Underscreened Kondo Compensation in a Superconductor
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| Format: | Preprint |
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2024
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| _version_ | 1866915515398619136 |
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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 |
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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 |