Condensed Matter Seminar Series
Full Counting Statistics of Yu-Shiba-Rusinov Bound States
With the help of scanning tunneling microscopy (STM) it has become possible to address single magnetic impurities on superconducting surfaces and to investigate the peculiar properties of the in-gap states known as Yu-Shiba-Rusinov (YSR) states. These systems are an ideal playground to investigate multiple aspects of superconducting bound states, such as the occurrence of quantum phase transitions or the interplay between Andreev transport physics and the spin degree of freedom, with profound implications for disparate topics like Majorana modes or Andreev spin qubits. However, until very recently YSR states were only investigated with conventional tunneling spectroscopy, missing the crucial information contained in other transport properties such as shot noise. In this work we adapt the concept of full counting statistics (FCS) to provide the deepest insight thus far into the spin-dependent transport in these hybrid atomic-scale systems. We illustrate the power of FCS by analyzing different situations in which YSR states show up including single-impurity junctions with a normal and a superconducting STM tip, as well as double-impurity systems where one can probe the tunneling between individual YSR states [Nat. Phys. 16, 1227 (2020)]. The FCS concept allows us to unambiguously identify every tunneling process that plays a role in these situations and to classify them according to the charge transferred on them. Moreover, FCS provides all the relevant transport properties, including current, shot noise and all the cumulants of the current distribution. In particular, our approach is able to reproduce the experimental results recently reported on the shot noise of a single-impurity junction with a normal STM tip [Phys. Rev. Lett. 128, 247001 (2022)]. We also predict the signatures of resonant (and non-resonant) Andreev reflections in the shot noise of these junctions, and we show that the tunneling between YSR states in a double-impurity junction is characterized by a universal behaviour of the Fano factor with a minimal value of 7/32, a new fundamental result in quantum transport. The FCS approach presented here can be naturally extended to investigate the spin-dependent superconducting transport in a variety of situations, such as atomic spin chains on surfaces or superconductor-semiconductor nanowire junctions, and it is also suitable to analyze multi-terminal superconducting junctions, irradiated contacts, and many other basic situations.