Exploring geometrical constraint effects of Cooper pairs

We report low-temperature electrical transport measurements on filled Al squares prepared by e-beam lithography featuring a sample size ranging from 130 nm to 530 nm. The values of the superconducting coherence length, $\xi$(0), were found to range from $\sim$100-210 nm. We found that phase diagrams in the magnetic field and temperature space feature quantized steps in samples with a size comparable with $\xi$(0), suggesting the emergence of quantized states in these smallest superconducting structures. These quantized states, which are not anticipated in Ginzburg-Landau theory, may be associated with the quantum size effects of Cooper pairs.