Impurities, Quantum Interference and Quantum Phase Transitions in s-wave superconductors

Abstract

We study the effects of quantum interference in impurity structures consisting of two or three magnetic impurities that are located on the surface of an s-wave superconductor. By using a self-consistent Bogoliubov-de Gennes formalism, we show that quantum interference leads to characteristic signatures not only in the local density of states (LDOS), but also in the spatial form of the superconducting order parameter. We demonstrate that the signatures of quantum interference in the LDOS are qualitatively, and to a large extent quantitatively unaffected by the suppression of the superconducting order parameter near impurities, which illustrates the robustness of quantum interference phenomena. Moreover, we show that by changing the interimpurity distance, or the impurities' scattering strength, the s-wave superconductor can be tuned through a series of first order quantum phase transitions in which the spin polarization of its ground state changes. In contrast to the single impurity case, this transition is not necessarily accompanied by a $\pi$-phase shift of the order parameter, and can in certain cases even lead to its enhancement. Our results demonstrate that the superconductor's LDOS, its spin state, and the spatial form of the superconducting order parameter are determined by a subtle interplay between the relative positions of the impurities and their scattering strength.

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• Wave-function engineering on superconducting substrates: Chiral Yu-Shiba-Rusinov molecules
• Magnetic impurities in a superconductor: Effect of domain walls and interference
• Calculations of in-gap states of ferromagnetic spin chains on \textit{s}-wave wide-band superconductors
• Systematic study of Mn atoms, artificial dimers and chains on superconducting Ta(110)
• Yu-Shiba-Rusinov States and Ordering of Magnetic Impurities Near the Boundary of a Superconducting Nanowire
• Zero energy modes in a superconductor with ferromagnetic adatom chains and quantum phase transitions
• RKKY interaction at helical edges of topological superconductors
• Effects of nonmagnetic disorder on the energy of Yu-Shiba-Rusinov states
• Spectral properties of superconductors with ferromagnetically ordered magnetic impurities
• Interplay between pairing and correlations in spin-polarized bound states
• Temperature dependent energy gap for Yu-Shiba-Rusinov states at the quantum phase transition