Rise and fall of Yu-Shiba-Rusinov bound-states in charge conserving $s$-wave one-dimensional superconductors

Abstract

We re-examine the problem of a magnetic impurity coupled to a superconductor focusing on the role of quantum fluctuations. We study in detail, a system that consists of a one-dimensional charge conserving spin-singlet superconductor coupled to a boundary magnetic impurity. Our main finding is that quantum fluctuations lead to the destruction of Yu-Shiba-Rusinov (YSR) intra-gap bound-states in all but a narrow region of the phase diagram. We carry out our analysis in three stages, increasing the role of the quantum fluctuations at each stage. First we consider the limit of a classical impurity and study the bulk semiclassically, finding YSR states throughout the phase diagram, a situation similar to conventional BCS superconductors. In the second stage, we reintroduce quantum fluctuations in the bulk and find that the YSR state is suppressed over half of the phase diagram, existing only around the quantum critical point separating the unscreened and the partially screened phases. In the final stage we solve exactly the full interacting model with arbitrary coupling constants using Bethe Ansatz. We find that including both the quantum fluctuating bulk and quantum impurity destabilizes the YSR state over most of the phase diagram allowing it to exist only in a small region, the YSR regime, between a Kondo-screened and an unscreened regime. Within the YSR regime a first order phase transition occurs between a spin singlet and doublet ground state. We also find that for large enough impurity spin exchange interaction a renormalized Kondo-screened regime is established. In this regime, not found for BCS superconductors, there is no YSR state and a renormalized Kondo temperature scale is generated.

References in corpus (7)

• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Spectral properties of locally correlated electrons in a BCS superconductor
• A Gapless Symmetry-Protected Topological Phase of Fermions in One Dimension
• Topological Yu-Shiba-Rusinov chain from spin-orbit coupling
• Interplay of topological phases in magnetic adatom-chains on top of a Rashba superconducting surface
• Exact Boundary Modes in an Interacting Quantum Wire
• Boundary-Induced Topological and Mid-Gap States in Charge Conserving One-Dimensional Superconductors

Cited by in corpus (9)

• Dissipation driven phase transition in the non-Hermitian Kondo model
• Kondo effect in the isotropic Heisenberg spin chain
• Transport and entanglement across integrable impurities from Generalized Hydrodynamics
• A spin chain with non-Hermitian $\mathcal{PT}-$symmetric boundary couplings: exact solution, dissipative Kondo effect, and phase transitions on the edge
• Edge modes and boundary impurities in the anisotropic Heisenberg spin chain
• The Kondo effect in the quantum $XX$ spin chain
• Spectral properties of fractionalized Shiba states
• Spin-charge Kondo effect for a quantum dot with side coupled Majorana zero mode
• Competing color superconductivity and color Kondo effect in quark matter