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The exchange scattering at magnetic adsorbates on superconductors gives rise to Yu-Shiba-Rusinov (YSR) bound states. Depending on the strength of the exchange coupling, the magnetic moment perturbs the Cooper pair condensate only weakly,…

Magnetic adatoms on a superconducting substrate undergo a quantum phase transition as their exchange coupling to the conduction electrons increases. For quantum spins, this transition is accompanied by screening of the adatom spin. Here, we…

Mesoscale and Nanoscale Physics · Physics 2022-06-22 Harald Schmid , Jacob F. Steiner , Katharina J. Franke , Felix von Oppen

A magnetic impurity on a superconducting substrate induces in-gap Yu-Shiba-Rusinov (YSR) bound states, whose intricate spatial structure crucially influences the possibilities of engineering collective impurity states. By means of a…

Superconductivity · Physics 2022-04-12 Mateo Uldemolins , Andrej Mesaros , Pascal Simon

Magnetic impurities have a dramatic effect on superconductivity by breaking the time-reversal symmetry and inducing so-called Yu-Shiba-Rusinov (YSR) low energy bound states within the superconducting gap. The spatial extent of YSR states is…

Mesoscale and Nanoscale Physics · Physics 2018-04-25 Shawulienu Kezilebieke , Marc Dvorak , Teemu Ojanen , Peter Liljeroth

Quantum magnetic impurities give rise to a wealth of phenomena attracting tremendous research interest in recent years. On a normal metal, magnetic impurities generate the correlation-driven Kondo effect. On a superconductor, bound states…

Magnetic adatoms on superconductors induce Yu-Shiba-Rusinov (YSR) states, which are key to the design of low-dimensional correlated systems and topological superconductivity. Competing magnetic interactions and superconducting pairing lead…

Mesoscale and Nanoscale Physics · Physics 2026-03-31 Lisa M. Rütten , Harald Schmid , Werner M. J. van Weerdenburg , Eva Liebhaber , Kai Rossnagel , Katharina J. Franke

We present a fully relativistic first principles based theoretical approach for the calculation of the spectral properties of magnetic impurities on the surface of a superconducting substrate, providing a material specific framework for the…

A magnetic impurity coupled to a superconductor gives rise to a Yu-Shiba-Rusinov (YSR) state inside the superconducting energy gap. With increasing exchange coupling the excitation energy of this state eventually crosses zero and the system…

Mesoscale and Nanoscale Physics · Physics 2018-09-26 K. Grove-Rasmussen , G. Steffensen , A. Jellinggaard , M. H. Madsen , R. Žitko , J. Paaske , J. Nygård

Conventional superconductors disordered by magnetic impurities demonstrate physical properties drastically different from their pristine counterparts. In our previous work [Phys. Rev. B 92, 245430 (2015)] we explored spectral and…

Mesoscale and Nanoscale Physics · Physics 2016-10-18 Daniel Persson , Oleksii Shevtsov , Tomas Löfwander , Mikael Fogelström

Excitations of individual and coupled spins on superconductors provide a platform to study quantum spin impurity models as well as a pathway toward realizing topological quantum computing. Here, we characterize, using ultra-low temperature…

A magnetic impurity in a fermionic superfluid hosts bound quasiparticle states known as Yu-Shiba-Rusinov (YSR) states. We argue here that, if the impurity is mobile (i.e., has a finite mass), the impurity and its bound YSR quasiparticle…

Quantum Gases · Physics 2015-03-10 Sarang Gopalakrishnan , Colin V. Parker , Eugene Demler

We study the properties of collective Yu-Shiba-Rusinov (YSR) states generated by multiple magnetic adatoms (clusters) placed on the surface of a superconductor. For magnetic clusters with equal distances between their constituents, we…

Superconductivity · Physics 2018-05-17 Simon Körber , Björn Trauzettel , Oleksiy Kashuba

The hybridization of Yu-Shiba-Rusinov states in dimers of magnetic impurities leads to molecular-like bonding and antibonding modes. In many-impurity systems, the interaction gives rise to YSR bands and can even result in the formation of a…

Superconductivity · Physics 2023-02-03 Felix Friedrich , Robin Boshuis , Matthias Bode , Artem Odobesko

As is well known, magnetic impurities adsorbed on superconductors, e.g. of the s-wave type, can introduce a bound gap-state (Yu-Shiba-Rusinov resonance). We here investigate within a minimal model how the impurity moment arranges with…

Superconductivity · Physics 2025-06-03 E. S. Andriyakhina , S. L. Khortsev , F. Evers

We investigate charge and spin conductance, charge and spin quantum noise, along with charge and spin $\Delta_T$ noise, as diagnostic tools to distinguish Yu-Shiba-Rusinov (YSR) states from Majorana-bound states (MBS) in a one-dimensional…

Mesoscale and Nanoscale Physics · Physics 2025-07-14 Sachiraj Mishra , Colin Benjamin

Scattering of superconducting pairs by magnetic impurities on a superconducting surface leads to pairs of sharp in-gap resonances, known as Yu-Shiba-Rusinov (YSR) bound states. Similarly to the interference of itinerant electrons scattered…

Superconductivity · Physics 2024-10-08 Artem Odobesko , Raffael L. Klees , Felix Friedrich , Ewelina M. Hankiewicz , Matthias Bode

We study the effects of a phase difference on Yu-Shiba-Rusinov (YSR) states in a spinful Coulomb-blockaded quantum dot contacted by a superconducting loop. In the limit where charging energy is larger than the superconducting gap, we…

Mesoscale and Nanoscale Physics · Physics 2016-04-20 Gediminas Kiršanskas , Moshe Goldstein , Karsten Flensberg , Leonid I. Glazman , Jens Paaske

An impurity hosting a magnetic moment coupled to a conventional $s$-wave superconductor gives rise to so-called Yu-Shiba-Rusinov (YSR) states with energies inside the superconducting gap. Depending on the coupling between the impurity and…

Superconductivity · Physics 2026-02-10 Andreas Theiler , Christian R. Ast , Annica M. Black-Schaffer

Motivated by recent experiments, which allow for fine tuning of the effective magnetic interaction between the impurity and the superconductor, we investigate the regime around the quantum phase transition where the system's ground state…

Superconductivity · Physics 2025-10-30 Andreas Theiler , Christian R. Ast , Annica M. Black-Schaffer

We predict that the occurence of zero energy Yu-Shiba-Rusinov(YSR) bound states in two different setups, metal-spin flipper-metal-s-wave superconductor ($N_{1}-sf-N_{2}-S$) and superconductor-metal-spin flipper-metal-superconductor…

Superconductivity · Physics 2024-12-17 Subhajit Pal , Colin Benjamin