Zlatko Tesanovic, continuing about SdH in superconductors.

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.