TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.1.006
TI  - Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena
PY  - 2025/07/02
UR  - https://scipost.org/SciPostPhys.19.1.006
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 1
SP  - 006
A1  - Iličin, Teodor
AU  - Žitko, Rok
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.19.1.006,
	title={{Variational solution of the superconducting Anderson impurity model and the band-edge singularity phenomena}},
	author={Teodor Iličin and Rok Žitko},
	journal={SciPost Phys.},
	volume={19},
	pages={006},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.1.006},
	url={https://scipost.org/10.21468/SciPostPhys.19.1.006},
}