Flux-quantization effect in superconducting niobium loops

Superconducting loops have periodical oscillation of critical temperature $T_{c}$ as a function of applied perpendicular magnetic field $H$ The corresponding periodicity is related to superconducting flux quantization, $h/2e$, due to size constraint. When the loop size shrinks, however, new phenomena can appear. For example, the oscillation can show a $h$/e rather than $h/2e$ periodicity if the hole diameter is comparable to the superconducting coherence length. We present experimental investigation of flux-quantization effect in mesoscopic superconducting niobium loops. We developed a new approach to fabricate high quality loops by combining electron-beam lithography with focused-ion-beam (FIB) milling techniques. Periodic oscillations were observed in both the $H-T$ phase diagram and the magnetoresistance. Analysis of the data with various theories will be presented