SciPost Submission Page
Josephson effect in strongly disordered metallic wires
by Mustafa E. Ismagambetov, Aleksey V. Lunkin, Pavel M. Ostrovsky
Submission summary
| Authors (as registered SciPost users): | Mustafa Ismagambetov · Aleksey Lunkin · Pavel Ostrovsky |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202503_00037v2 (pdf) |
| Date accepted: | June 24, 2025 |
| Date submitted: | June 16, 2025, 3:08 a.m. |
| Submitted by: | Ostrovsky, Pavel |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study localization effects in Josephson junctions with two superconductors connected by a strongly disordered metallic wire of length $L$. The conventional description of the Josephson effect in such systems, based on the quasiclassical Usadel equation, neglects electron interference and is only applicable when $L$ is shorter than the localization length $\xi$ in the wire. We develop a more general theory for the Josephson effect using the non-linear sigma model that fully accounts for electron interference, and hence localization. We show that for $L \gg \xi$, three qualitatively different regimes of the Josephson current arise depending on the ratio of the superconducting order parameter $\Delta$ and the mean level spacing in the localization volume $\Delta_\xi$. We derive the average supercurrent as a function of the phase difference for all three regimes. Quite unexpectedly, we observe that the Ambegaokar-Baratoff relation between the average critical current and the normal-state conductance still holds in the strongly localized state when $\Delta_\xi \gg \Delta$ and $\xi \ll L \ll (\xi/\pi^2) \ln^2(\Delta_\xi/\Delta)$.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
1. Two new paragraphs in the end of page 10 and on page 14 (the last paragraph before conclusion) discussing possible application of the scattering matrix formalism to the calculation of the supercurrent.
2. Two new paragraphs on page 15 in the conclusion section discussing effects of nonzero temperature, dephasing and time-reversal symmetry breaking.
3. New references [14, 17, 22, 23, 24]
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)