# 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

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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.