Erik S. Samuelsen | Searcharxiv

arXiv2026

Interaction effects on Andreev states from an electromagnetic environment

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 $G_Q Z \ll 1$, 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 $G_Q Z \ll 1$, and we briefly sketch non-perturbative models relevant for the situations.

cond-mat.supr-con↗

arXiv2025

Andreev molecules at distance

Andreev molecule states arise from hybridization of Andreev bound states in different Josephson Junctions. Extensive theoretical and experimental research concentrates on direct coherent electron coupling between the junctions: this implies the distance between the junctions is of the order of superconducting coherence length, that is, short. We propose and discuss the possibility to create Andreev molecules at long (in principle, arbitrary long) distance between the junctions. In this case, the hybridized states are excited quasi-particle singlets and the coupling is provided by an embedding electric circuit. To achieve a strong hybridization, one aligns the energies of the Andreev bound states with associated phase differences. In fact, a recent experiment realizes such setup. With circuit theory we derive the hybridization level splitting and estimate the scale of the effect. Since the phenomenon encompasses excited states, we derive and solve the associated Lindblad equation under condition of persistent resonant excitation. By analyzing the resulting dissipative dynamics we identify relevant regimes where the hybridization and resonant excitation peaks are most pronounced. The low-frequency mutual inductance of the Josephson junctions is an important signature of the molecular state and associated non-local Josephson effect. We demonstrate the peak structures for both mutual and self-inductance, and compute them in various frequency regimes. In an interesting common case the embedding circuit includes an oscillator, which can be used both to enhance hybridization and for state readout with two-tone spectroscopy. We derive and solve Lindblad equations for the conditions of two-tone spectroscopy to demonstrate the the readout of molecular states.

cond-mat.supr-con↗