Investigation of the phase diagrams of small superconducting squares of Al

An isolated superconductor with its size comparable to or smaller than its zero temperature superconducting coherence length should not host Abrikosov vortices, but may in principle still feature spatial variation in the superconducting order parameter. We report low-temperature electrical transport measurements on simply connected filled Al squares prepared by e-beam lithography featuring a lateral sample size ranging from 126 nm to 616 nm, with their zero-temperature superconducting coherence lengths, ξ(0), ranging from ∼88-111 nm. We found that phase diagrams for these samples in the magnetic field and temperature space exhibit the expected features for vortex admission in large devices, but no vortex admission when the size becomes comparable to ξ(0). In the smallest samples we observe steps in the phase diagram that may be attributable to the effects of the measurement leads.