THE PHYSICS OF HIGHER TEMPERATURE SUPERCONDUCTORS

QUESTIONS AND RESPONSES

I. Introduction


At the Conference that opened this Program, the session leaders posed a set of questions to the speakers and by extension to all the participants. Similarly, questions were posed at many of our Wednesday Discussion Sessions. As we enter the last few weeks of our Program, it seems natural to return to those questions. On this Wiki, we have formatted a list of these questions. We also provide a place where you may respond. These inputs will help us in our responsibility to disseminate what we have achieved over the summer toward defining a fresh agenda for the field.

II. How to Proceed


Below you will find two lists of the questions. The first is for you to scan to find the questions of interest to you. The second is the same list but with provision for you to enter your comments. There are already some comments entered, so the organization should be self evident. Note that the entries in the Table of Contents are active and allow you to skip directly to the section you want.

In order to enter your comments (or to add additional questions), you will need to activate the "Edit" button on the top right corner of the screen. Once you have done that the editor bar will appear at the top of the page. Most of the functions you might want are available there. Just put your cursor on the button and the function of that button will pop up. If you see "Protected" where the "Edit" button should be, you will need to sign in to the Wiki using you ID and password. You should have earlier received and email inviting you to join the Wiki. If there are any problems, just let us know at beasley@stanford.edu.

III. List of Questions (See section IV for responses)


• FROM CONFERENCE:


1.0 The Landscape of Higher Tc Superconductivity (E. Fradkin)
1.1 What have we learned on what makes high Tc from the cuprates and other materials?
1.2 What makes a material be “high Tc”? Chemistry? Dimensionality? Luck?
1.3 More is different?
1.4 What can theory reasonably (and honestly) say about Tc and how to raise it (or lower it?)?
1.5 Do we need a new conceptual framework to deal with this problem?


2.0 Lessons from Materials Theory (P. Hirschfeld)
2.1 What are the prospects for direct Eliashberg-style 1st principles computation of pairing interaction in electronic pairing systems with weak-intermediate strength interactions?
2.2 In the absence of such tools, how can theory guide the search for higher Tc?
2.3 In the cuprate and other strongly correlated materials, are there issues where traditional DFT calculations can contribute, where strong correlations play a less important role?
2.4 What are the prospects of applying current methods to problems of inhomogeneous superconductivity in real materials: surfaces, grain boundaries and Josephson junctions …?
2.5 If you look into the future 5 years and assume continued improvements in computer speed and memory, what superconductivity problems could one tackle that are out of reach now?


3.0 Experimental Search Panel (I. Bozovic)
3.1 What are the lessons from history?
3.2 What pattern do you see among known “high-Tc” superconductors?
3.3 Have we exhausted the cuprates, pnictides, MgB2, BKBO …?
3.4 What new family of compounds would you wish to investigate, and why?
3.5 What new techniques (of synthesis, processing or testing) should we try?
3.6 Do you see a chance for, and value in, metastable high-Tc phases?
3.7 Could theorists help, and how?
3.8 Is there any thing you tried but did not report because it did not work?
3.9 Are we walled-in conceptually? Any out-of-the-box thoughts?


4.0 Pairing Mechanisms 
(M. Norman)
4.1 In the case of electron-electron interactions, is the concept of a pairing “glue” even meaningful?
4.2 If your theory advocates an instantaneous interaction, does this mean the pairs have no dynamics, or just that the theory has not developed to the extent to address this question?
4.3 If your theory ignores phonons, can you really get away with that? Do you think phonons are even relevant?
4.4 What are the spectroscopic signatures predicted for your theory? Is a McMillan-Rowell inversion or related procedure possible for your theory? Is this question meaningful?
4.5 What would your theory predict in regards to collective modes? Is this even an important question?


5.0 Spectroscopy 
(J. Campuzano)
5.1 What exactly are the assumptions that go into your data analysis?
5.2 How general are these assumptions?
5.3 Is it possible to make progress without these assumptions?
5.4 Why?
5.6 Do you think that the same “nominal” compounds (e.g., different cations) have different ground states?
5.7 How can experimentalists clear up this mess?

6.0 Emergent Spatial Structure and its Role (J. Zaanen)
6.1 Is there a direct relation between the ‘momentum space dichotomy’ and stripy things?
6.2 Are the STS stripy things a surface artifact?
6.3 Is there an experimental observable that in a sharp and quantitative manner distinguishes strongly organized ‘fluctuating stripes’ from more ‘gaseous’ interpretations?
6.4 Are Anderson’s ‘stripes a red herring?


7.0 Pnictides and Beyond
(E. Abrahams)
7.1 What properties of pnictides inform us as to where to look for higher temperature superconductors?
7.2 Is there nesting of Fermi surfaces in the actual materials and what conclusions can be drawn from the answer?
7.3 Is there a resolution of the conflicting results on the pairing symmetry and why is it important?
7.4 Is there orbital order in the antiferromagnetic state and does it matter?
7.5 What is the nature of the quantum criticality and will it tell us anything about the superconductivity?

8.0 Exotic Mechanisms of Superconductivity (L. Balents)
8.1 What is the evidence- theoretical or experimental – that spin liquid physics is actually beneficial for superconductivity?
8.2 If exotic physics is behind higher Tc superconductivity, can it give some guidance for the search for new materials? Is two-dimensionality important? Low spin?
8.3 Many exotic states seem almost to be defined by their featureless appearance when viewed with standard experimental techniques. Can you suggest what kind of experiment might provide a clear smoking gun signature? Can the problem benefit from improvements in spectroscopic or local probes?
8.4 Are they any true exotic ground states or important quantum critical points in the cuprates at T = )? If not, in what range of
ω, T, H and x does exotic physics apply and is it in any way universal?
8.5 Is (your) exotic theory quantitative (beyond scaling laws and exponents)? Is there any hope for clear experimental confirmation otherwise?


9.0 Further Afield (E. Fradkin)
9.1 What is the future of “designer materials” approach?
9.2 What can we learn from the experiments with cold atoms? Can they be made colder than LSCO in real terms?
9.3 Will we know if the Hubbard model (in 2D) is superconductor, say, in five years?
9.4 How can novel quantum information ideas deal with the fermion sign problem? Can they? The Grassmann Chip?
9.5 What it the future of quantum Monte Carlo(s) in this context?


• FROM DISCUSSIONS:


1.0 Discussion of the Fe-superconductors (D. Scalapino)
1.1 Are the Fe materials strongly, intermediately or weakly coupled?
1.2 How should one understand the magnetic and structural phase transitions: J1-J2 models, Fermi
surface nesting, orbital ordering, ... ?
1.3 Resistivity (similarities between the pnictides, the cuprates and the organics).
1.4 Is there strange metal behavior in the Fe materials?
1.5 Does quantum criticality play an important role in these materials?

1.6 Is the pairing mechanism in the Fe superconductors the "same" as in the cuprates? If it is the "same", which "same" is it? (Can we forget about phonons/)
1.7 What is the symmetry fo the gap? Can there be nodes? How does the answer depend upon the material? What does that tell us about the pairing mechanism?
1.8 What measurments can pin down th gap structure, and can we think of new ones?


2.0 Ba1-xKxBiO3 Revisited: Discussion Topics (M.Rice)
2.1 Origin of CDW order in BiBaO3 with Bi3+ & Bi5+ local sites: Coulomb (Varma) or Lattice Forces (Franchini et al PRL`09)? Bi is a Valence Skipper.
2.2 Mechanism of Superconductivity with Tc = 30K in BKBO : Negative U or Strong Coupling El-Phonon?
2.3 Similarities and Contrasts between the two Phase Diagrams
e.g. SC Tc & Doping Range: BKBO (30K & x > 0.4) Cuprates(130K & x> 0.04).
2.4 Anomalous Normal State of BKBO => Low Energy Model
2.5 What can we learn from BKBO about the prospects for a useful High Temperature Superconductor?

3.0 Discussion of Strange Metal State (S. Sondhi)
3.1 What are the facts in need of explanation?
• There is a Fermi surface but without (Fermi liquid scaling) of quasiparticles. Anisotropic lifetimes (different powers?)
• Power laws in transport. Different ranges for longitudinal and Hall resistances
• Nothing dramatic in low frequency susceptibilities that correlates with transport scaling and T. But various instabilities at 400K and below
• Thermodynamics featureless
3.2 Top down explanation (cf FL theory)
• Consider the Hubbard model (or something like it). Start at bandwidth and carry out exact RG towards the FS where low energy objects live. Arrive near unstable fixed point by 1000K.
• Unstable fixed point. Must be building up singular and/or retarded couplings –else get FL behavior. Contain multiple growing susceptibilities. Exist in other materials? Allow doping dependent termination of strange metal regime to be understood in a natural way.
• DMFT is producing growing retardation. Strange metal already in k independent self energy? Can one import RG into DMFT?
• Stable phase too much? (D-wave Bose liquid)
3.3 Bottom up explanation
• Quantum critical point between T=0 phases leads to a quantum critical funnel
• Needed: Criticality over most of Fermi surface –else hot spots shorted by cold spots. Explanation for why a single power in transport lifetime. Doubled critical Fermi surface if transition between Fermi surfaces. Fluctuations at small q (Spin chirality, nematic, phase fluctuations). Explanation of modest susceptibilities and small corrections to scaling, including in the scaling variable choice.




IV. List of Questions With Responses


• FROM CONFERENCE:


1.0 The Landscape of Higher Tc Superconductivity (E. Fradkin)

1.1 What have we learned on what makes high Tc from the cuprates and other materials?

1.2 What makes a material be “high Tc”? Chemistry? Dimensionality? Luck?

1.3 More is different?

1.4 What can theory reasonably (and honestly) say about Tc and how to raise it (or lower it?)?


Beasley: The primary ingredient would appear to be a AF with large J. From this, one has a high pairing energy scale. The next step is to make these pair-like entities mobile (doping, t, dimensionality). This is a useful level guidance for searching. Ancillary questions are whether the number of bands matters, is frustration helpful.
Mazin: I would emphasize that the large J above may be of different origin, as it seems to be the case in in cuprates (Hubbard U) vs Fe-based s/c, FeBSC (Hund's J). The role of dimensionality is still open. If anything, it only hurts the mobilty. I can see two ways in which dimensionality may be helpful: (1) it makes DOS independent on doping, that is to say, on the size of the Fermi surface and (2) it makes the system more fluctuation, everything else being the same.
Beasley: I would add here that more synthesis of materials that explore these questions would be very helpful. In an admittedly self serving vein, I would point out the recent work of our group on using epitaxy to grow a tetragonal phase of CuO, which is monoclinic in its equilibrium state. By extrapolation from the other monoxides J should be quite high. But can it be doped?


1.5 Do we need a new conceptual framework to deal with this problem?

Beasley: Given the criticality of getting higher superfluid density, we need a conceptual framework from which to understand in highly correlated materials the distribution of oscillator strength in sigma 1, and how to get more at energies less than the gap. Failure to do this will limit the Tc of any highly correlated material due to phase fluctuations.


2.0 Lessons from Materials Theory (P. Hirschfeld)

2.1 What are the prospects for direct Eliashberg-style 1st principles computation of pairing interaction in electronic pairing systems with weak-intermediate strength interactions?

2.2 In the absence of such tools, how can theory guide the search for higher Tc?

Beasley: In the case of doping into covalent bands, it may be the theory can provide predictive guidance (not Tc itself).
Mazin: In case of electron-phonon coupling, we have rather advanced tools - on the level of actually computing Tc with some reasonable accuracy, - as long as nonadiabaticity, anharmonicity and nonlinearity are not involved, as they often are in the strongly coupled systems. There is no conceptual problems there (at least for the last two offenders), but the computational load (and programming effort) is orders of magnitude bigger than for the standard Migdal-Eliashberg calculations.

In the case of more highly correlated materials, progress in searching will likely go faster, which is hugely important, if there is ongoing intimate interaction between the synthesizers and those calculating electronic structure.


2.3 In the cuprate and other strongly correlated materials, are there issues where traditional DFT calculations can contribute, where strong correlations play a less important role?

Mazin: Is there is any material, including strongly correlated, where DFT calculations have contributed NOTHING? I do not think so. As a very minimum, they provide highly accurate orbital-independent mean field Hamiltonians (in some sense, the best possible within this limitation). Another often overlooked use of DFT calculations is that they provide an accurate result for a well defined approximation, something that hardly any approach sports, and as such failures of DFT are nearly as informative as its successes.
2.4 What are the prospects of applying current methods to problems of inhomogeneous superconductivity in real materials: surfaces, grain boundaries and Josephson junctions …?


Beasley: This may be the poor cousin to raising Tc, but it is critically important from the practical materials science point of view. Hopefully, Alex Gurevich will comment here.
Gurevich:I think LDA and DFT can be invaluable to understand the electronic structure near defects like dislocation cores, grain boundaries (GBs) and interfaces. Current blocking by GBs is already crucial for applications of cuprates today and may become the key characteristic by which usefulness of any putative RTS will be judged, no matter how high Tc is. The problem is that the competing orders and the proximity of SC state to AF insulating/semimetallic state seems to enhance SC pairing, yet precipitation of the very same AF phase on GBs results in strong current blocking. This behavior is aggravated by low carrier density (long screening length) and crystalline anisotropy characteristic of either cuprates and pnictides. To improve things, it would be very useful to know: 1. how can GBs be doped to push its chemical potential away from the competing state without interfering much with SC pairing? 2. Is there any nontrivial magnetic order induced at defects? 3. How does the charge coupling in the chain of GB dislocations, and local Coulomb correlations in the dislocation cores change the chemical potential at GB and how can the atmospheres of segregated impurities affect it? Those are basically the normal state properties, for which LDA/DFT could be applied. Once these characteristics are known, they can be used to evaluate the suppression of the SC order parameter at defects, current blocking by GBs, pinning by dislocation cores, etc. to optimize superconducting materials.

2.5 If you look into the future 5 years and assume continued improvements in computer speed and memory, what superconductivity problems could one tackle that are out of reach now?

Beasley: From the point of view of an experimentalist, it is just as important to make standard codes widely available and user friendly, so that experimentalists can use them routinely. The creative energies of theorist should be on extending the frontier of what they can do, and working with experimentalists to test the utility of their codes for more highly correlated materials.

Additional question from a respondent
Y. Sudhaka: I have a question. Can DFT be used to show that large -U results in systems showing charge disproportionation such as BaBiO3. That is can one justify Chandra Varma's picture that non-linear electronic screening effects lead to -U. Actually, using DFT to model non-linear screening would be useful in Pnictides as well if you believe Sawatzky's picture.

C. Varma: The answer in my opinion is that a properly designed DFT should be able to discover the physics of the non-linear screening leading to the universality of valence skipping in a range of elements. This will require doing DFT with a set of constraints.
If anyone is interested in actually doing these calculations, I will be happy to discuss with them, what the suitable constraints might be.


I. Mazin: This is correct, the nonlinear screening should be accounted for in DFT. One can argue whether LDA/GGA are good enough approximations for that, and I believe they are. That is to say, DFT calculations should produce a ground state for with spontaneously nonequivalent bismuths, and this exactly what they do - if, as Khomski pointed out, O are allowed to breathe. Where the resulting state, with a charge transfer from one Bi to the other, one can call "negative U", even though the actual charge transfer is less than 1, is an terminological issue, not physical. Of course, the same is true for the pnictides as well, nonlinear screening is included in DFT. Chandra is also right in the sense that you can gain additional insight from doing some constraint calculations, even though the effect itself appears in the standard unconstrained DFT calculations.

3.0 Experimental Search Panel (I. Bozovic)

3.1 What are the lessons from history?

3.2 What pattern do you see among known “high-Tc” superconductors?


Beasley: Spin, charge and lattice all can lead to high Tc. The pattern is an imbalance of searches in the various sectors.
Geballe:
Enhanced Tcs themselves give lots of evidence that interactions outside of the CuO2 layers[ i.e. in the charge reservoir layers and in the single and double chain layers] are responsible for the enhancement. I think it is still an open question as to whether the enhancement is due to additional pairing mechanisms [eg neg U centers] or because the CuO2 layers couple in the third dimension more effectively [than say in optimally doped 214 cuprates] by processes such as resonant pair tunneling thru the charge reservoir layers, or by metallic processes in the chain layers[this last empirical observation needs theoretical teeth]

3.3 Have we exhausted the cuprates, pnictides, MgB2, BKBO …?


Beasley: Perhaps for these specific materials in terms of Tc, but by no means the lessons they provide for further searching. Also, we need a proper microscopic theory in addition to qualitative guidance.

Mazin: I would like to see a practical implementation of the Gorkov-Barzykin-Agterberg (x2-y2)+iz2 superconductivity, which requires a cubic system with symmetry-related pockets at X points, and proximity to magnetism. Inverse magnetic perovskites such as CuMn3N come to mind.

3.5 What new techniques (of synthesis, processing or testing) should we try?

Geballe: More support for high pressure synthesis and high pressure measurements.

3.6 Do you see a chance for, and value in, metastable high-Tc phases?

Mazin: a chance of, yes (most definitely). Value? I am not sure.

3.7 Could theorists help, and how?


Mazin: yes. There are theorists (like Daniel Khomskii), who actually do have some gut feeling about what compound can do what, and that gut feeling, not being more useful than the similar gut feeling of experimentalists, is different, as that is important.


3.8 Is there anything you tried but did not report because it did not work?

3.9 Are we walled-in conceptually? Any out-of-the-box thoughts?

4.0 Pairing Mechanisms 
(M. Norman)

4.1 In the case of electron-electron interactions, is the concept of a pairing “glue” even meaningful?
Mazin: I am not sure it is meaningful to ask this question, for it is largely a matter of taste. To me, the concept of a pairing "glue" is quite meaningful.

Tremblay: Even at strong coupling in the Hubbard model, the spectral weight of the off-diagonal self-energy seems to reflect the dynamics of bosonic excitations that are also measured by the local spin susceptibility. That can be seen without Migdal-Eliashberg assumptions. As suggested by Scalapino, this is probably the closest one can come to defining a pairing glue: looking at retardation in the pair dynamics.

4.2 If your theory advocates an instantaneous interaction, does this mean the pairs have no dynamics, or just that the theory has not developed to the extent to address this question?

Tremblay: Even in BCS theory with an instantaneous interaction, one must assume a cutoff (Debye frequency) and that cutoff reflects an underlying dynamics. Such a cutoff must exist quite generally.

4.3 If your theory ignores phonons, can you really get away with that? Do you think phonons are even relevant?

4.4 What are the spectroscopic signatures predicted for your theory? Is a McMillan-Rowell inversion or related procedure possible for your theory? Is this question meaningful?

4.5 What would your theory predict in regards to collective modes? Is this even an important question?


5.0 Spectroscopy 
(J. Campuzano)

5.1 What exactly are the assumptions that go into your data analysis?

5.2 How general are these assumptions?

5.3 Is it possible to make progress without these assumptions?

5.4 Why?

5.6 Do you think that the same “nominal” compounds (e.g., different cations) have different ground states?

5.7 How can experimentalists clear up this mess?


Beasley: ARPES has emerged as a profoundly important spectroscopy for correlated materials. That said, the range of materials for which it has been applied is too limited. Surface effects need to be addressed directly as well as extension to 3D materials (which will be required for really high Tc material) must be undertaken.

6.0 Emergent Spatial Structure and its Role (J. Zaanen)

6.2 Is there a direct relation between the momentum space dichotomy’ and stripy things?

6.3 Are the STS stripy things a surface artifact?

6.4 Is there an experimental observable that in a sharp and quantitative manner distinguishes strongly organized ‘fluctuating stripes’ from more ‘gaseous’ interpretations?

6.5 Are Anderson’s ‘stripes a red herring?

7.0 Pnictides and Beyond
(E. Abrahams)

7.1 What properties of pnictides inform us as to where to look for higher temperature superconductors?
Mazin: Proximity to magnetism and to a QCP, as in the cuprates, are unlikely to be a coincidence. That is to say, it makes sense to look for HTSC in near-magnetic materials. On the other hand, Mott-Hubbard physics (strong on-site Coulomb correlations) does not appear to be necessary.
Tremblay: The layered superconducting organics (BEDT) also have a ratio of U/t similar to high Tc and they are close to a Mott transition. What seems to come out of the Hubbard model is that intermediate coupling is where the highest Tc occurs. That is also where the Mott transition begins to show up. So I would say that Mott physics is not necessary but it is quite likely to be nearby whenever "optimal" high temperature superconductivity is present.

7.2 Is there nesting of Fermi surfaces in the actual materials and what conclusions can be drawn from the answer?
Mazin: in all actual materials, including FeSe and the newly discovered vanadate (yes, there too), the re is nesting, but in most cases it is rather poor. Moreover, in vases where it is poor already in the undoped state, the undoped materials superconduct (vanadate), and where is is actually not bad it has to be disrupted to some extent by one or the other mean.

The conclusion is, nesting seems to be intimately related with the pairing, but a sharp structure in the momentum space is no good. Rather, one wants to have a broad peak that provided pairing interaction between all electron and all holes.
Tremblay: Antiferromagnetism must be frustrated in some way (doping, bad nesting) to leave room for superconductivity. But the frustration must not be too strong otherwise one looses the tendency to singlet pair formation. This is quite clear from the generalized phase diagram of the BEDT materials.

7.3 Is there a resolution of the conflicting results on the pairing symmetry and why is it important?
Mazin: I do not see any conflicting results on pairing symmetry. I see conflicting results on presence or absence of nodes, and there are fairly plausible explanations (Maier-Hirschfeld-Scalapino, Kuroki et al, and others) why this may be material-dependent.

7.4 Is there orbital order in the antiferromagnetic state and does it matter?
Mazin: yes, calculations clearly show that the large magnetic moment induces an orbital ordering. I have not seen any indication of an orbital ordering effects in the paramagnetic state, and it is very clear that no Jahn-Teller physics is possible (parameters are just way to far from those that allow for any JT). I do not see why it would matter.

7.5 What is the nature of the quantum criticality and will it tell us anything about the superconductivity?
Mazin: It is related to the predicted and observed "stripe" ordering. Curiously, while the exact nature of this ordering is under dispute, it may not be that important for superconductivity. Probably the most important thing is the structure of spin fluctuations in the momentum space, not the microscopic origin of this structure.

Beasley: I am not sure, but would note that as shown in Emilia Morosan’s talk here this summer, it appears that Cux TiSe2 should be added to the list of empirical examples. Note that there is no magnetism in this material.

8.0 Exotic Mechanisms of Superconductivity (L. Balents)

8.1 What is the evidence- theoretical or experimental – that spin liquid physics is actually beneficial for superconductivity?


Balents: I asked this question because the situation seems somewhat mixed. RVB theory remains a major candidate in the cuprates. At least at the level of variational wavefunctions for the superconducting state, it seems to be quite successful. It also historically gave a simple picture (within slave bosons, for instance) for the difference between the pairing and phase coherence scales, which is related to the pseudogap. However, the general idea of doping a spin liquid as a mechanism for superconductivity does not seem to be very robust experimentally, so far. In the cuprates, one has antiferromagnetism at low doping, and one can invoke magnetic fluctuations rather than spin liquid physics. In other materials, spin liquids have been hard to find, and when we do, they do not seem to be especially beneficial for superconductivity. An interesting experimental comparison can be made in the kappa-ET organics, where one can compare a spin liquid material and an antiferromagnetic one. The two materials differ very little structurally. On applying pressure, both become superconducting, but as Kanoda described in the conference, the superconductivity seems stronger in the antiferromagnetic one. The 3d hyperkagome material, Na4Ir3O8, which appears to be a spin liquid, has recently been hole doped by Takagi using Na deficiency, and does not become superconducting, at least above 0.5K or so.

So does this mean RVB as a superconducting mechanism is wrong? I tend to think it is not so simple. One possibility is that RVB superconductivity requires the "right" kind of spin liquid. It is pretty clear that the spin liquid should have a preformed pair gap to get a superconductor on doping. Not all spin liquids have this. The organic material seems, at least above say 5K, to be described by the "spinon Fermi sea" type of spin liquid. In this state, the spinons are not paired, and there is no gap. So doping this thing doesn't naturally give a superconductor (it gives a metal, actually). In general, such a spinon Fermi sea state is most likely close to the Mott transition. So perhaps a speculation is that for RVB superconductivity requires a spin liquid not too close to the Mott transition. Maybe the kagome antiferromagnets that have studied recently are better candidates. They haven't been doped yet, but we can be hopeful!



full-CDMFT-phase-diagram.jpg
CDFMT Phase Diagram



Tremblay: This phase diagram is for the zero-temperature half-filled square lattice t-t'-U Hubbard model. The region marked spin liquid within CDMFT just corresponds to a region where simple magnetic order is not found. The d-wave superconductivity is separated by a first order Mott transition from that "spin liquid" phase.




phase_diagram.jpg
BEDT Lattice

This is analogous to what was found in the anisotropic triangular lattice (BEDT lattice). Although it does not show on that plot, the strongest superconductivity as a function of U at fixed t' occurs near the first-order transition to either AFM or spin liquid. Its maximum strength weakens as t' increases past t'=t. So on the square lattice at half-filling superconductivity seems to prefer to be separated from the spin liquid by a first-order transition whereas on the anisotropic triangular lattice, it seems to also arise when separated from an AFM phase boundary by a first-order transition. So the detailed answer seems to be lattice dependent, even though in both cases the spin liquid is separated from superconductivity by a first-order boundary.


8.2 If exotic physics is behind higher Tc superconductivity, can it give some guidance for the search for new materials? Is two-dimensionality important? Low spin?

8.3 Many exotic states seem almost to be defined by their featureless appearance when viewed with standard experimental techniques. Can you suggest what kind of experiment might provide a clear smoking gun signature? Can the problem benefit from improvements in spectroscopic or local probes?

8.4 Are they any true exotic ground states or important quantum critical points in the cuprates at T = )? If not, in what range of
w, T, H and x does exotic physics apply and is it in any way universal?

8.5 Is (your) exotic theory quantitative (beyond scaling laws and exponents)? Is there any hope for clear experimental confirmation otherwise?

9.0 Further Afield (E. Fradkin)

9.1 What is the future of “designer materials” approach?

9.2 What can we learn from the experiments with cold atoms? Can they be made colder than LSCO in real terms?

9.3 Will we know if the Hubbard model (in 2D) is superconductor, say, in five years?

9.4 How can novel quantum information ideas deal with the fermion sign problem? Can they? The Grassmann Chip?

9.5 What it the future of quantum Monte Carlo(s) in this context?

• FROM DISCUSSIONS:


1.0 Discussion of the Fe-superconductors (D. Scalapino)

1.1 Are the Fe materials strongly, intermediately or weakly coupled?
Mazin: weak to intermediate. By now I think it has been firmly established both by the experiment (Stanford, Ekaterinenburg) and by DFT calculations.

1.2 How should one understand the magnetic and structural phase transitions: J1-J2 models, Fermi, surface nesting, orbital ordering, ... ?
Mazin: My conviction is that (a) the structural transition is entirely driven by the magnetism. Nematic picture of Kivelson et al and Xu and Sachdev definitely capture a large part of the right physics, while our "antiphasons" represent a complementary view of the same physics. Second, (b), I believe that neither J1-J2 not nesting models capture the right physics; the right view, in my opinion, is to consider the moments as localized (and driven by the local Hund's rule interaction), but their interaction defined by itinerant mechanism (with nesting playing a key role).

1.3 Resistivity (similarities between the pnictides, the cuprates and the organics).

Mazin: This is apparently a part of the general properties of proximity to a QCP. It is not clear to me whether it is simply a symptom of QCP, or it is relevant for superconductivity by itself.
Tremblay: Experimentally, e-doped cuprates, pnictides and quasi-one-d conductors have very similar resistivities with a AT+BT^2 behavior in the overdoped regime, with the A coefficient vanishing at the same doping as Tc in the overdoped regime. So there seems to be correlation between the behavior of the resistivity and Tc.

1.4 Is there strange metal behavior in the Fe materials? Does quantum criticality play an important role in these materials?

Tremblay: In the three systems I mentioned above, an AFM (SDW) quantum critical point is present.

2.0 Ba1-xKxBiO3 Revisited: Discussion Topics (M.Rice)

2.1 Origin of CDW order in BiBaO3 with Bi3+ & Bi5+ local sites:
Coulomb (Varma) or Lattice Forces (Franchini et al PRL`09)?
Bi is a Valence Skipper.

Khomski: It looks to me that these two factors usually work together. The local, atomic nature of, say, Bi as a valence skipper is definitely important. But it seems that it alone would not give really negative U: one needs to ''push it a bit" by lattice displacements (breathing type here) to make it really attractive. This is our experience, not with Bi, but with similar valence skippers like Fe4+ --> Fe3+ + Fe5+, or Ni3+ doing the same, etc. Cluster calculations show that for these states (in contrast e.g. to the Fe3+, which is completely stable) effective U is strongly reduced, say from 5 eV to 0.2 eV, but it still remains (small) positive.

2.2 Mechanism of Superconductivity with Tc = 30K in BKBO :
Negative U or Strong Coupling El-Phonon?

Khomski: And one needs something extra - e.g. lattice relaxation, contraction around Fe5+ and expansion around 3+, to push it finally to negative. We did not do it for Bi etc., but I know that there are similar claims for example for Au (Au2+ always segregates into 1+ and 3+ - e.g. CsAuCl3 (usually one even writes the formula as Cs2Au1^(1+)Au2^(3+)Cl6). Thus it seems that this valence skipping is needed as a "preparation" for further efficient work of electron-lattice coupling, but in itself it is not sufficient. Maybe one can say that in case of valence skippers the corresponding "responsivity" to phonons is strongly enhanced.

Khomski: Another factor which is probably important here - at least it seems to crucial for our Fe and Ni compounds - is the role of oxygen holes. I do not have a definite statement on that yet, but I am pretty sure that what we call Bi5+ (and Fe5+) is not really 5+, but with a lot of oxygen holes. One can even see here some connection to cuprates with "Cu3+". But how in details it works here, I can not say at present; just some crude ideas (e.g. two oxygen holes want to bind into pairs, 2O^(1-) ---> O^(2-) + O^0, like in hydrogen peroxide H2O2; again something like "negative-U " on oxygens).


2.3 Similarities and Contrasts between the two Phase Diagrams
e.g. SC Tc & Doping Range: BKBO (30K & x > 0.4) Cuprates(130K & x> 0.04).

2.4 Anomalous Normal State of BKBO => Low Energy Model ?

2.5 What can we learn from BKBO about the prospects for a
useful High Temperature Superconductor?

3.0 Discussion of Strange Metal State (S. Sondhi)

3.1 What are the facts in need of explanation?

• There is a Fermi surface but without (Fermi liquid scaling) of quasiparticles. Anisotropic lifetimes (different powers?)
• Power laws in transport. Different ranges for longitudinal and Hall resistances
• Nothing dramatic in low frequency susceptibilities that correlates with transport scaling and T. But various instabilities at 400K and below
• Thermodynamics featureless

3.2 Top down explanation (cf FL theory)

• Consider the Hubbard model (or something like it). Start at bandwidth and carry out exact RG towards the FS where low energy objects live. Arrive near unstable fixed point by 1000K.

• Unstable fixed point. Must be building up singular and/or retarded couplings –else get FL behavior. Contain multiple growing susceptibilities. Exist in other materials? Allow doping dependent termination of strange metal regime to be understood in a natural way.

• DMFT is producing growing retardation. Strange metal already in k independent self energy? Can one import RG into DMFT?

• Stable phase too much? (D-wave Bose liquid)

3.3 Bottom up explanation

• Quantum critical point between T=0 phases leads to a quantum critical funnel

• Needed: Criticality over most of Fermi surface –else hot spots shorted by cold spots. Explanation for why a single power in transport lifetime. Doubled critical Fermi surface if transition between Fermi surfaces. Fluctuations at small q (Spin chirality, nematic, phase fluctuations). Explanation of modest susceptibilities and small corrections to scaling, including in the scaling variable choice.


Tremblay: Concerning the shorting of hot spots by cold spots, one must take into account that resistivity comes purely from umklapp scattering when the mechanism is electron-electron scattering. Until a calculation of resistivity that includes vertex corrections is done, I believe this issue is open.

Another issue is how high in temperature can quantum critical behavior be observed? In the electron-doped cuprates, the experiments reported in Nature by the Greven group show that at the critical doping, the correlation length is still about 30 lattice spacings at 150K. In the z=2 universality class where xsi decreases only as 1/sqrt(T), this would mean that we need to go huge temperatures before we reach a lattice spacing of unity. In Two-Particle Self-Consistent calculations for the Hubbard model, one finds scaling of the correlation length (with small logarithmic corrections) up to temperatures of order hopping. I think that we have evidence that the electron-doped cuprates behave quite closely like one expects for an AFM quantum critical point and that the pseudogap is a fluctuating precursor to AFM.