Yu-Shiba-Rusinov states in 2D superconductors with arbitrary Fermi contours

Abstract

Magnetic impurities on a superconductor induce sub-gap Yu-Shiba-Rusinov (YSR) bound states, localized at the impurity site and fading away from it for distances up to several nanometers. In this article, we present a theoretical method to calculate the spatial distribution of the YSR spectrum of a two-dimensional superconductor with arbitrary Fermi contours (FCs) in the presence of magnetic impurities. Based on the Green's Function (GF) formalism, we obtain a general analytical expression by approximating an arbitrary contour shape to a regular polygon. This method allows us to show the connection between the spatial decay (and, hence, the extension) of YSR states and the shape of the FC of the host superconductor. We further apply this formalism to compute the evolution of YSR states in the presence of a nearby impurity atom, and compare the results with Scanning Tunneling Microscopy (STM) measurements on interacting manganese dimers on the $\beta$-Bi2Pd superconductor. The method can be easily extended to any arbitrary number of magnetically coupled impurities, thus, providing a useful tool for simulating the spectral properties of interacting YSR states in artificial atomic nanostructures.

10 pages, 4 figures

References in corpus (24)

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• Orbital Picture of Yu-Shiba-Rusinov Multiplets
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• Gap inversion in one-dimensional Andreev crystals
• Spectral properties of Andreev crystals

Cited by in corpus (8)

• Engineering anomalous Floquet Majorana modes and their time evolution in helical Shiba chain
• Tailoring phase transition from topological superconductor to trivial superconductor induced by magnetic textures of a spin-chain on a $p$-wave superconductor
• Boosting the STM's spatial and energy resolution with double-functionalized probe tips
• Bound states around impurities in a superconducting bilayer
• Hyperbolic fringe signal for twin impurity quasiparticle interference
• Robust Spin Polarization of Yu-Shiba-Rusinov States in Superconductor/Ferromagnetic Insulator Heterostructures
• Diluted Yu-Shiba-Rusinov arrays on the $\beta$-Bi${}_2$Pd anisotropic superconductor
• Anisotropy of Yu-Shiba-Rusinov states in NbSe${}_2$