Thursday Aug 16th
Our Thursday morning Patio Discussion began with the continuation of Zlatko Tesanovic's
presentation about electrons in the vortex state of superconductors. Since yesterday, he
has written a set of notes on this topic, which are linked here (Zlatko's notes.)
Zlatko said he'd finished yesterday, but would take questions. Piers Coleman (the blogger here) asked him if he could give his opinion about the semi-classical approach that Grisha Volovik has introduced for describing the motion of quasiparticles in a vortex lattice.
In a moment of gest, Zlatko said that the main difference between his theory and Zlatko's theory, was that "He is wrong, we are right"! Actually, later, Zlatko made it quite clear that he has the highest opinion of Grisha Volovik. Here's the main point of the discussion. Volivik's idea, he said, is that in a uniform superflow of superfluid velocity v_s, the Green's function becomes
G(k,\omega) --> G(k, omega - k v_s)
where the change in omega is the famous Doppler shift. Zlatko said, this is good if there is a length scale to compare with, but in a d-wave superconductor, the nodes mean that the system is critical, so at absolute zero, the relevant length scale is infinite. In point of fact, once the temperature is finite, provided the thermal length is small enough there is a cross-over to the regime where the semi classical regime is OK.
Zlatko then gave a quick resume of the previous day's discussion.
Chandra Varma asked whether Zlatko could provide a simple criterion for the characteristic field or energy scale where the quantum nature of quasiparticle-vortex interactions becomes important. (Beyond Volovik's semi-classical theory). Zlatko did not directly answer Chandra's question, but made an alusion to work by Doug Bonn, who found a break-down of the Uemura scaling behavior rho~T_c in highly underdoped YBCO. In Bonn's work, the superfluid stiffness in 2D cuprate systems scales like T_c^2. I did not understand the link between this remark, and Chandra Varma's question.
Thursday, August 16, 2007
Zlatko Tesanovic, continuing about SdH in superconductors.
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In direct response to Chandra's question, Zlatko pointed out that the quantum interactions between quasiparticles and vortices/antivortices are important everywhere inside the underdoped dSC/pseudogap state (ie, below E/T/H scales set by Delta*), provided that the pseudogap has a significant pairing component. This is something that Chandra disputed -- he does not accept that the pseudogap has a pairing origin (see the blog of Varma's talk).
Zlatko then argued that, at the very least, one should concede that such quantum character must be important everywhere inside the underdoped section of the Nernst dome, given the fact that the Nernst effect is the traditional experimental method for detecting vortex fluctuations.
Furthermore, Zlatko stressed that there is a direct way of observing the thermodynamic signature of quantum vortex-antivortex fluctuations: Recent experiment by Lemberger (http://www.arxiv.org/abs/0707.2397 ; they also give an account of the previous work by Bonn et al and the relationship between the two) on very thin films of underdoped YBCO show a 2D KT transition, with Tc collapsing with reduced doping -- the value of Tc, however, obeys perfectly the quantum 2D scaling law, all the way up to Tc ~ 40K. Extreme quantum nature of vortex-antivortex excitations (see also the blog of Nikolic's talk) translates directly into the quantum nature of their interactions with fermionic quasiparticles.
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