Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena
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 w...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SciPost
2025-07-01
|
| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.19.1.006 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849428815488483328 |
|---|---|
| author | Teodor Iličin, Rok Žitko |
| author_facet | Teodor Iličin, Rok Žitko |
| author_sort | Teodor Iličin, Rok Žitko |
| collection | DOAJ |
| description | 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 $U = 2\Delta$, where $\Delta$ is the BCS gap. At this point, the band-edge effects make the eigenenergy scale in a singular way as $\Gamma^{2/3}$, where $\Gamma$ is the hybridization strength. Away from this special point, regular $\Gamma$-linear behavior is recovered, but only for $\Gamma ≲ (U/2-\Delta)^2/\Delta$. 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 $U<2\Delta$ ABS region, it also includes a small part of the $U>2\Delta$ YSR region for finite values of $\Gamma$, as long as some ABS wavefunction component is admixed. |
| format | Article |
| id | doaj-art-eb4a08a2cdf74209a0d5a92b261c4aa0 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-eb4a08a2cdf74209a0d5a92b261c4aa02025-08-20T03:28:33ZengSciPostSciPost Physics2542-46532025-07-0119100610.21468/SciPostPhys.19.1.006Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomenaTeodor Iličin, Rok ŽitkoWe 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 $U = 2\Delta$, where $\Delta$ is the BCS gap. At this point, the band-edge effects make the eigenenergy scale in a singular way as $\Gamma^{2/3}$, where $\Gamma$ is the hybridization strength. Away from this special point, regular $\Gamma$-linear behavior is recovered, but only for $\Gamma ≲ (U/2-\Delta)^2/\Delta$. 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 $U<2\Delta$ ABS region, it also includes a small part of the $U>2\Delta$ YSR region for finite values of $\Gamma$, as long as some ABS wavefunction component is admixed.https://scipost.org/SciPostPhys.19.1.006 |
| spellingShingle | Teodor Iličin, Rok Žitko Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena SciPost Physics |
| title | Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena |
| title_full | Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena |
| title_fullStr | Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena |
| title_full_unstemmed | Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena |
| title_short | Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena |
| title_sort | variational solution of the superconducting anderson impurity model and the band edge singularity phenomena |
| url | https://scipost.org/SciPostPhys.19.1.006 |
| work_keys_str_mv | AT teodorilicinrokzitko variationalsolutionofthesuperconductingandersonimpuritymodelandthebandedgesingularityphenomena |