# Posted in August 2011

## El condor pasa

I must be free to fly where I will…

Hear this here

Mother of God, by your prayings, let your Son to free me from the scum and earthy burdens, let me be His creation, a free flying soul…

## Summary of a discussion session

of the dirty superconductor workshop that was closed yesterday. It’s also posted to the workshop blog. It’s been a marvelous workshop: thank you,Lorentz center and the organizers

*Discussion Session I Summary: Quantum Phase slips*

The discussion was mostly under the sign of the recent report of Oleg

Astafiev concerning the realization of phase-slip qubit with InO nanowires.

It was noted that a number of features in these devices do not correspond to

usual assumptions about what is good and what is bad for big values of

phase-slip amplitude. Big resistance per square in combination with

significant Tc is certainly thought to be needed for the effect. However,

the issue that required discussion is relatively big width and height of

the wires that by factors exceed coherence length expected for the material.

Another issue concerned the effect of uncompensated charged impurities

readily available in insulating subtrate. The charge induced by these

impurities could lead to a total compensation of the phase-slip magnitude.

It has been noted that a phase-slip in a wire that is wider than coherence

length can be seen as a tunneling of Abrikosov vorthex across the wire. The

fact that the tunneling amplitude is appreciable means that such a vorthex

bears a relatively small energy, perhaps at the scale of quasiparticle

energy, and can be regarded as an elementary excitantion of the dirty

superconductor. An analogy has been drawn with a vortex in Coulomb-blockaded

Josephson junction arrays where a vortex has no core and could have zero

energy. This suggestion is however different from earlier works and

hypotheses concerning dirty superconducting films and Josephson junction

arrays where the possibility of quantum tunneling of already created

Abrikosov vortices has been considered.

Lev Ioffe has outlined his many-body numerical simulations that lead him to

an estimate of phase-slip amplitude in InOx while using a few-site lattice

model. He also suggested that the phase-slip amplitude can be dominated just

by a single optimal path somewhere in the wire, this being in agreement with

other suggestions that weak links can determine the actual magnitude. Such

assumption may aslo explain why the charged impurities do not significantly

reduced the phase-slip amplitude.

It has been noted that the observation of Astafiev is very encouraging for

nanostructuring of the wires to produce more controllable phase-slip devices

where the Coulomb blockade effect can be readily and inambiguosly observed.

The simplest suggestion would be to make two constrictions in the wire

corresponding to two weak links.

It looks like that the report of Astafiev has moved the focus of attention

from the material-science issues to more practical questions. While it

remains to be seen if phase-slips can be observed in traditional candidate

materials like NbSi, TiN, MoGe; InO seems to work. Nano-fabrication and

nano-desing of InO-based devices will probably absorb the attention of

experimentalis for years coming.

## Blog dirty superconductor workshop

blogging is a must today, almost the only way to prove somebody’s existence: “Bloggo ergo sum”, as Descartes would put it today. So we in this dirty superconductor workshop also have an extensive blog, here’s the LINK

.

Below is my post to this blog: report on one of the talks.

Vladimir Kravtsov: Electron cooling rate in amorphous films near superconducting-insulating transition

What can we learn from the giant I-V jumps experiments?

The talk presented overwiev of the work made in collaboration with B.L. Altshuler, V.E. Kravtsov, I.V. Lerner, I.L. Aleiner in response for experimental

findings of M. Ovadia, B. Sacépé, and D. Shahar. The experiment has demonstrated a set of hysteretic I-V curves with order-of magnitude jumps and spectacular temperature dependence. It turned out in 2008 that these curves in all details can be explained if electron overheating is taken into account.

An ultimately simple and elegant phenomenological theory is based on a single equation:

IV= joule heating = cooling rate of electrons to phonon bath, and takes as input the linear temperature-dependent resistance R(Te). The speaker outlined the details of the theory demonstrating its sensitivity to the assumptions concerning the temperature dependence of the resistance and cooling rate presenting several simple solution. Further, he concentrated on the coolest part of the story: temperature-dependent electron cooling rate!

He mentioned that the experimental evidence of strong decoupling of electrons and phonons in insulators undermines usual assumptions that the phonon-assistant electron hopping is the dominant transport mechanism in insulators. The temperature dependence extracted from the experimental data clearly demonstrates the rate proportional to T^6 at hight magnetic fields. T^6 law has been derived for common metals yet by Albert Schmid in seventies. It is somehow puzzling that the proportionality coefficient is 2-4-5 orders magnitude larger than the theory of common metal would predict if extended to localized states (the precise number of orders of magnitudes depends on the estimations of sound velocity). The computation of the coefficient for localized states requires more attention but the power law seem to hold: the speaker argued that the fact that the electron states are localized should not by itself lead to Arrhenius law in temperature dependence.

The most dramatic part of the talk concerned the cooling rate extracted from yet

unpublished data at low magnetic fields. The data did display Arrehius law with energy gap of 1.75 K. The speaker argued that this is a clear manifestation of preformed localized electron pairs in the material. He outlined general problems with forming such pairs in insulator if Coulomb interaction is taken into account. He made use of analogy with double-ionization to assure himself and the audience that Nature permits such things.

The talk provoked a discussion that has started slowly but soon become overheated and

involved multiple parties. Sasha Finkelstein has asked a question about phonon-assistant hoping and expressed his surprise with low energy scale invloved

that is in apparent contradiction with Coulomb energy estimations. The blogger wondered why the cooling rate was assumed to be such a simple function of two temperatures. The answer was that this form was obtained yet by Schmid but eventually

has no apparent reason to be general. Misha Gershezon has shared his experience in measuring colling rates and posed a series of questions addressed to experimentalists and concerned with time scales of cooling. Zvi Ovadyahu mentioned that overheating bistability is readily observed at room temperature. Why does one have to go to low temperatures? The answer: to get cooling rate at low temperatures.

The discussions in groups have lasted at least half an hour after the talk.

## Phase-slip qubit realized?

I’m in Leiden this week, participating in a workshop “Strongly Disordered Superconductors and Electronic Segregation” organized by Mikhail Feigel’man and Teun Klapwijk.

The main event of today (my seminal talk excluding:) ) was a sensational report of Oleg Astafiev of NEC. He has outlined his recent measurements on devices where InO was playing the role of a disordered superconductor. He made use of a desing proposed bij Hans Mooij and Kees Harmans about six years ago, so called phase-slip qubit. And the observation seems to show a well-developed lifted anticrossing of flux states corresponding to the phase-slip amplitude of more than 4 GHz.

As any pioneering experiment, this one rises some questions, especially around the numbers involved. However, it all looks real, for me at least.

## Quantum phase slips in superconducting wires with weak links

is the topic of another cond-mat submission today, please follow the

LINK. This is the outcome of post-doc term of Mihajlo Vanevic, who worked two last days voluntary to accomplish this submission. It was a hard project, results of which are more interesting, and – forgive me this expression – elegant then we expected in the beginning. Mihajlo does not want to stay in West anymore: he gets reseach position in Belgrado.

Here’s the abstract:

*Quantum phase slips are traditionally considered in homogeneous diffusive wires. We argue that even in realistic, apparently homogeneous wires, the phase slips can occur at weak links where the local resistivity is slightly higher. We model the weak link as a general coherent conductor and obtain accurate estimate of the quantum phase-slip amplitude. We speculate on a better estimation of the amplitude for homogeneous wires as well.
*

## Re-flows on arxiv

,finally. I’m quite proud of and excited by the paper. The excitement was so high that I’ve been working yesterday the whole day on the text, fixing small things, but, quite embarassingly, have completely forgotten to run it through a spell-checker… Oh.

Here’s the LINK.

The abstract is rather long:

We demonstrate that the condensed matter quantum systems encompassing two

reservoirs connected by a junction permit a natural definition of flows of

conserved measures, Renyi entropies. Such flows are similar to the flows of

physical conserved quantities such as charge and energy. We develop a

perturbation technique that permits efficient computation of Renyi entropy

flows and analyze second- and fourth order contributions. Second-order

approximation was shown to correspond directly to the transition events in the

system and thereby to posess a set of “intuitive” features. The analysis of

fourth-order corrections reveals a more complicated picture: the “intuitive”

relations do not hold anymore, and the corrections exhibit divergencies in

low-temperature limit manifesting an intriguing non-analytical dependence of

the flows on coupling strength in the limit of weak couplings and vanishing

temperatures.

## Unphysics of quantum information

rocks. I’ve just finished my major contibution to the field: paper on flows of Renyi entropies.Will put in on cond/mat in several days.

## 111

My grandfather Aleksei Ivanovich Nazarov would turn 111 years old today. He has lived 82 years. I always admired the degree of change that took place in society in the course of his life span. He’s born in a poor peasant family. He and his brothers and sisters did not get any shoes till they got ten years old. He died in postindustrial society where the first personal computers just become accessible. If I project the change during my life span, I find it bigger than pleasant, yet much smaller than he has experienced. Or perhaps the projection is just wrong? Or perhaps I’m yet to see my grand(grand)children walking barefoot.

## Gerwin Koolstra

made a record on Friday, 5.8.2011 by sucsessfully passing the examination in Fairly Tales of Theoretical Physics. He’s the first student ever to pass the examination!(And the first to attempt this action

.) It’s my sincere hope that he won’t be last one. We had a bunch of good motivated students during the course.

The threshold that made the examination less popular than we want is the requirement to make three problems from the home work and document the solution. This is indeed a little time investment. I believe that Gerwin Koolstra has proven that this investment pays back soon.