# Theory Meets Experiment in Low-Dimensional Structures with Correlated Electrons

## Prague, Czech Republic, July 1 – 4, 2019

#### How small a superconductor can be?

*(1) Laboratoire de Physique et d'Étude des Matériaux, Ecole de Physique et Chimie Industrielles, CNRS, Sorbonne Université, Paris, France, (2) Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Sud, Marcoussis, France*

In 1959, physicist P. W. Anderson conjectured that superconductivity can exist only in objects where superconducting gap energy is larger than its electronic energy level spacing. In our work [1,2], we were able to address this limit in single nanoparticles of various sizes without suffering from inverse proximity effect. Here we report on a scanning tunneling spectroscopy study of superconducting lead nanocrystals grown on the (110) surface of InAs. The electronic transmission at the InAs/nanocrystal interface is weak; this leads to Coulomb blockade and enables the extraction of electron addition energy of the nanocrystals. The addition energy displays superconducting parity effect, a direct consequence of Cooper pairing. Due to the electrons forming Cooper pairs when an electron is added to the nanocrystal superconductor, the additional energy is different whether there is an even or odd number of electrons. Studying this parity effect as a function of nanocrystal volume, we ﬁnd the suppression of Cooper pairing when the mean electronic level spacing overcomes the superconducting gap energy, thus demonstrating unambiguously the validity of the Anderson criterion.

[1] Superconducting parity effect across the Anderson limit, S. Vlaic, S. Pons, T. Zhang, A. Assouline, A. Zimmers, C. David, G. Rodary, J.-C. Girard, D. Roditchev, H. Aubin, Nature Comm. 8, 14549 (2017).

[2] Quantum confinement effects in Pb nanocrystals grown on InAs, T. Zhang, S. Vlaic, S. Pons, A. Assouline, A. Zimmers, D. Roditchev, H. Aubin and G. Allan, C. Delerue, C. David, G. Rodary, J.-C. Girard, Phys. Rev. B 97, 214514 (2018).