Among the mysteries surrounding unconventional, strongly correlated superconductors is the possibility of spatial variations in their superfluid density. We use atomic-resolution Josephson scanning tunneling microscopy to reveal a strongly inhomogeneous superfluid in the iron-based superconductor FeTe0.55Se0.45. By simultaneously measuring the topographic and electronic properties, we find that this inhomogeneity in the superfluid density is not caused by structural disorder or strong inter-pocket scattering, and does not correlate with variations in Cooper pair-breaking gap. Instead, we see a clear spatial correlation between superfluid density and quasiparticle strength, putting the iron-based superconductors on equal footing with the cuprates and demonstrating that locally, the quasiparticles are sharpest when the superconductivity is strongest. When repeated at different temperatures, our technique could further help elucidate what local and global mechanisms limit the critical temperature in unconventional superconductors. Superconductivity emerges when electrons pair up to form so-called Cooper pairs andthen establish phase coherence to condense into the macroscopic quantum state that is the superfluid. Cooper pairing is governed by the binding energy of the pairs, ΔPB, while the phase coherence or stiffness, governs the superfluid density, nsf. 1,2 For conventional superconductors like aluminum or lead, the superfluid density is spatially homogeneous because the lattice constant is much smaller than the Cooper pair size of a few tens of nanometer, and because the large superfluid density guarantees a high phase stiffness. In unconventional, strongly correlated superconductors the situation is very different for the following reasons: (i) the Cooper pair size, roughly given by the coherence length, is smaller; (ii) the superfluid density is smaller (iii), more disorder exists due to dopant atoms or intrinsic tendencies for phase separation or charge order; and (iv) the superconducting gap changes sign. Despite much progress 3,4 , we lack a theoretical understanding of these strongly correlated superconductors.

By using scanning tunneling microscopy (STM) we find and characterize dispersive, energy-symmetric in-gap states in the iron-based superconductor FeTe0.55Se0.45, a material that exhibits signatures of topological superconductivity, and Majorana bound states at vortex cores or at impurity locations. We use a superconducting STM tip for enhanced energy resolution, which enables us to show that impurity states can be tuned through the Fermi level with varying tip-sample distance. We find that the impurity state is of the Yu-Shiba-Rusinov (YSR) type, and argue that the energy shift is caused by the low superfluid density in FeTe0.55Se0.45, which allows the electric field of the tip to slightly penetrate the sample. We model the newly introduced tip-gating scenario within the single-impurity Anderson model and find good agreement to the experimental data.

Measuring the effective charge At low enough temperatures, superconductors are capable of conducting electricity without any resistance because of the formation of so-called Cooper pairs of electrons. Cooper pairs typically form at the same critical temperature at which superconductivity sets in. In certain materials, they are thought to form above that temperature, but showing this property directly in an experiment is tricky. Bastiaans et al . used tunneling noise spectroscopy to measure the effective charge of current carriers in the disordered superconductor titanium nitride. As expected, below the critical temperature, the effective charge was equal to two electron charges. However, this behavior persisted above the critical temperature, indicating that electron pairs exist in that regime. —JS

We have imaged the current noise with atomic resolution in a Josephson scanning tunneling microscope with a Pb-Pb junction. By measuring the current noise as a function of applied bias, we reveal the change from single electron tunneling above the superconducting gap energy to double electron charge transfer below the gap energy when Andreev processes become dominant. Our spatially resolved noise maps show that this doubling occurs homogeneously on the surface, also on impurity locations, demonstrating that indeed the charge pairing is not influenced by disruptions in the superconductor smaller than the superconducting coherence length.

Conventional scanning tunneling microscopy (STM) is limited to a bandwidth of circa 1kHz around DC. Here, we develop, build and test a novel amplifier circuit capable of measuring the tunneling current in the MHz regime while simultaneously performing conventional STM measurements. This is achieved with an amplifier circuit including a LC tank with a quality factor exceeding 600 and a home-built, low-noise high electron mobility transistor (HEMT). The amplifier circuit functions while simultaneously scanning with atomic resolution in the tunneling regime, i.e. at junction resistances in the range of giga-ohms, and down towards point contact spectroscopy. To enable high signal-to-noise and meet all technical requirements for the inclusion in a commercial low temperature, ultra-high vacuum STM, we use superconducting cross-wound inductors and choose materials and circuit elements with low heat load. We demonstrate the high performance of the amplifier by spatially mapping the Poissonian noise of tunneling electrons on an atomically clean Au(111) surface. We also show differential conductance spectroscopy measurements at 3MHz, demonstrating superior performance over conventional spectroscopy techniques. Further, our technology could be used to perform impedance matched spin resonance and distinguish Majorana modes from more conventional edge states.