Universal scaling of tunable Yu-Shiba-Rusinov states across the quantum phase transition

Abstract

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 emerge inside the superconducting gap called the Yu-Shiba-Rusinov (YSR) states. Theoretically, quantum impurity problems have been successfully tackled by numerical renormalization group (NRG) theory, where the Kondo and YSR physics are shown to be unified and the normalized YSR energy scales universally with the Kondo temperature divided by the superconducting gap. However, experimentally the Kondo temperature is usually extracted from phenomenological approaches, which gives rise to significant uncertainties and cannot account for magnetic fields properly. Using scanning tunneling microscopy at 10mK, we apply a magnetic field to several YSR impurities on a vanadium tip to reveal the Kondo effect and employ the microscopic single impurity Anderson model with NRG to fit the Kondo spectra in magnetic fields accurately and extract the corresponding Kondo temperature unambiguously. Some YSR states move across the quantum phase transition (QPT) due to the changes in atomic forces during tip approach, yielding a continuous universal scaling with quantitative precision for quantum spin-1/2 impurities.

12 pages, 10 figures, including supplementary information

References in corpus (14)

• The numerical renormalization group method for quantum impurity systems
• Energy resolution and discretization artefacts in the numerical renormalization group
• Spectral properties of locally correlated electrons in a BCS superconductor
• Long-range Kondo signature of a single magnetic impurity
• Microscopic resolution of the interplay of Kondo screening and superconducting pairing: Mn-phthalocyanine molecules adsorbed on superconducting Pb(111)
• Tuning interactions between spins in a superconductor
• Observation of tunable single-atom Yu-Shiba-Rusinov states
• Interfering tunneling paths through magnetic molecules on superconductors: Asymmetries of Kondo and Yu-Shiba-Rusinov resonances
• Superconducting Quantum Interference at the Atomic Scale
• Interplay Between Yu-Shiba-Rusinov States and Multiple Andreev Reflections
• Tunneling processes between Yu-Shiba-Rusinov bound states
• Kondo effect at low electron density and high particle-hole asymmetry in 1D, 2D, and 3D
• NRG calculations of the ground-state energy: application to the correlation effects in the adsorption of magnetic impurities on metal surfaces
• Kondo physics of magnetic adatoms on metallic surfaces when the onset of the surface conduction density of states crosses the Fermi level

Cited by in corpus (6)

• Tracking a Spin-Polarized Superconducting Bound State across a Quantum Phase Transition
• The PointGroupNRG code for numerical renormalization group calculations with discrete point-group symmetries
• Spin Entanglement -- A Unifying Principle for Superconductors and Molecular Bonding
• Temperature dependent energy gap for Yu-Shiba-Rusinov states at the quantum phase transition
• A Large-$N$ Approach to Magnetic Impurities in Superconductors
• Yu-Shiba-Rusinov States in Ising Superconductors