types of alternating layers with $\delta$ and $\delta'$ connections, and show that the existence of energy bands in which the quantum flux can flow only in selected directions. 
Taksu Cheon and Sergey S. Poghosyan
quant-ph cond-mat.mes-hall math-ph math.MP