Exploring geometrical constraint effects of Cooper pairs

TL;DR

This study investigates how geometrical constraints influence Cooper pairs in nanoscale superconductors, revealing quantized states that suggest quantum size effects beyond traditional theories.

Contribution

It provides experimental evidence of quantized states in small superconducting squares, highlighting effects not predicted by Ginzburg-Landau theory.

Findings

Quantized steps observed in phase diagrams of small samples.

Quantized states likely linked to quantum size effects of Cooper pairs.

Sample sizes comparable to coherence length show distinct quantum behavior.

Abstract

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.