In-plane Anisotropic Superconductivity in YBa$_{2}$Cu$_{3}$O$_{7-\sigma}$/ BiFeO$_{3}$ Heterostructure

We demonstrate a correlation between the periodic domain structure of multiferroic BiFeO$_{3}$ thin films and the anisotropic superconducting of YBa$_{2}$Cu$_{3}$O$_{7-\sigma}$/BiFeO$_{3}$ heterostructures. Two types of periodic domain structures in BFO -- 71$^{\circ}$ and 109$^{\circ}$ are used to manipulate the superconductor, YBCO, and an anomalous superconducting behavior, which shows different transition regions parallel or perpendicular to the domain walls of BFO respectively, is observed. The superconducting transition region is much broader when the current goes perpendicularly to the domain walls in BFO than parallel. The difference of Tc is about 40 K, in other words the YBCO shows one dimensional superconducting behavior within 40 K.