De meningen ge-uit door medewerkers en studenten van de TU Delft en de commentaren die zijn gegeven reflecteren niet perse de mening(en) van de TU Delft. De TU Delft is dan ook niet verantwoordelijk voor de inhoud van hetgeen op de TU Delft weblogs zichtbaar is. Wel vindt de TU Delft het belangrijk - en ook waarde toevoegend - dat medewerkers en studenten op deze, door de TU Delft gefaciliteerde, omgeving hun mening kunnen geven.

Posts in category Research

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!

PhD position in condensed matter theory

I would like to announce a PhD opening with me at the department of Quantum NanoScience at Delft University of Technology. According to Dutch standards, this is a 4-year employment with gross salary up to 2,718 euro.

The project concerns superconducting junctions, topological effects and superconducting qubits. In its short form, it can be found here.

The preferable starting date is 1-1-2016 and can be negotiated. The applications will be considered till 10-11-2015. The applicants are encouraged to send me their CV, motivation letters, and the list of referees. It is also useful to make a test and enclose the results.

Please do not hesitate to ask any questions!

Look forward to a good collaborator!

Keldysh formalism for multiple parallel worlds

this paper with M. Ansari has appeared on arxiv today: see it here. This is our contribution to the forthcoming Special JETP issue dedicated to 85th anniversary of Prof. L. V. Keldysh.

We present here a compact and self-contained review of recently developed Keldysh formalism for multiple parallel worlds. The formalism has been applied to consistent quantum evaluation of the flows of informational quantities, in particular, to evaluation of Renyi and Shannon entropy flows. We start with the formulation of standard and extended Keldysh technique in single world in a form convenient for our presentation. We explain the use of Keldysh contours encompassing multiple parallel worlds In the end, we shortly summarize the concrete results obtained with the method.


Usually it is quite boring to write about the workshops and conferences, but not about this one. The long title is Frontiers of Quantum and Mesoscopic Thermodynamic and it was held in Prague, 27 July – 1 August 2015. The conference, as all other conferences in series, has been organized with a good care and a warm twist. Among usual things, like meeting many old friends and attending few interesting talks, my mind was rebooted by a plenty of impressions that are best described as surrealistic, almost out-of-world. Just some highlights:

– attended a concert of (well, mostly) classical musics every evening during a week

– heard the vice-president of Czech Academy of Science complaining about unjust separation of physics and musics in the structure of his establishment

– seen Gerard t’Hooft being publicly kissed by a mid-aged lady in an eye-catching garment. She had a medal for him, you see.

– listened to the same Gerard t’Hooft talking about super-determinism in gloomy theatrical environment so the cold horror of predestination grabbed my heart

– signing my book for Marlan Scully, a legend of my student times (have never met him before)

– had a too-much-wine dinner in an establishment that looked like a benedictine monastery from one side and a country-side restaurant from another side. We had a concert in their chapel, so that was the first option for sure

I could go on with the list. Many thanks to the organizers!

Paper to commemorate Markus Buttiker

who has passed away on Oct 4, 2013 in the age of 63. There will be a special issue of Physica E devoted to his memory.

From the conclusions:
“In conclusion, we have provided a technical and comprehensive introduction to the Keldysh action formalism for a multi-terminal scatterer with special emphasis on superconducting leads. We have derived a very general and compact formula and have elaborated on simple important examples to demonstrate the variety of its applications.

I did this to commemorate Markus Buttiker, the pioneer of scattering approach to quantum transport, one of the fathers of this big, prosperous and fruitfully developing research field. I admire not only his research merits: throughout 25 years of our acquaintance I was appreciating much his daring to remain himself, to keep his own research style, research topics and idea sets in times where the close following of a quickly changing scientific fashion seemed to be a must. He was also a charming personality and a good friend.”

The paper can be found here.

Exact correspondence between Renyi entropy flows and physical flows

has been published today.
Reference: Mohammad H. Ansari and Yuli V. Nazarov, Phys. Rev. B 91, 174307 (2015)

Silence and ERC Advanced Grant proposal

I didn’t write much to the blog for almost a couple of months. An excuse for this is I’ve been busy preparing an important grant proposal. Not that it really took every minute of my working time – yet for me it is psychologically difficult to prepare proposals, and any unrelated activity eventually gives a feeling of guilt – whatever irrational it may be.

Anyway, I’m almost done and will submit the proposal soon. It is in development of the recent ideas about topological properties of superconducting junctions. Below is the title and the abstract.

Higher-dimensional topological solids realized with multi-terminal superconducting junctions (HITSUPERJU)

Recently I revealed a deep operational analogy between an exotic material and an electronic device, i.e. between a 3-dimensional topological solid and a 4-terminal superconducting junction. Specifically, the 3d Weyl singularities revealed in the energy spectrum of this quantum device give rise to quantized trans-conductance in two leads that is typical for 2-dimensional topological Quantum Hall materials. The quantized value can be tuned with the third control phase.

I propose to capitalize on this breakthrough by realizing artificial n-dimensional (topological) solid materials by (n+1)-terminal superconducting junctions. This seemed to be fundamentally forbidden so far. In particular, in the framework of one research direction I will address the realization of higher Chern numbers. The edges and interfaces are important in topological solids, they need to be structured. For the artificial topological materials made with multi-terminal superconducting junctions such structuring is impossible in geometric coordinate space. However, the fact that the charge and superconducting phase are quantum-conjugated quantities provide the unique possibility for the structuring in multi-dimensional charge space that I will access in the framework of another direction. These two research directions will be supplemented by a more technical effort devoted to computational (quantum) dynamics of multi-terminal superconducting junctions.

The proposed way to “conquer” higher dimensions for condensed matter physics is of clear fundamental importance. Exciting applications are at the horizon, too. The exotic quantum states under consideration can be topologically protected and thus useful for quantum information processing. Quantized trans-resistance as well as other topological invariants may be important in metrology. More generally, the research proposed will boost the whole field of electronic devices wherever topology guarantees the discrete stability of device characteristics.

Strong effects of weak ac driving in short superconducting junctions

has been published in PRB couple of days ago.
DOI: 10.1103/PhysRevB.91.104522

You can find the preprint here.

We study a short superconducting junction subject to a dc and ac phase bias. The ac modulation changes the occupation of the Andreev bound states formed at the constriction by transitions between bound states and the continuum. In a short junction, the non-equilibrium Andreev bound state population may relax through processes that conserve parity of the occupation number on the same bound state and processes that do not conserve it. We argue that the parity conserving processes occur on a much faster time scale. In this case, even a weak driving may lead to a large deviation of the supercurrent from its equilibrium value. We show that this effect is accompanied by a quasiparticle current which may lead to a measurable charge imbalance in the vicinity of the junction. Furthermore, we study the time evolution of the supercurrent after switching off the ac drive. On a time scale where parity relaxation is negligible, the supercurrent relaxes to a stationary non-equilibrium state. Finally, we briefly outline the regime of ultraweak driving where the ac-induced processes occur on a time scale comparable to parity relaxation.

Evaluation from VvTP

The VvTP, our student society, has a contact group that evaluates the courses given and provides a feedback for the teachers. This is what I got on Wednesday:

Advanced Quantum Mechanics:
Nazarov is very enthusiastic about the content of the course. He is following the book very closely: that’s a very good thing. The book is very good. Students like this, there is a clear structure in the course. A bit more examples would be nice though, to have some practical view. The problems are very compatible with the book and lectures. Students say that it takes a long time making them, because you really have to understand the content.

The presentations which the students have to prepare are quite good. It would be appreciated if the focus of the course would be a bit more practical in the lectures. Students like the way Nazarov did a survey himself. They appreciated the fact that he is clearly trying to improve his way of teaching. A possible improvement would be to give a quick summary of the content covered at the end of each lecture.’

Actually, it’s pretty encouraging evaluation, thank you). I promise to give the summary every lecture. But, well, my memory is not as good as it used to be X years ago. Perhaps I need to ask assistance from the audience? πŸ™‚

Quantum Transport:
β€˜12 students attending in total. The homework is pretty nice. The course is about applications, but the lectures are not that much into it. Maybe there could be some more exercises to practice and get a better insight.β€˜

A bit surprised that the course is about the applications: but well, it’s rather a compliment πŸ™‚ I hated home work, especially extensive one, when I was a student. Good, perhaps next year I can make more of it.

Multi-terminal Josephson junctions as topological materials

if you ask me, is a splendid piece of research. I mentioned the submission earlier: now the preprint is available here.

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 a straightforward realization of tunable topological materials in nβˆ’1 dimensions. For nβ‰₯4, the Andreev subgap spectrum of the junction can accommodate Weyl singularities in the space of the nβˆ’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 2e^2/(πℏ).

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