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Tunneling spectroscopy is an important tool for the study of both real-space and momentum-space electronic structure of correlated electron systems. However, such measurements often yield noisy data. Machine learning provides techniques to reduce the noise in post-processing, but traditionally requires noiseless examples which are unavailable for scientific experiments. In this work we adapt the unsupervised Noise2Noise and self-supervised Noise2Self algorithms, which allow for denoising without clean examples, to denoise quasiparticle interference data. We first apply the techniques on simulated data, and demonstrate that we are able to reduce the noise while preserving finer details, all while outperforming more traditional denoising techniques. We then apply the Noise2Self technique to experimental data from an overdoped cuprate ((Pb,Bi)$_2$Sr$_2$CuO$_{6+\delta}$) sample. Denoising enhances the clarity of quasiparticle interference patterns, and helps to obtain a precise extraction of electronic structure parameters. Self-supervised denoising is a promising tool for denoising quasiparticle interference data, facilitating deeper insights into the physics of complex materials., Comment: 7 pages, 5 figures, plus 4 pages and 5 figures appendix

Majorana bound states are putative collective excitations in solids that exhibit the self-conjugate property of Majorana fermions - they are their own antiparticles. In iron-based superconductors, zero-energy states in vortices have been reported as potential Majorana bound states, but the evidence remains controversial. Here, we use scanning tunneling noise spectroscopy to study the tunneling process into vortex bound states in the conventional superconductor NbSe2, and in the putative Majorana platform FeTe0.55Se0.45. We find that tunneling into vortex bound states in both cases exhibits charge transfer of a single electron charge. Our data for the zero-energy bound states in FeTe0.55Se0.45 exclude the possibility of Yu-Shiba-Rusinov states and are consistent with both Majorana bound states and trivial vortex bound states. Our results open an avenue for investigating the exotic states in vortex cores and for future Majorana devices, although further theoretical investigations involving charge dynamics and superconducting tips are necessary., Comment: 15 pages, 4 figures, and 16 pages for supplementary information

The cuprate high-temperature superconductors exhibit many unexplained electronic phases, but it was often thought that the superconductivity at sufficiently high doping is governed by conventional mean-field Bardeen-Cooper-Schrieffer (BCS) theory[1]. However, recent measurements show that the number of paired electrons (the superfluid density) vanishes when the transition temperature Tc goes to zero[2], in contradiction to expectation from BCS theory. The origin of this anomalous vanishing is unknown. Our scanning tunneling spectroscopy measurements in the overdoped regime of the (Pb,Bi)2Sr2CuO6+{\delta} high-temperature superconductor show that it is due to the emergence of puddled superconductivity, featuring nanoscale superconducting islands in a metallic matrix[3,4]. Our measurements further reveal that this puddling is driven by gap filling, while the gap itself persists beyond the breakdown of superconductivity. The important implication is that it is not a diminishing pairing interaction that causes the breakdown of superconductivity. Unexpectedly, the measured gap-to-filling correlation also reveals that pair-breaking by disorder does not play a dominant role and that the mechanism of superconductivity in overdoped cuprate superconductors is qualitatively different from conventional mean-field theory.

The idea that preformed Cooper pairs could exist in a superconductor above its zero-resistance state has been explored for unconventional, interface, and disordered superconductors, yet direct experimental evidence is lacking. Here, we use scanning tunneling noise spectroscopy to unambiguously show that preformed Cooper pairs exist up to temperatures much higher than the zero-resistance critical temperature $T_{C}$ in the disordered superconductor titanium nitride, by observing a clear enhancement in the shot noise that is equivalent to a change of the effective charge from 1 to 2 electron charges. We further show that spectroscopic gap fills up rather than closes when increasing temperature. Our results thus demonstrate the existence of a novel state above $T_{C}$ that, much like an ordinary metal, has no (pseudo)gap, but carries charge via paired electrons.