An unconventional vortex state in a superconducting bilayer where one layer has a hole

An ultrathin superconducting bilayer creates a coreless fractional vortex when only the second layer has a hole. The quantization is broken by the hole, and the normal core disappears. The magnetic flux is no longer confined near the normal core. The divergence of the magnetic flux density is truncated around the center. We propose basic design of a practical device to realize a coreless fractional vortex.