Josephson potentials for single impurity Anderson impurity in a junction between two superconductors

This is a collection of the results from an extensive set of numerical renormalization group (NRG) calculations for the single-impurity Anderson model coupled to two superconducting leads described by the Bardeen-Cooper-Schrieffer (BCS) Hamiltonian, with a  superconducting phase difference phi.

All calculations are performed for the same BCS gap Delta=0.1. Each subdirectory contains the data sets for a given value of charge repulsion parameter U. In each case the hybridisation Gamma and the on-site potential delta=epsilon+U/2 are swept. For each of these, the phase difference phi is swept from 0 to pi in 50 steps.

Contents
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U=0.01
U=0.05
U=0.1
U=0.125
U=0.25
U=0.4
U=0.5
U=0.5-asymmetry
U=0.5-B=0.001
U=0.5-B=0.01
U=0.5-B=0.02
U=0.5-B=0.03
U=0.5-B=0.04
U=0.5-Bsc=0.001
U=0.5-Bsc=0.01
U=0.5-Bsc=0.04
U=0.5-new
U=0.5-z=0.5
U=0.75
U=1
U=1.25-new
U=1.5-new
U=1.75-new
U=2
U=3

Each directory contains the input file (param) and a set of perl scripts for running the calculations, as well as for post-processing the results. For most cases, there are also Mathematica notebooks for visulisation of the results, as well as a collection of plots (pdf files) of the key properties.

The raw results are contained in the archive raw.tar. The Josephson potentials are contained in another archive, results-final.tar.gz. Finally, the results are also stored in tabulated files Vr_1.dat, Vr_2.dat, Va_1.dat, Va_2.dat. The parsing of these files is demonstrated in the Mathematica notebook files.

Directories with -new in the name contain the results in an extended range of the hybridisation Gamma and on-site potential epsilon.

Directories with -z=0.5 in the name contain the results of a calculation for a different discretization mesh in the NRG for testing discretization effects (those are small for the quantity of main interest, the Josephson potential).

Directories with -B=value in the name contain the results for the case with a local magnetic field (Zeeman term) applied on the impurity site, while those with -Bsc=value in the name contain the results for the case with a magnetic field in the superconductor.

The calculations have been performed with the NRG code "NRG Ljubljana", https://github.com/rokzitko/nrgljubljana, http://nrgljubljana.ijs.si/, commit number e6f73ff299d155c6ca9aefded45d67c48f34de0e.

The computation has been performed on HPC VEGA, https://doc.vega.izum.si/.

Note added at a later time: The U=2 data set contains some outliers due to premature termination of some calculations; the outliers are easy to spot, however.