I would like to determine the manner in which vortices of Cooper pairs move through type-II superconductors by observing transitions in the magnetic flux trapped in a YBCO ring.
Pairs of electrons in a superconducting ring can be approximately described by a one-dimensional wavefunction varying around the ring. The eigenstates are plane waves with discrete wavenumbers determined by single-valuedness of the wavefunction. These wavenumbers correspond to discrete values of supercurrent and therefore magnetic flux trapped in the ring. The amount of flux must be a multiple of h/2e, half of the "quantum of flux," f0.
A vortex consists of pairs circulating around a core of normal (non-superconducting) material through which the magnetic flux they generate passes. In a ring, transitions between amounts of trapped flux require that a vortex pass from circulating around the ring's hole to circulating around a core that then moves through and out of the ring.
One can make vortex movement energetically favorable by applying a magnetic flux that differs from the trapped flux by multiple quanta. Thermal excitation then allows vortices to form and move. Their path and rate of escape may be tied to defects in the material or to the configuration of normal and superconducting regions of material.
Experimental setup including dipping probe in dewar and lock-in amplifier.
At this point, I am attempting to see the proper quantization of trapped flux. I have placed a local probe of magnetic field strength near the center of a superconducting ring.
YBCO ring on Hall probe viewed optically through LAO substrate. See ring image below for scale.
The probe employs the Hall effect to measure the component of magnetic field along the ring's axis. Detailed description.
The ring is etched from a thin film of the superconductor YBCO. The topography was imaged with an atomic force microscope (AFM). Detailed description.
AFM image of ring etched from film of YBCO on LAO substrate.
The ring is chosen from many on a large substrate. The substrate is placed on the hall probe and visually manipulated into place under a microscope. The combination of Hall probe and ring is mounted on a chip carrier and placed in a dipping probe. I dip the probe in a dewar of liquid nitrogen (77K). A thermometer and heating coils in thermal contact with the chip carrier allow for temperature control. A solenoid for trapping magnetic flux in the ring is wound around the outside of the probe can and driven by a current source which can be switched out of the circuit in order to extinguish the magnetic field and observed the escape of trapped flux. Detailed description.