Joe Thompson: "Proximity of Superconductivity and Magnetism in the 115s"

Joe described his work with T. Park and other collaborators on CeRhIn5,
a member of the 115-family of heavy fermion materials that are layered
derivatives of the cubic CeIn3. The attached figure shows the
magnetic/superconducting phase diagram as a function of pressure,
magnetic field, and temperature.

At a sufficiently high magnetic field (above 9T), increasing pressure
induces a quantum phase transition (at P1) from an antiferromagnetic metal
phase to a non-magnetic metal phase. There is some indication that
the transition is second order. Yet, dHvA measurements of Onuki's group
find a jump in the Fermi surface, with effective mass showing a tendency
of divergence at P1. In the low-pressure AF phase, the f-electrons are
localized since the measured Fermi surface is similar to that seen
in the f-less reference material LaRhIn5. In the higher-pressure non-magnetic
phase, on the other hand, the same f-electrons are itinerant because
the measured Fermi surface is similar to that of the bandstructure
calculations in which these f-electrons are assumed mobile.

Joe went on to describe the pressure-induced transitions inside the
superconducting part of the phase diagram. For finite fields (which
are smaller than 9T), there is evidence for the second-order nature
of the transition from a co-existing AF+SC phase (which appears to
be homogeneous) to a pure SC phase. At H=0, the residual specific
heat coefficient was found to undergo a rapid decrease as the pressure
is increased through a threshold value (P2, smaller than P1),
as did the Fermi velocity fitted from the finite-T Hc2.

Joe suggested that the f-electrons remain localized in the SC+AF
phase. He did so based on the aforementioned dHvA observation
of localized f-electrons in the high field AF state, along with
the observation that the ordered moment at temperatures just above
Tc of the AF+SC phase is large.

There was discussion about how strong an evidence the above entail
for the localized nature of the f-electrons inside the AF+SC phase.
There was also discussion on the extent to which the change of \gamma
and v_F across P2 should be associated with the transition in magnetism,
or is instead a reflection of a distinction in superconductivity between
the co-existing AF+SC phase and the pure SC one.

Joe went on to describe the effect of Cd-doping in Co-115 and Ir-115.
A co-existing AF+SC region occurs in the Cd-doped Co-115, but is absent
in the Cd-doped Ir-115.

The main questions that Joe raised are:

* What is the nature of the 4f electrons when they participate
simultaneously in magnetism and superconductivity?

* If we accept the notion that the f-electrons are localized while
participating in the superconductivity, what implications does it
have for the non-Fermi liquid behavior in the normal state?

* In particular, does it suggest some form of Kondo breakdown?

Herb Mook: Search for Magnetism in YBCO Superconductors

H. Mook, ORNL

“Search for Magnetism in YBCO Superconductors”

H. Mook described his work with P. Bourges and their collaborators at the Laboratoire Léon Brillouin (LLB), Saclay, France. The doping corresponded to O(6.6). The Oxygen chain ordering was striking and corresponded to the Ortho-II state (for details, see the reference below). The large crystal weighing 25g was previously studied for the detection of d-density wave: Mook et al. Phys. Rev. B 66, 144513 (2002). Mook reiterated that the previous experiment did exhibit evidence of d-density wave although the signal was weak. The present experiment was designed to detect circulating currents proposed by C. M. Varma in the same sample.

What makes this effort puzzling is that in an unpublished work done at NIST no evidence for circulating currents was found, while the same sample examined in LLB showed strong evidence of circulating currents in agreement with the experiment of B. Fauqué et al. Phys. Rev. Lett. 96, 197001 (2006). To quote Mook, “If you can see it in France, why can’t you see it here?” The joke apart, there may be some serious reasons for this. The beam at LLB was better, with a higher flux and therefore higher intensity. More importantly, the flipping ratio, crucially important for polarized neutron scattering, was much larger, 70 as opposed to 23.3 in the NIST experiment. According to Mook these factors contributed significantly to the success of the measurement in LLB.

Indeed, the rise of the spin flip intensity at (101) at 200K was very sharp and continued through without the slightest hint of the superconducting transition. However, no such scattering was found at (200). The size of the moment is not yet known but the scattering cross section is 1 mb, probably corresponding to a few hundredths of a Bohr magneton. The real difficulty is that the observed direction of the moments is at an angle of 45 degrees, not along the c-direction.

P. A. Lee suggested that it would be useful to repeat the previous measurements at
(1/2,1/2) at LLB. I completely agree.

The bigger issue involves the elusive signatures of magnetic order in the pseudogap phase of high temperature superconductors. I find it particularly puzzling that the same sample shows two signatures of orbital magnetic order: one that breaks translational symmetry of the lattice and the other that does not. However, it is heartening that competing groups are now collaborating to unravel some of the mysteries of the pseudogap. This is real progress.

Laura Greene: Andreev reflection in Ce 115's

Laura presented point-contact spectroscopy results on CeCoIn5/Au contact,
namely the data on normalized tunneling conductance for the wide range of
temperatures. Data shows an asymmetry which appears below certain temperature,T*, most probably associated with a formation of a heavy Fermi liquid. As CeCoIn5 becomes superconducting, the small (~13%) Andreev signal is
observed. Laura presented fits to the data based on the the Blonder-Tinkham-Klapwijk (BTK) model. To account for an asymmetry, the "Kondo-like" resonance peak is included in the density of states. The Andreev reflection data for various tunneling directions convincingly shows the d-wave symmetry of the order parameter. To account for an amplitude of Andreev signal it is assumed that there are two contributions coming from the light gapless Fermi surface and heavy Fermi surface which is gapped. Questions from the audience (C. Capan, A. Balatsky, A. Millis, Q. Si) were mostly concerned with the origin of an asymmetry in tunneling conductance and whether one might think of this asymmetry as a result of the formation of a heavy quasiparticles. Laura's BIG QUESTIONS are:

1. Why does BTK model works so well?

2. What would be theoretical justification for "two-fluid" picture of gapless
and gapped Fermi surfaces?

3. Does the peak in the density of states exist?

Jim Allen: Quasi-1D "Purple Bronze" Evidence for a new state of matter.

J. W. Allen, U. Michigan

"Evidence, arguments and challenges for showing a new quantum state of
matter in the normal phase of quasi-1D Li_0.9Mo_6O_17"


Jim Allen gave an extensive review of the highly anisotropic physics of Blue Bronze. This material is a quasi-1D conductor that develops superconductivity at 1.9 K. This system has a resistance anisotropy

rho|| : rho _|_ (1): rho _|_(2) = 1:10:25

Down to about 26K, rho|| follows a T^0.4 variation and rho _|_ follows a T^1.15 variation.
Below this temperature, both resistivities show an upturn. The upturn was initially thought to be the result of a spin or charge density wave, but susceptibilility, optics, photo-emission and X-ray diffraction seem to rule this out.

Jim described that ARPES appears to suggest this system is more likely to be a Luttinger Liquid, and in the spectra, they can see a holon peak and a spinon edge. The photo-emission spectra show a power-law A(E) ~ (E-E_F)^alpha, where alpha is temperature dependent .

This temperature dependent exponent can, it seems be understood in terms of a two band Luttinger Liquid, undergoing a cross-over from a two band fixed point to a one-band fixed point.

There are several questions raised by this system

• Can the large t_perp (of order 100K) be reconciled with the quasi-one dimensional behavior seen at lower temperatures?
• Band theory predicts two quasi-one dimensional bands, yet only one is observed in ARPES (figure above). Is this because a gap is starting to develop in the second band - and if so - can this be modelled theoretically?
• Does the superconductivity restore the 3 dimensionality to the electron fluid?
  

Experimental Talks and Discussion.

Today's experimental talks will be individually blogged by five members of the audience. Please feel free to comment on any of the postings.

J. W. Allen, U. Michigan

"Evidence, arguments and challenges for showing a new quantum state of
matter in the normal phase of quasi-1D Li_0.9Mo_6O_17"

J. Thompson, LANL

"Proximity of Superconductivity and Magnetism in the 115s"

L. Greene, UIUC

"Andreev reflection in heavy-fermion superconductors and order parameter symmetry
in CeCoIn5"

H. Mook, ORNL

"Search for magnetic order in the YBCO superconductors"

N. Curro, LANL

"Antiferromagnetic droplets in the 115 superconductors"

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.