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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2503.18902 |
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| _version_ | 1866916830924242944 |
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| author | Iličin, Teodor Žitko, Rok |
| author_facet | Iličin, Teodor Žitko, Rok |
| contents | We propose a set of variational wavefunctions for the sub-gap spin-doublet and spin-singlet eigenstates of the particle-hole symmetric superconducting Anderson impurity model. The wavefunctions include up to two Bogoliubov quasiparticles in the continuum which is necessary to correctly capture the weak-coupling asymptotics in all parameter regimes. The eigenvalue problems reduce to solving transcendental equations. We investigate how the lowest singlet state evolves with increasing charge repulsion $U$, transitioning from a proximitized state (a superposition of empty and doubly occupied impurity orbitals, corresponding to an Andreev bound state) to a local moment that is Kondo screened by Bogoliubov quasiparticles (Yu-Shiba-Rusinov state). This change occurs for $U = 2Δ$, where $Δ$ is the BCS gap. At this point, the band-edge effects make the eigenenergy scale in a singular way as $Γ^{2/3}$, where $Γ$ is the hybridization strength. Away from this special point, regular $Γ$-linear behavior is recovered, but only for $Γ\lesssim (U/2-Δ)^2/Δ$. The singular behavior thus extends over a broad range of parameters, including those relevant for some quantum devices in current use. The singular state is an equal-superposition state with maximal fluctuations between the local impurity charge configurations. Accurately capturing the band-edge singularity requires a continuum model, and it cannot be correctly described by discrete (truncated) models such as the zero-bandwidth approximation or the superconducting atomic limit. We determine the region of parameter space where the second spin-singlet state exists: in addition to the whole $U<2Δ$ ABS region, it also includes a small part of the $U>2Δ$ YSR region for finite values of $Γ$, as long as some ABS wavefunction component is admixed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena Iličin, Teodor Žitko, Rok Superconductivity We propose a set of variational wavefunctions for the sub-gap spin-doublet and spin-singlet eigenstates of the particle-hole symmetric superconducting Anderson impurity model. The wavefunctions include up to two Bogoliubov quasiparticles in the continuum which is necessary to correctly capture the weak-coupling asymptotics in all parameter regimes. The eigenvalue problems reduce to solving transcendental equations. We investigate how the lowest singlet state evolves with increasing charge repulsion $U$, transitioning from a proximitized state (a superposition of empty and doubly occupied impurity orbitals, corresponding to an Andreev bound state) to a local moment that is Kondo screened by Bogoliubov quasiparticles (Yu-Shiba-Rusinov state). This change occurs for $U = 2Δ$, where $Δ$ is the BCS gap. At this point, the band-edge effects make the eigenenergy scale in a singular way as $Γ^{2/3}$, where $Γ$ is the hybridization strength. Away from this special point, regular $Γ$-linear behavior is recovered, but only for $Γ\lesssim (U/2-Δ)^2/Δ$. The singular behavior thus extends over a broad range of parameters, including those relevant for some quantum devices in current use. The singular state is an equal-superposition state with maximal fluctuations between the local impurity charge configurations. Accurately capturing the band-edge singularity requires a continuum model, and it cannot be correctly described by discrete (truncated) models such as the zero-bandwidth approximation or the superconducting atomic limit. We determine the region of parameter space where the second spin-singlet state exists: in addition to the whole $U<2Δ$ ABS region, it also includes a small part of the $U>2Δ$ YSR region for finite values of $Γ$, as long as some ABS wavefunction component is admixed. |
| title | Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena |
| topic | Superconductivity |
| url | https://arxiv.org/abs/2503.18902 |