Open Discussion and Short Presentations

Tuesday, 31st July.

Open Discussion and short presentations.
10.30am-1.pm Bethe Meeting Place.

The group met to discuss the structure of the workshop. Five speakers
gave their perspective on some of the open questions in this field.

1. Andre Marie Tremblay, Sherbrooke.

"Antiferromagnetism vs d-wave superconductivity: Insights
from the organics"

2. Gabi Kotliar, Rutgers.

"Superconductivity near the Mott transition."


3. Qimiao Si, Rice.

"Quantum Criticality and Superconductivity in Heavy Fermions"

4. Doug Scalapino, UCSB.

"Some issues motivated by the cuprate problem".

5. Subir Sachdev, Harvard.

" Fractionalization on the route from Neel order to d-wave superconductivity"


Summary of Discussions

1. Andrey Marie Tremblay: "Antiferromagnetism vs d-wave superconductivity: Insights
from the organics"

Andrey emphasized that an ultimate test of our understanding of unconventional superconductivity, is to see how successful the theory is when applied to a diverse set of componds. The Organic superconductors display many aspects in common with the 115
and the high temperature superconductors - proximity to antiferromagnetism, frustration and Mott physics.

Andrey discussed the K- (ET)2 X layered organics. The physics of these systems is believed to be described by a 2D Hubbard model on a triangular lattice, with hopping t and t'. You can think of them like the cuprates, but with only one t' cross-link per square plaquet. Unlike the cuprates, by changing the anion X that separates the layers, you can tune t'/t

U ~ 400 meV
t ~ 30 meV
t'/t - (0.6 - 1.1 variation).

Andrey presented the results of a cluster dynamical mean field theory calculation on this model. Without pairing it has a 1st order Mott Transition line. For larger U/t, the system develops antiferromagnetism, or spin liquid. For smaller U/t, it enters a d-wave sc phase and then a metal.

Questions: At large frustration, does the d-wave sc become unstable to new symmetries - e.g p-wave symmetry?

Gabi Kotliar questioned the similarity with the cuprates. Here, the superfluid stiffness is a maximum near the Mott transition, whereas it goes to zero at the Mott transition in the cuprates. Others questioned whether this is due to the difference between doping and U/t tuning.

Also - here the temperature dependence of the superfluid stiffness has an anomalous T^3/2 variation.

2. Gabi Kotliar, Rutgers.

"Superconductivity near the Mott transition."

Gabi discussed the phase diagram of the t-J model of high temperature superconductors, contrasting the predictions of slave boson theory, with that of cluster dynamical field theory
(CDMFT). CDMFT predicts significant anisotropies in k-space that are absent from a slave boson theory. In particular

• The rate at which the quasiparticle renormalization constant Z goes to zero in the approach to the Mott transition, is much faster in the antinodal regions. (Measured in the superconducting phase).
• The v_Delta - the component of the qp velocity coming from momentum dependence of the gap, decreases with the doping (linearly? ), whereas v_F remains doping independent.

This last point has some important consequences. In particular, the T coefficient of the
superfluid spin stiffness, "a" in

rho = rho_0 - a T

becomes doping independent, rather than proportional to doping squared, as in RVB theory.
A similar feature is seen in the omega coefficient of chi''(omega) in Raman spectroscopy, which is predicted to be doping independent.

Gabi's questions:

• Are these features observed experimentally?
• What is the origin of this doping dependence?
• Can we understand the solutions to the CDMFT in a simple language, perhaps analytically?

3. Qimiao Si, Rice.

"Quantum Criticality and Superconductivity in Heavy Fermions"

Qimiao started his presentation with the remark

" Most of the really interesting questions about heavy fermion superconductivity have not been deeply explored.

What are these questions? Qimiao began his talk with a summary of the key properties of heavy electron quantum critical points, taking as examples, CeCu_6-x Au_x (doping tuned), CePd_2Si_2 (pressure tuned) and YbRh_2Si_2 (field tuned).

He later turned to discuss the case of the 115 materials, showing a phase diagram that was quite similar to that presented by Andre-Marie Tremblay. 115 materials have the chemical formula

CeX In_5

where X= Co, Rh, Ir. They are layered heavy electron systems that display antiferromagnetism and superconductivity. Application of pressure to CeRhIn5 leads to a transition from antiferromagnetism, to a region of co-existent superconductivity, then into a purely superconducting phase. However, if you apply a magnetic field to remove the sc, there is a single QCP between the antiferromagnet and paramagnet, where the Fermi surface volume appears to "jump". This jump is associated with the delocalization of f-electrons.

Qimiao asked:

• Can superconductivity co-exist with a state that appears to undergo "fermi surface fluctuations" ?
• How should one characterize superconductivity that forms a dome above a second order QCP, particularly one where the Fermi surface jumps?

4. Doug Scalapino, UCSB.

"Some issues motivated by the cuprate problem".

Doug Scalapino asked the question:

What is the (mother) phase that underlies superconductivity?

As an example of the importance of this question, he discussed two different models of how superconductivity emerges from an antiferromagnetic Mott insulator:

Antiferromagnetically mediated pairing, in which the "mother state" of the superconductor is
a nearly antiferromagnetic metal. In this scenario, the omega dependence of the gap function
Delta(k,omega) should reflect the underlying spectral function of the spin fluctuations.

RVB model of superconductivity, in which the "mother state" of the superconductor is a spin liquid - a Mott insulator without Neel order. In this case, one might expect a disconnect between chi(q,omega) and the frequency dependence of the gap function.

But beyond this, Doug listed all sorts of possible "mother states" of high temperature superconductors:

Stripes
d-symmetry CDWs
d-symmetry SDWs
2-leg ladders
Orbitally ordered states

"Now you may not agree of the starting point, or the mother state, but the important point is that there are a lot of different materials, and room enough for everyone!" (paraphrased).

Doug also mentioned the challenge of the s-wave superconductor Barium Potassium Bismuthate (Ba_1-xKx BiO_3) where T_c ~ 40K. He asked whether the underlying mechanism here is solely phonons, or does charge disproportionation

2Ba(4+) <----> Ba (3+) + Ba(5+)

play an important role?

There was a lot of discussion.

Andy Millis raised the issue of the Taillefer group measurements, that reveal a small Fermi surface in the high field state of underdoped high temperature superconductors. He asked - should we regard this as a "mother state" of the high temperature superconductor, or is it just a competing state?

Thomas Vojta felt that if the transition between competing states was second order, then they would still influence one another.

Shankar asked whether we should consider Grandmother states?!

Sudip Chakravarty pointed out that in simple systems like Pb, there was no ambiguity about the mother state - it was a Ferm liquid with e-phonon interactions, but already once one gets to V3Si, the underlying state might already be a CDW.

There was a philosophical discussion about why it was, when physicists manage to link
Arpes data with spin fluctuation data, it is no widely accepted..... Doug said something about Physicists being quite artful at fitting selected data....




5. Subir Sachdev, Harvard.

" Fractionalization on the route from Neel order to d-wave superconductivity"

Subir posed his questions at the beginning of his talk. They are:

• Is the low doping limit of cuprate superconductors a BCS state (+ some other unconventional order), or is it exotic or "fractionalized"?
• If there is an exotic state at low doping - can this state be obtained by doping a Neel state (and not a non-existent spin liquid?)

Subir then discussed some work he has recently done with Senthil, Levin and others,
in which they discuss the effect of doping the deconfined quantum critical point that is thought
to separate a Neel state from a valence bond solid. The key point about this, is that the quasiparticles of the state that emerges are "fractional", in the sense that they carry a non-trivial gauge charge. These particles, they believe, are possibly the origin of the pockets seen in the Taillefer experiment. Subir also described how, when they pair, they form a conformally invariant fluid, in which the superfluid stiffness has a T-dependence that is independent of doping - rather like the results of the Kotliar work

rho_s(x,T) = constant - R T

where R is universal.