Underscreened Kondo Compensation in a Superconductor

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Main Authors: Manaparambil, Anand, Moca, Cătălin Paşcu, Zaránd, Gergely, Weymann, Ireneusz
Format: Preprint
Published: 2024
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author Manaparambil, Anand
Moca, Cătălin Paşcu
Zaránd, Gergely
Weymann, Ireneusz
author_facet Manaparambil, Anand
Moca, Cătălin Paşcu
Zaránd, Gergely
Weymann, Ireneusz
contents A magnetic impurity with a larger $S=1$ spin remains partially screened by the Kondo effect when embedded in a metal. However, when placed within an $s$-wave superconductor, the interplay between the superconducting energy gap $Δ$ and the Kondo temperature $T_K$ induces a quantum phase transition from an underscreened doublet Kondo to an unscreened triplet phase, typically occurring when $Δ/T_K\approx 1$. We investigate the Kondo compensation of the impurity spin resulting from this partial screening across the quantum phase transition, which together with the spin-spin correlation function serves as a measure of the Kondo cloud's integrity. Deep within the unscreened triplet phase, $Δ/T_K\gg 1$, the compensation vanishes, signifying complete decoupling of the impurity spin from the environment, while in the partially screened doublet phase, $Δ/T_K\ll 1$, it asymptotically approaches $1/2$, indicating that half of the spin is screened. Notably, there is a universal jump in the compensation precisely at the phase transition, which we accurately calculate. The spin-spin correlation function exhibits an oscillatory pattern with an envelope function decaying as $\sim 1/x$ at short distances. At larger distances, the superconducting gap induces an exponentially decaying behavior $\sim \exp(-x/ξ_Δ)$ governed by the superconducting correlation length $ξ_Δ$, irrespective of the phase, without any distinctive features across the transition. Furthermore, the spectral functions of some relevant operators are evaluated and discussed. In terms of the methods used, a consistent description is provided through the application of multiplicative, numerical and density matrix renormalization group techniques.
format Preprint
id arxiv_https___arxiv_org_abs_2412_13687
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Underscreened Kondo Compensation in a Superconductor
Manaparambil, Anand
Moca, Cătălin Paşcu
Zaránd, Gergely
Weymann, Ireneusz
Mesoscale and Nanoscale Physics
Superconductivity
A magnetic impurity with a larger $S=1$ spin remains partially screened by the Kondo effect when embedded in a metal. However, when placed within an $s$-wave superconductor, the interplay between the superconducting energy gap $Δ$ and the Kondo temperature $T_K$ induces a quantum phase transition from an underscreened doublet Kondo to an unscreened triplet phase, typically occurring when $Δ/T_K\approx 1$. We investigate the Kondo compensation of the impurity spin resulting from this partial screening across the quantum phase transition, which together with the spin-spin correlation function serves as a measure of the Kondo cloud's integrity. Deep within the unscreened triplet phase, $Δ/T_K\gg 1$, the compensation vanishes, signifying complete decoupling of the impurity spin from the environment, while in the partially screened doublet phase, $Δ/T_K\ll 1$, it asymptotically approaches $1/2$, indicating that half of the spin is screened. Notably, there is a universal jump in the compensation precisely at the phase transition, which we accurately calculate. The spin-spin correlation function exhibits an oscillatory pattern with an envelope function decaying as $\sim 1/x$ at short distances. At larger distances, the superconducting gap induces an exponentially decaying behavior $\sim \exp(-x/ξ_Δ)$ governed by the superconducting correlation length $ξ_Δ$, irrespective of the phase, without any distinctive features across the transition. Furthermore, the spectral functions of some relevant operators are evaluated and discussed. In terms of the methods used, a consistent description is provided through the application of multiplicative, numerical and density matrix renormalization group techniques.
title Underscreened Kondo Compensation in a Superconductor
topic Mesoscale and Nanoscale Physics
Superconductivity
url https://arxiv.org/abs/2412.13687