Destructive regime in Al loops prepared by e-beam lithography

For doubly connected superconductors, cylinders, loops, or rings, the fundamental fluxoid quantization leads to oscillations in the superconducting transition temperature (T$_c$) with the applied flux. This is known as the Little-Parks effect. For sufficiently small loops, with a circumference smaller than $\pi$$\xi$(0), where $\xi$(0) is the zero temperature coherence length, superconductivity is completely destroyed near the half-flux quanta. This ``destructive regime" emerges because of the competition between the kinetic energy carried by the supercurrent, and the condensation energy of the system. Theoretically, it has been shown that adding a tail to the loop can increase the condensation energy and possibly eliminate the destructive regime. We present electrical transport measurements on Al loops defined by e-beam lithography with a size comparable to $\xi$(0). The loops were varied to have different condensation energies by adding explicit tails, and by lengthening and shortening the measurement leads. We observed strongly enhanced Little-Parks oscillations due to the reduction of the sample size, and the transition to the destructive regime when the size of sample was further reduced. These experimental results will be examined in the context of the competition between the kinetic and condensed energies. Work supported by NSF.