RECORD
Andreev non-Hermitian Hamiltonian for open Josephson junctions from Green's functions
Superconductivity · Submitted 2 Dec 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that, as a rule of thumb, the Andreev NH description is accurate when the spectral overlap between the Andreev bound states (ABS) and the near-gap continuum states is negligible, i.e. when the ABS energies lie sufficiently far from the superconducting gap relative to their line-width.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We investigate the transport properties of open Josephson junctions (JJs) through a minimal effective non-Hermitian (NH) approach derived from the equilibrium Green's function (GF) formalism. Specifically, we consider a JJ with a quantum dot barrier coupled to a normal metal reservoir. The coupling introduces an imaginary self-energy term in the JJ Hamiltonian which can be naturally accounted for in the NH formalism. While most approaches to similar problems work with the full junction Hamiltonian we propose a scheme for deriving an effective NH Hamiltonian for the Andreev levels only, that we compute from the singular part of the barrier GF. To establish the range of applicability of this NH model we benchmark our results for both the dot density of states and the supercurrent against exact GF predictions in different transport regimes. We find that, as a rule of thumb, the Andreev NH description is accurate when the spectral overlap between the Andreev bound states (ABS) and the near-gap continuum states is negligible, i.e. when the ABS energies lie sufficiently far from the superconducting gap relative to their line-width. This method not only highlights the effective physics of the JJ but also offers a scalable framework for studying large-size devices.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We investigate the transport properties of open Josephson junctions (JJs) through a minimal effective non-Hermitian (NH) approach derived from the equilibrium Green's function (GF) formalism. | contribution 0.99 | 0.93 | 0.07 | asserted 0.95 |
| s1 | Specifically, we consider a JJ with a quantum dot barrier coupled to a normal metal reservoir. | method 0.46 | 0.52 | 0.02 | asserted 0.98 |
| s2 | The coupling introduces an imaginary self-energy term in the JJ Hamiltonian which can be naturally accounted for in the NH formalism. | method 0.86 | 0.43 | 0.04 | asserted 0.96 |
| s3 | While most approaches to similar problems work with the full junction Hamiltonian we propose a scheme for deriving an effective NH Hamiltonian for the Andreev levels only, that we compute from the singular part of the barrier GF. | contribution 0.71 | 0.88 | 0.08 | asserted 0.97 |
| s4 | To establish the range of applicability of this NH model we benchmark our results for both the dot density of states and the supercurrent against exact GF predictions in different transport regimes. | method 0.93 | 0.95 | 0.06 | asserted 0.89 |
| s5 | We find that, as a rule of thumb, the Andreev NH description is accurate when the spectral overlap between the Andreev bound states (ABS) and the near-gap continuum states is negligible, i.e. when the ABS energies lie sufficiently far from the superconducting gap relative to their line-width. | result 0.88 | 0.96 | 0.71 | asserted 0.96 |
| s6 | This method not only highlights the effective physics of the JJ but also offers a scalable framework for studying large-size devices. | interpretation 0.89 | 0.57 | 0.13 | asserted 0.95 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We investigate the transport properties of open Josephson junctions (JJs) through a minimal effective non-Hermitian (NH) approach derived from the equilibrium Green's function (GF) formalism. Specifically, we consider a JJ with a quantum dot barrier coupled to a normal metal reservoir. The coupling introduces an imaginary self-energy term in the JJ Hamiltonian which can be naturally accounted for in the NH formalism. While most approaches to similar problems work with the full junction Hamiltonian we propose a scheme for deriving an effective NH Hamiltonian for the Andreev levels only, that we compute from the singular part of the barrier GF. To establish the range of applicability of this NH model we benchmark our results for both the dot density of states and the supercurrent against exact GF predictions in different transport regimes. We find that, as a rule of thumb, the Andreev NH description is accurate when the spectral overlap between the Andreev bound states (ABS) and the near-gap continuum states is negligible, i.e. when the ABS energies lie sufficiently far from the superconducting gap relative to their line-width. This method not only highlights the effective physics of the JJ but also offers a scalable framework for studying large-size devices.
Human review
How the literature uses it
What this paper does with the arXiv papers it cites
What it cites · 11 sentences without a confident label
Cites as background 3 papers
-
In closed systems the supercurrent is tightly related to the GF poles [ref] , this connection in open junctions is still the object of current investigations [ref] .
Thermodynamics of Non-Hermitian Josephson junctions with exceptional points · Current formula · 0.91
-
In closed systems the supercurrent is tightly related to the GF poles [ref] , this connection in open junctions is still the object of current investigations [ref] .
Non-Hermitian minimal Kitaev chains · Current formula · 0.91
-
In closed systems the supercurrent is tightly related to the GF poles [ref] , this connection in open junctions is still the object of current investigations [ref] .
2408.01289 · Current formula · 0.91
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.