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Abstract: Proximity induced superconductivity in a normal conductor is a rich field of experimental and theoretical investigations in many systems. In the last decade, it has been particularly at the heart of the quest for realizing topological modes in hybrid superconductor-nanowire nanodevices. Yet surprisingly, it turns out that there was a clear lack of investigations in simple systems. We therefore took on to investigate an elemental nanowire in the 1D limit (an ultra-clean carbon nanotube) coupled to a superconducting lead. We observe for the first time a long standing prediction of random matrix theory (RMT), dating back to 2001, that mesoscopic fluctuations of the mini-gap in a conductor follow a universal distribution (1). The statistical distribution of the mini-gap recorded over 60 consecutive charge states in our device shows a universal behavior with a transition when time reversal symmetry is broken, as predicted by RMT. Interestingly, mesoscopic fluctuations of the minigap were precisely predicted to lead to ubiquitous nontopological edge states clustering towards zero energy. We do indeed observe ubiquitous and robust zero bias conductance peaks in our device that cannot host topological modes by design, as expected by RMT. The RMT predictions that we confirm are very general and must be present in any system showing disorder, even if it is weak. It therefore unambiguously calls for alternative probes than transport measurement to identify Majorana modes in 1D systems. Microwave photons in a cavity are a promising powerful platform (2) that I will discuss.
Ref.: (1) L. C. Contamin et al., Nature Communications 13, 6188 (2022). (2) L. C. Contamin et al., Npj Quantum Inf. 7, 171 (2021).
