Interaction effects on Andreev states from an electromagnetic environment
Abstract
Here we present a detailed theoretical investigation of the environment-induced interaction correction to the ground states and addition energies in a short superconducting junction. We derive general formulas for these corrections linking them to the frequency-dependent admittance of the junction and the environment impedance. We specify two environmental models: that of an external impedance and the Mattis-Bardeen model. In both cases we assume GQ Z ≪ 1, where GQ is the conductance quantum and Z the typical environmental resistance. While an expectation is that the typical scale of the relative correction is of the order GQ Z, we have found that in many cases the dimensionless scale L GQ Δ provides a better estimation, where Δ is the superconducting energy gap and L an external inductance. We discuss the logarithmic renormalizations of the energies by low- and high-frequency phase fluctuations and single out a non-superconducting contribution related to the renormalization of transmission eigenvalues. We investigate in detail the peculiarities of the corrections at: i. small phases, where the interaction causes a current jump, ii. Andreev bound state energies close to the gap edge, iii. Andreev bound state energies close to Fermi level. In all these cases the correction may become comparable with the unperturbed energy, even for GQ Z ≪ 1, and we briefly sketch non-perturbative models relevant for the situations.
Related
- Multiple Andreev Reflection Spectroscopy of Spin-Resolved Proximity States
- Dissipative quantum mechanics of Andreev bound states
- Aharonov-Bohm interference probing of chiral Andreev edge states via scanning gate microscopy
- Electromagnetic emission at the Langmuir frequency from laser interaction with an unmagnetized plasma
- Norm of resonance states in quantum scattering and electromagnetic systems
BibTeX
@misc{samuelsen2026interaction,
title = {{Interaction effects on Andreev states from an electromagnetic environment}},
author = {Erik S. Samuelsen and Yuli V. Nazarov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01935},
eprint = {2609.01935},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01935},
}
RIS
TY - UNPB
TI - Interaction effects on Andreev states from an electromagnetic environment
AU - Erik S. Samuelsen
AU - Yuli V. Nazarov
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01935
UR - https://arxiv.org/abs/2609.01935
AB - Here we present a detailed theoretical investigation of the environment-induced interaction correction to the ground states and addition energies in a short superconducting junction. We derive general formulas for these corrections linking them to the frequency-dependent admittance of the junction and the environment impedance. We specify two environmental models: that of an external impedance and the Mattis-Bardeen model. In both cases we assume G_Q Z ≪ 1, where G_Q is the conductance quantum and Z the typical environmental resistance. While an expectation is that the typical scale of the relative correction is of the order G_Q Z, we have found that in many cases the dimensionless scale L G_Q Δ provides a better estimation, where Δ is the superconducting energy gap and L an external inductance. We discuss the logarithmic renormalizations of the energies by low- and high-frequency phase fluctuations and single out a non-superconducting contribution related to the renormalization of transmission eigenvalues. We investigate in detail the peculiarities of the corrections at: i. small phases, where the interaction causes a current jump, ii. Andreev bound state energies close to the gap edge, iii. Andreev bound state energies close to Fermi level. In all these cases the correction may become comparable with the unperturbed energy, even for G_Q Z ≪ 1, and we briefly sketch non-perturbative models relevant for the situations.
ER -