# Weblog Yuli Nazarov

## Supercurrents in chiral channels originate from upstream information transfer: a theoretical prediction

This is the title of (relatively) new arxiv submission, first with Xiao-Li Huang.

It can be found here.

**Abstract:**

*It has been thought that the long chiral edge channels cannot support any supercurrent between the superconducting electrodes. We show theoretically that the supercurrent can be mediated by a non-local interaction that facilitates a long-distance information transfer in the direction opposite to electron flow. We compute the supercurrent for several interaction models, including that of an external circuit. *

## Nature news and views

Quite unexpectedly, I’ve published something in Nature, specifically in News ans Views:

**Quantum physics: Destruction of discrete charge**

*Electric charge is quantized in units of the electron’s charge. An experiment explores the suppression of charge quantization caused by quantum fluctuations and supports a long-standing theory that explains this behaviour. See Letter p.58*

Yuli V. Nazarov

*Nature 536, 38–39 (03 August 2016) | doi:10.1038/536038a*

Full text can be seen here.

## PhD and post-doc openings

In the framework of ERC Advanced Grand *Higher-dimensional topological solids realized with multi-terminal superconducting junctions*

(HITSUPERJU) I would like to announce

- 2 Ph.D. positions, duration 4 years, it is possible to start from 1-8-2016 while the preferable starting date is 1-12-2016
- 1 post-doc position, duration 2 years, starting date spring 2017.

Here you can find a short description of the project.

To apply, please send

- your CV,
- motivation letter with the references to the project content,
- the names of three referees,
- importantly, the results of the TEST

to my e-mail address

While the test is more appropriate for Ph.D. candidates, aspiring postdocs are also requested to make it.

I look forward to fruitful collaboration!

## Survey AQM #1

Here are the results of the first survey of AQM course. It took place on Feb 26. There were 36 participants. Main numbers are as follows:

Mark lectures: 7.4 Mark PPS: 6.7 Overall mark: 7.3

*Better than last year. Still lack of PPS appreciation.*

Read more

## Nature Communications

Another publication with Grenoble friends. The preprint is available for almost a year, it had a complex history of submissions and interactions with referees Anyway, it feels like my best paper so far.

Title: **Multi-terminal Josephson junctions as topological matter **

Authors: Roman-Pascal Riwar, Manuel Houzet, Julia S. Meyer & Yuli V. Nazarov

Ref: Nature Communications 7, Article number: 11167, doi:10.1038/ncomms11167

Abstract:* Topological materials and their unusual transport properties are now at the focus of modern experimental and theoretical research. Their topological properties arise from the bandstructure determined by the atomic composition of a material and as such are difficult to tune and naturally restricted to ≤3 dimensions. Here we demonstrate that n-terminal Josephson junctions with conventional superconductors may provide novel realizations of topology in n−1 dimensions, which have similarities, but also marked differences with existing 2D or 3D topological materials. For n≥4, the Andreev subgap spectrum of the junction can accommodate Weyl singularities in the space of the n−1 independent superconducting phases, which play the role of bandstructure quasimomenta. The presence of these Weyl singularities enables topological transitions that are manifested experimentally as changes of the quantized transconductance between two voltage-biased leads, the quantization unit being 4e2/h, where e is the electric charge and h is the Planck constant.*

## Density of states in gapped superconductors with pairing-potential impurities

This is the title of a recent publication with my Grenoble friends.

Phys. Rev. B 93, 104521 – Published 21 March 2016

Text at Arxive

**Abstract:**

We study the density of states in disordered s-wave superconductors with a small gap anisotropy. We consider disorder in the form of common nonmagnetic scatterers and pairing-potential impurities, which interact with electrons via an electric potential and a local distortion of the superconducting gap. Using quasiclassical Green functions, we determine the bound-state spectrum at a single impurity and the density of states at a finite concentration of impurities. We show that, if the gap is isotropic, an isolated impurity with suppressed pairing supports an infinite number of Andreev states. With growing impurity concentration, the energy-dependent density of states evolves from a sharp gap edge with an impurity band below it to a smeared BCS singularity in the so-called universal limit. Within one spin sector, pairing-potential impurities and weak spin-polarized magnetic impurities have essentially the same effect on the density of states. We note that, if a gap anisotropy is present, the density of states becomes sensitive to ordinary potential disorder, and the existence of Andreev states localized at pairing-potential impurities requires special conditions. An unusual feature related to the anisotropy is a nonmonotonic dependence of the gap edge smearing on impurity concentration.

## ERC Advanced Research Grant

Wow, it looks I got one! I wrote about working on the proposal. It was more than 9 months ago.

A short proposal description can be viewed here.

I hope to post more job announcements soon!

## Unveiling mysteries

with my Grenoble collaborators. Fresh submission.

**How many quasiparticles can be in a superconductor?**

Anton Bespalov, Manuel Houzet, Julia S. Meyer, Yuli V. Nazarov

*Experimentally and mysteriously, the concentration of quasiparticles in a gapped superconductor at low temperatures always by far exceeds its equilibrium value. We study the dynamics of localized quasiparticles in superconductors with a spatially fluctuating gap edge. The competition between phonon-induced quasiparticle recombination and generation by a weak non-equilibrium agent results in an upper bound for the concentration that explains the mystery.*

## Sixth Lecture Advanced Quantum Mechanics 2016

was about classical stuff, representation of oscillators – rather technical and preparatory, but necessary, and, with several anecdotes, not boring.

The timing was good, though I could go faster in the first half of the lecture and slower in the second half. However, I’ve a bad feeling of not being understood completely. Perhaps next time I need to reserve time to make several simple calculations explicitly — you never know.

My question “Who does not know what vector potential is?” usually was answered positively by 20% of students. This time no single hand was risen. I wonder if the education has been improved or the question was not understood

## Engineering topological materials

It’s been a while I’ve submitted something with experimentalists, yet it has happened, rather fast and unexpected. Volia!

**The ω-SQUIPT: phase-engineering of Josephson topological materials**

*E. Strambini, S. D’Ambrosio, F. Vischi, F. S. Bergeret, Yu. V. Nazarov, F. Giazotto*

Abstract:

*Multi-terminal superconducting Josephson junctions based on the proximity effect offer the bright opportunity to tailor non trivial quantum states in nanoscale weak-links. These structures can realize exotic topologies in multidimensions as, for example, artificial topological superconductors able to support Majorana bound states, and pave the way to emerging quantum technologies and future quantum information schemes. Here, we report the first realization of a three-terminal Josephson interferometer based on a proximized nanosized weak-link. Our tunneling spectroscopy measurements reveal transitions between gapped (i.e., insulating) and gapless (i.e., conducting) states, those being controlled by the phase configuration of the three superconducting leads connected to the junction. We demonstrate the topological nature of these transitions: a gapless state necessarily occurs between two gapped states of different topological index, very much like the interface between two insulators of different topology is necessarily conducting. The topological numbers characterizing such gapped states are given by superconducting phase windings over the two loops forming the Josephson interferometer. Since these gapped states cannot be transformed to one another continuously withouth passing through a gapless condition, these are topologically protected. Our observation of the gapless state is pivotal for enabling phase engineering of more sophisticated artificial topological materials realizing Weyl points or the anomalous Josephson effect.
*