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Posted in 2016

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
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

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.

Tomohiro Yokoyama

has left us for further post-doc career in Japan. He stayed with me as a post-doc – eventually, a JSPS fellow, from 6.4.2014. We have worked on Andreev bound states in superconducting heterostructures, with and without spin-orbit interaction. We still have to finish a (very big) paper. Thank you, Tomohiro, with you I did the stuff I wouldn’t do otherwise. Best luck with your new job!

On blogging in general :)

I cannot blog on time. I cannot stop blogging at all: I have a feeling, most likely irrational , that the life passes by without a trace if I don’t do this. To balance between this, I’d like to use a rather dirty trick of back-dating. Please do not be surprised.

First lecture Advanced Quantum Mechanics: 2016

This year I got a very convenient lecture room, zaal E, that can house almost an infinite number of students and has a slanted floor. I gave the same course in this room yet 10 years ago. It took a bit of time to adjust: and I could enjoy again. An inconvenience is that the lectures take place on early Monday morning 🙁

Despite this, the audience was full – not unusual for the first lecture. I took time explaining the rules of the course (those I myself find rather complex). Not that I felt understood, but I said what I had to. The stuff went rather fast. Nobody has heard of Heisenberg picture, no single hand – all right, but with this it went only faster. Still I was very vague about qubits and had to skip the harmonic oscillator – too much time lost in the beginning.

I had like 4 minutes for density matrix – no preliminary knowledge as well. Looked enough, but I have discovered that the outlining of the partial trace is too abstract to be taught that quickly …

Fortunately, there was enough time on Thursday. The presentations were fine, including density matrix from thermodynamical point of view. And I told about partial trace, slowly and with details – that seemed to go into open ears. Fine!

PhD or post-doc position in theory of spin qubits in semiconducting heterostructures


In the framework of collaboration with experimental group of Lieven Vandersypen I would like to announce an opening that can be either on PhD (4 years) or post-doc (3 years) level, at the department of Quantum NanoScience at Delft University of Technology.

The successful candidate is expected to

  • have some research experience concerning theoretical spin and semiconductor physics
  • work in close and persistent interaction with experimentalists
  • be flexible with respect to short-term research planning
  • like the combination of analytical and numerical methods

The appointment can commence as early as 15-2-2016 while the starting date can be negotiated. The applications will be considered till the success of the search. The applicants are encouraged to send me their CV, motivation letters, and the list of referees. It is also very useful to make a short test and enclose the results.

Please do not hesitate to ask any questions!

Look forward to a good collaborator!

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