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Spectral response of Josephson junctions with low-energy quasiparticles

by Anna Keselman, Chaitanya Murthy, Bernard van Heck, Bela Bauer

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Submission summary

Authors (as registered SciPost users): Anna Keselman · Chaitanya Murthy · Bernard van Heck
Submission information
Preprint Link: scipost_201906_00002v1  (pdf)
Date accepted: 2019-10-01
Date submitted: 2019-06-19 02:00
Submitted by: Keselman, Anna
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Condensed Matter Physics - Computational
Approaches: Theoretical, Computational


We study nanowire-based Josephson junctions shunted by a capacitor and take into account the presence of low-energy quasiparticle excitations. These are treated by extending conventional models used to describe superconducting qubits to include the coherent coupling between fermionic quasiparticles, in particular the Majorana zero modes that emerge in topological superconductors, and the plasma mode of the junction. Using accurate, unbiased matrix-product state techniques, we compute the energy spectrum and response function of the system across the topological phase transition. Furthermore, we develop a perturbative approach, valid in the harmonic limit with small charging energy, illustrating how the presence of low-energy quasiparticles affects the spectrum and response of the junction. Our results are of direct interest to on-going experimental investigations of nanowire-based superconducting qubits.

Published as SciPost Phys. 7, 050 (2019)

Submission & Refereeing History

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Submission scipost_201906_00002v1 on 19 June 2019

Reports on this Submission

Anonymous Report 1 on 2019-8-19 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_201906_00002v1, delivered 2019-08-19, doi: 10.21468/SciPost.Report.1120


(1) Timely. The manuscript focuses on a timely and technologically important problem
(2) The authors' numerical approach allows for an easy extension to realistic models which would help the ongoing experimental effort.
(3) Simple analytical models that help clarify the physics coming out of the numerical simulations.
(4) Clear introduction and exposition; I enjoyed reading it.


(1) In my opinion, the weakest point, if it can be seen as one, is that the manuscript's lack of a strong punchline. However, its main result that the junctions are too complicated to distinguish topological transitions in a transmon setup is definitely worthy of publication.


The present manuscript focuses on an interesting problem: the dynamics of a Josephson junction in the presence of low lying quasiparticles (particularly that formed by a pair of Majorana bound states). The authors focus on a transmon setup and calculate both numerically and analytically the spectral function of the charge operator as well as the excitation spectra of the junction across the topological transition. Presence of Andreev bound states of nontopological origin, a likely complication, is also considered. The numerical method adopted by the authors seems extendable to much more realistic models which would increase the relevance of the present work to ongoing experimental effort. As I mention above, the main result that the Josephson junctions might be too complicated to observe distinguishing signatures of topological transitions in a transmon setup is definitely worth publishing. Therefore I recommend publication after the minor revisions decribed below are done.

Requested changes

Fig 3c: supply legend for the colored-dashed lines

I would like to ask the authors to consider publishing their code.

  • validity: top
  • significance: high
  • originality: high
  • clarity: top
  • formatting: excellent
  • grammar: excellent

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