Spectral properties of Shiba sub-gap states at finite temperatures

Abstract

Using the numerical renormalization group (NRG), we analyze the temperature dependence of the spectral function of a magnetic impurity described by the single-impurity Anderson model coupled to superconducting contacts. With increasing temperature the spectral weight is gradually transferred from the $\delta$-peak (Shiba/Yu-Shiba-Rusinov/Andreev bound state) to the continuous sub-gap background, but both spectral features coexist at any finite temperature, i.e., the $\delta$-peak itself persists to temperatures of order $\Delta$. The continuous background is due to inelastic exchange scattering of Bogoliubov quasiparticles off the impurity and it is thermally activated since it requires a finite thermal population of quasiparticles above the gap. In the singlet regime for strong hybridization (charge-fluctuation regime) we detect the presence of an additional sub-gap structure just below the gap edges with thermally activated behavior, but with an activation energy equal to the Shiba state excitation energy. These peaks can be tentatively interpreted as Shiba bound states arising from the scattering of quasiparticles off the thermally excited sub-gap doublet Shiba states, i.e., as high-order Shiba states.

9 pages, 10 figures

References in corpus (13)

• Continuous-time Monte Carlo methods for quantum impurity models
• The numerical renormalization group method for quantum impurity systems
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• Tunneling processes into localized subgap states in superconductors
• Josephson current through a single Anderson impurity coupled to BCS leads
• Shiba states and zero-bias anomalies in the hybrid normal-superconductor Anderson model
• Magnetic anisotropy effects on quantum impurities in superconducting host
• Perturbation theory for an Anderson quantum dot asymmetrically attached to two superconducting leads
• Vibrational Andreev bound states in magnetic molecules

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• Temperature Induced Shifts of Yu-Shiba-Rusinov Resonances in Nanowire-Based Hybrid Quantum Dots
• Unified theory of quantum phase transitions in quantum dots with gapped host bands
• Effective low-energy models for superconducting impurity systems
• Quantum phase transition in magnetic nanographenes on a lead superconductor
• Zero energy modes in a superconductor with ferromagnetic adatom chains and quantum phase transitions
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• Superconducting quantum dot and the sub-gap states
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• Enhanced negative nonlocal conductance in an interacting quantum dot connected to two ferromagnetic leads and one superconducting lead
• Scalable Effective Models for Superconducting Nanostructures: Applications to Double, Triple, and Quadruple Quantum Dots
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