Collective energy gap of preformed Cooper-pairs in disordered superconductors

In most superconductors the transition to the superconducting state is driven by the binding of electrons into Cooper-pairs. The condensation of these pairs into a single, phase coherent, quantum state takes place concomitantly with their formation at the transition temperature, $T_c$. A different scenario occurs in some disordered, amorphous, superconductors: Instead of a pairing-driven transition, incoherent Cooper pairs first pre-form above $T_c$, causing the opening of a pseudogap, and then, at $T_c$, condense into the phase coherent superconducting state. Such a two-step scenario implies the existence of a new energy scale, $Delta_{c}$, driving the collective superconducting transition of the preformed pairs. Here we unveil this energy scale by means of Andreev spectroscopy in superconducting thin films of amorphous indium oxide. We observe two Andreev conductance peaks at $pm Delta_{c}$ that develop only below $T_c$ and for highly disordered films on the verge of the transition to insulator. Our findings demonstrate that amorphous superconducting films provide prototypical disordered quantum systems to explore the collective superfluid transition of preformed Cooper-pairs pairs.

Interplay Between Electron Over-Heating and ac Josephson Effect

We study the response of high-critical current proximity Josephson junctions to a microwave excitation. Electron over-heating in such devices is known to create hysteretic dc voltage-current characteristics. Here we demonstrate that it also strongly influences the ac response. The interplay of electron over-heating and ac Josephson dynamics is revealed by the evolution of the Shapiro steps with the microwave drive amplitude. Extending the resistively shunted Josephson junction model by including a thermal balance for the electronic bath coupled to phonons, a strong electron over-heating is obtained.