Abstract: Recently, gate-mediated supercurrent suppression in superconducting nanobridges has been reported in many experiments. This could be either a direct or an indirect gate effect. The microscopic understanding of this observation has not been clear until now. Using the quasiclassical Green's function method, we show that a small concentration of magnetic impurities at the surface of the bridges can significantly help to suppress superconductivity and hence the supercurrent inside the systems while a gate field is applied. This is because the gate field can enhance the depairing through the exchange interaction between the magnetic impurities at the surface and the superconductor. We also obtain a symmetric suppression of the supercurrent with respect to the gate field, a signature of a direct gate effect. We discuss the parameter range of applicability of our model and how it is able to qualitatively capture the main aspects of the experimental observations. Future experiments can verify our predictions by modifying the surface with magnetic impurities.

S. Chakraborty, D. Nikolić, J. C. Cuevas, F. Giazotto, A. Di Bernardo, E. Scheer, M. Cuoco, and W. Belzig
Phys. Rev. B 108, 184508 – published 13 November 2023
DOI: 10.1103/PhysRevB.108.184508
related to project A02

Abstract: Light–matter coupling allows control and engineering of complex quantum states. Here we investigate a hybrid superconducting–semiconducting Josephson junction subject to microwave irradiation by means of tunnelling spectroscopy of the Andreev bound state spectrum and measurements of the current–phase relation. For increasing microwave power, discrete levels in the tunnelling conductance develop into a series of equally spaced replicas, while the current–phase relation changes amplitude and skewness, and develops dips. Quantitative analysis of our results indicates that conductance replicas originate from photon assisted tunnelling of quasiparticles into Andreev bound states through the tunnelling barrier. Despite strong qualitative similarities with proposed signatures of Floquet–Andreev states, our study rules out this scenario. The distortion of the current–phase relation is explained by the interaction of Andreev bound states with microwave photons, including a non-equilibrium Andreev bound state occupation. The techniques outlined here establish a baseline to study light–matter coupling in hybrid nanostructures and distinguish photon assisted tunnelling from Floquet–Andreev states in mesoscopic devices.

D. Z. Haxell, M. Coraiola, D. Sabonis, M. Hinderling, S. C. ten Kate, E. Cheah, F. Krizek, R. Schott, W. Wegscheider, W. Belzig, J. C. Cuevas, and F. Nichele 
Nat Commun 14, 6798 - published 26 October 2023
DOI: 10.1038/s41467-023-42357-5
related to project A02 and A03

Abstract: Magnetic impurities on superconductors lead to bound states within the superconducting gap, so called Yu-Shiba-Rusinov (YSR) states. They are parity protected, which enhances their lifetime, but makes it more difficult to excite them. Here, we realize the excitation of YSR states by microwaves facilitated by the tunnel coupling to another superconducting electrode in a scanning tunneling microscope (STM). We identify the excitation process through a family of anomalous microwave-assisted tunneling peaks originating from a second-order resonant Andreev process, in which the microwave excites the YSR state triggering a tunneling event transferring a total of two charges. We vary the amplitude and the frequency of the microwave to identify the energy threshold and the evolution of this excitation process. Our work sets an experimental basis and proof-of-principle for the manipulation of YSR states using microwaves with an outlook towards YSR qubits.

J. Siebrecht, H. Huang, P. Kot, R. Drost, C. Padurariu, B. Kubala, J. Ankerhold, J. C. Cuevas, and C. R. Ast
Nat. Commun. 14, 6794 - published 25 October 2023
related to project A02 and A03

Abstract: Motivated by recent experiments [Nat. Phys. 16, 1227 (2020)], we present here a theoretical study of the DC Josephson effect in a system comprising two magnetic impurities coupled to their respective superconducting electrodes and which exhibit Yu-Shiba-Rusinov (YSR) states. We make use of a mean-field Anderson model with broken spin symmetry to compute the supercurrent in this system for an arbitrary range of parameters (coupling between the impurities, orientation of the impurity spins, etc.). We predict a variety of physical phenomena such as (i) the occurrence of multiple 0-π transitions in the regime of weak coupling that can be induced by changing the energy of the YSR states or the temperature; (ii) the critical current strongly depends on the relative orientation of the impurity spins and it is maximized when the spins are either parallel or antiparallel, depending on the ground state of the impurities; and (iii) upon increasing the coupling between impurities, triplet superconductivity is generated in the system and it is manifested in a highly nonsinusoidal current-phase relation. In principle, these predictions can be tested experimentally with the existing realization of this system and the main lessons of this work are of great relevance for the field of superconducting spintronics.

S. Chakraborty, D. Nikolić, R. S. Souto, W. Belzig, and J. C. Cuevas
Phys. Rev. B 108, 094518 – published 27 September 2023
DOI: 10.1103/PhysRevB.108.094518
related to project A02

Abstract:  In hybrid Josephson junctions with three or more superconducting terminals coupled to a semiconducting region, Andreev bound states may form unconventional energy band structures, or Andreev matter, which are engineered by controlling superconducting phase differences. Here we report tunnelling spectroscopy measurements of three-terminal Josephson junctions realised in an InAs/Al heterostructure. The three terminals are connected to form two loops, enabling independent control over two phase differences and access to a synthetic Andreev band structure in the two-dimensional phase space. Our results demonstrate a phase-controlled Andreev molecule, originating from two discrete Andreev levels that spatially overlap and hybridise. Signatures of hybridisation are observed in the form of avoided crossings in the spectrum and band structure anisotropies in the phase space, all explained by a numerical model. Future extensions of this work could focus on addressing spin-resolved energy levels, ground state fermion parity transitions and Weyl bands in multiterminal geometries. 

M. Coraiola, D. Z. Haxell, D. Sabonis, H. Weisbrich, A. E. Svetogorov, M. Hinderling, S. C. ten Kate, E. Cheah, F. Krizek, R. Schott, W. Wegscheider, J. C. Cuevas, W. Belzig, and F. Nichele
Nat Commun 14, 6784 - published 25 October 2023
related to project A02 and A03

Abstract: 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 paper 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 in 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 nonresonant) multiple Andreev reflections in the shot noise and Fano factor of single-impurity junctions with two superconducting electrodes and show that the FCS approach allows us to understand conductance features that have been incorrectly interpreted in the literature. In the case of double-impurity junctions we show that the direct tunneling between YSR states is characterized by a strong reduction of the Fano factor that reaches a minimum value of 7/32, a significant 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 multiterminal superconducting junctions, irradiated contacts, and many other basic situations.

D. C. Ohnmacht, W. Belzig, and J. C. Cuevas
Phys. Rev. Research 5, 033176 – published 11 September 2023
DOI: 10.1103/PhysRevResearch.5.033176
related to project A02