KITP - 11

Quantum Phase Transitions

Week 11
21st March - 25th March, 2005

Bloggers: Andrey Chubukov & Piers Coleman

This was the week of the APS March meeting, but many participants preferred the quiet of Santa Barbara to the crowded Conference Center at Los Angeles. The weather continued to be touchy and on Tuesday, we had 2.5 ins of rain! By the end of the week however, the weather had turned sunny again, and we're all hoping this is how it will stay for the remainder of the program. Mike Norman has left our ranks, to return to Argonne National Lab in Chicago, with his digital camera, so for the moment, there will be no more "action shots" of the black-board and presentations. Mike - thanks for helping out with the blog for the past five weeks.

On Tuesday, we had an informal session on ruthenates and Ce-based 115 materials, with Andy Schofield and Andrey Chubukov leading a lively discussion. The Thursday Founder's Room discussion focussed on the "kink" observed by ARPES in the dispersion of electrons in the normal state of cuprate superconductors. Is this kink due to phonons, or some other mass renormalization process? To find the answer to this question, read on!

Participants
Blackboard Seminar
Experimental Seminar
Thursday Discussion

Participants present. Click on participant to read questions that they have posed.

Abrahams, Elihu
Chubukov, Andrey
Coleman, Piers
Efetov, Kostya
Eshrig, Mathias
Feldman, Dima
Geshkenbein, Vadim
Kroha, Johannes
Larkin, Anatoli
Monien, Hartmut

Morr, Dirk
Pepin, Catherine
Posazhennikova, Anna
Schofield, Andrew
Schmalian, Joerg
Si, Qimiao
Turlakov, Misha Weng, Zheng-Yu
Yakovenko,Victor

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Monday Blackboard Discussion. Not held this week.

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Discussion Seminar, 12.30pm Tuesday, March 22nd.

At an SDW quantum critical point the Fermi surface reconstructs leading to sharp corners of the Fermi surface with radius of curvature /v_F. The the usual weak-field magnetotransport requires that quasiparticles do not precess around the corners between scattering events: . This can never be met at a field driven quantum critical point and leads to new behaviour.	Andy Schofield began with a discussion of his current work in collaboration with Joe Fenton at the University of Birmingham, UK (unpublished). They point out that the collapse of an energy scale at a QCP can have important consequences for transport. They showed that the weak-field regime for magneto transport with an SDW gap of size is . This means that the order of limits and is important. Andy argued that at a field driven QCP, one should expect discontinuities in the conductivity, and that at a non-field driven QCP in a clean metal, the magnetoresistance would be linear in field. He speculated that this effect might be seen in clean Cr_1-xV_x.
In the second presentation, Andrey Chubukov reviewed recent experimental work by L. Taillefer and co-workers (cond-mat/0503342)on thermal conductivity in CeCoIn₅. This material becomes superconducting at T_c =2.3K$, and there are experimental reasons to believe that superconductivity is of d_x2_-y symmetry. The issue they addressed is how the system properties evolve upon adding non-magnetic impurities which in their case were introduced by substituting Ce by La.
	This group measured the specific heat of Ce_1-x La_x CoIn₅ and found that T_cis depressed, and that furthermore, as x increases, a residual, normal component of develops, growing with doping.This is consistent with theory, where impurities in a $d-$wave superconductor produce a finite DOS near the nodes, with a magnitude of DOS which scales with La doping, x .
The group also measured thermal conductivity. In the normal state, should scale inversely with the Lanthanum concentration, x, by the Wiedemann-Franz law, and this precise behavior was indeed observed. In a superconducting state, the theory of Durst and Lee and others predicts that should be independent of x, for the normal state 1/x dependence is now balanced by the DOS which scales as x. Surprisingly, they observed that still follows a 1/x dependence. Taillefer et al conjectured that a possible explanation may be that a portion of electrons (from one of the two Fermi surface sheets) does not participate in the pairing. Hopefully, theorists will address this issue in near future.

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Discussion: 4:30 pm Thursday, March 24th Founders Room.

kink

The "kink" in the electron dispersion, after A. Lanzara, P. V. Bogdanov, X. J. Zhou, S. A. Kellar, D. L. Feng, E. D. Lu, T. Yoshida, H. Eisaki, A. Fujimori, K. Kishio, J. -I. Shimoyama, T. Noda, S. Uchida, Z. Hussain, Z.-X. Shen, Nature 412, 510-514 (2001), cond-mat/0102227.

On Thursday, we all paid respect to our own media-driven craziness, and discussed in great detail the ``kink'' in the cuprates. Elihu Abrahams presented a detailed overview of the experimental situation. He formulated several questions for the experimentalists:

--- what is the temperature, doping and angular dependence of the kink?

--- how strong is the isotope effect?

--- what is the role of bi-layers?

and for theorists:

--- phonons vs spin fluctuations?

--- the role of strong correlations?

--- why doesn't the high energy dispersion extrapolate to k_F?

--- a possible relation between the kink and the pairing mechanism?

Dirk Morr presented the ``phonon story'' (but was he really playing the role of Devils advocate?), following recent work by Tom Devereaux and co-workers. The ``phonon'' explanation of the kink involves two phonon modes, the B_1g mode at 35 meV, which is responsible for the kink near antinodal points, and the breathing mode at 70 meV, which is responsible for the kink along the nodal direction. The coupling
constant for the breathing mode is very small, and this eliminates an S-shape dispersion, which one would generally expect when a fermion is coupled to a mode. At the same time, the observed velocity renormalization along nodal direction is believed to be of order one, so some other, non-phonon mechanism must be responsible for this.

Matthias Eschrig discussed recent neutron scattering results on the effect of the replacement eq7 on the resonance peak. The data show that the position of the peak does not change, but the resonance becomes broader.

Werner Hanke discussed his current work on the role of vertex corrections for the coupling to bosons. He argued that, when Mott physics is relevant, vertex corrections are large, and cannot be neglected.

Finally, Andrey Chubukov presented a ``spin-fluctuation'' scenario for the kink. He described recent work with Mike Norman on the angular, temperature and doping dependence of the fermionic dispersion. He argued that in the spin-fluctuation scenario, the normal state dispersion has crossover ( called a ``soft kink'' by one of participants) at a frequency where the system crosses over from a Fermi liquid to a non-Fermi liquid regime.The crossover frequency is smaller for antinodal fermions. Above the crossover, the real part of the self-energy is nearly flat , and this gives rise to a linear dispersion which interpolates inside the Fermi surface. In the superconducting state, the magnetic scenario predicts an s-shape dispersion for antinodal fermions due to the coupling to the spin $(\pi,\pi)$ resonance, but no s- shape dispersion for nodal fermions which do not couple to the resonance by symmetry reasons. Andrey argued that this explanation is consistent with the data.

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