Big Issues, Questions and Insights from the conference. Weds, 1st October 2014.

Strong Correlations and Unconventional Superconductivity:Towards a Conceptual Framework

Edited by Piers Coleman

Strong Correlations and Unconventional Superconductivity: Towards a Conceptual Framework

Following the excitement of last weeks conference, we decided to devote this week's discussion session to the highlights, questions, insights and
major issues arising out of the meeting. We divided the meeting into five areas, iron based, cuprate, organic, heavy fermion and triplet-based superfluids,
The presenter outlined in five minutes what she or he thought were the key issues, and we then had about 15 minutes of discussion. Each section was blogged, and you can read the blogs below.

Area

Presenter

Blogger

Iron based SC

Luca de Medici

Leni Boscones

Cuprate

Catherine Pepin

Andrey Chubukov

Organics

Stuart Brown

Sri Raghu

Heavy Fermions

Piers Coleman

Andriy Nevidomskyy

He-3/Triplet SC

Sri Raghu

Jim Sauls

Questions, Insights and Developments in Iron-based superconductors.

Presenter: Catherine Pepin

Blogger: Andrey Chubukov

The summary on the cuprates was given by Catherine Pepin from CEA, Saclay. In view of the blogger, she did an excellent job and presented the summary in an elegant and simple, yet fully physically sound manner.

Catherine briefly described cuprate talks at the conference, starting with the talk by M. Rice, who argued that pseudogap is the crossover region in which the system shows simultaneously tendencies towards magnetism and superconductivity. She then described talks by P. Lee and D. Agterberg on finite-momentum pairing state (pair-density-wave), which provides good explanation of the ARPES data and can potentially break time-reversal symmetry. She then discussed the talk on S. Kivelson on intertwined orders, vestigial nematic order, and enhancement of Tc by nematic fluctuations, and the talk by T. Maier on the interplay between the role of charge and spin fluctuations for superconductivity near a CDW instability. She finally discussed the talk by S. Sachdev on (i) predominantly d-wave form-factor of CDW order parameter and (ii) on the development of CDW with required momentum (Q,0/(0,Q) from pre-existing state of matter FL*.

Catherine made a observation that the prevailing leitmotiv of the discussions on pseudogap in the cuprates is that competing order alone does not explain the physics and, most likely, emerges from already pre-existing pseudogap state. She cited earlier works by A. Kampf and co-authors in this regard. She also discussed four other scenarios for pseudogap/competing order, not presented at the conference.
She listed several fundamental unresolved issues

Is there a “mother state” from which all ordered states emerge

Can any theory explain linear in T resistivity

Is Mott physics an important ingredient in the analysis of the cuprates

What is the proper interplay between strong and weak coupling approaches

The discussion followed. S. Kivelson made a remark that Amperian pairing discussed by Lee/Agterberg and pair-density-wave (PDW) discussed earlier by him and co-authors break the same symmetries and are essentially the same orders. D. Scalapino elaborated on the discussion about his work with T. Maier on the contributions from charge and spin fluctuations to superconductivity near CDW instability. A. Nevidomskyy asked about the number of QCP’s in the cuprates. J. Zaanen commented on the absence of information of \omega/T scaling in the strange metal phase and J. Tranquada briefly discussed optical data above T*.
There were numerous remarks and brief arguments from many participants.

Questions, Insights and Developments in Iron-based superconductors.

Presenter: Luca de Medici

Blogger: Leni Boscones

After solving problems with the computers, with the help of Piers Coleman. Luca de Medici starts to tell us about the main highlights in iron superconductors. He has singled out three themes Single-layer FeSe: (@ Zhou’ s talk). Grown first on graphene and then on STO. He reminds us the phase diagram as a function of annealing how it goes from normal phase then N+S, then Superconducting . There are claims of SC close to 100 K. He mentions that in this system the topology of the Fermi surface is different to that in the 122 systems. There is no pocket at the Gamma point. He wonders whether the interpocket nesting has to be replaced by intrapocket nesting. In @Hong Ding’s talk we saw how the Fermi surface in LiFeAs doped with cobalt, evolves from being nested to non- nesting situation. This questions the relevance of Fermi surface nesting for superconductivity. Role of local Mott vs Hund’s coupling. Mostly from @Kotliar and @MingYi. Luca highlights the results presented regarding the strength of correlations by Gabi Kotliar and MingYi. In particular Kotliar pointed that Tc is maximized at intermediate correlation strength. Ming Yi showed many experimental results on the strength on correlations, including evidence of a temperature induced orbital-selective Mott transitions in chalcogenides which was explained theoretically by Rong Yu Nematic correlations. There were many talks about nematic fluctuations, among them those given by experimentalists Anna Boehmer, Ian Fisher and Pencheng Dai. It was pointed that 122 and FeSe have the same nematic susceptibility but different magnetism. The shear modulus measurements are highlighted. Anna Boehmer made a point on the fact that magnetic fluctuations and nematic seem connected in some materials but not in others. Discussion starts:
Piers emphasizes his interest on the fact that there is no hole pocket at Gamma. He considers that this means that the proposal of s+- gap symmetry fails. Andrey Chubukov says that there is in principle no problem with that. According to Piers what fails it is the coskx+cosky dependence. Andrey says that there are several scenarios, one can have s+- between electron pockets, it could also be d-wave.
The main point is that the band at the Gamma point does not cross the Fermi level, it is close, 80 meV below. Andrey Chubukov points that Hong Ding’s sees it 60 meV below but it seems that there is another band which is not seen in ARPES, but that it crosses the Fermi level. Zhou says that these data are not convincing. There are some doubts on which material we are talking about, finally it is clarified that it is about alkaline doped chalcogenides. Zhou points that they see a flat band, very strong band below Fermi level.
Zaanen and Scalapino question whether it is possible that an xy band is not seen. This question remains open. According to Piers the main issue if the band is finally not there the question is how Coulomb interaction is avoided and sc appears.

The discussion moves to Hund’s issue. It is pointed that Hunds coupling is maybe important but not necessarily the driver. Jan Zaanen asks whether the nematicity can be understood in DMFT and similar techniques?, i.e. whether there is a connection between Hund’s coupling and nematicity. So far the studies have been done in the paramagnetic state, so there is no answer to this question. Andrey Chubkov asks about experimental evidence that the band narrows? Luca says that in some series one sees how it happens with doping, in the chalcogenides it is with temperature.
It is also stated that contrary to Kotliar’s argument, calculations confirm that Mott physics plays an important role
Are nematic correlations uncorrelated with superconductivity? Piers Coleman seems to remember that some experimentalists raised this question, maybe Anna Boehmer. Other people remember that she pointed out that based on NMR measurements in FeSe the nematicity is not connected to magnetic fluctuations. It does not seem to be so clear whether anybody said that nematicity was not related with superconductivity.

Questions, Insights and Developments in Organic Superconductors

Presenter: Stuart Brown

Blogger: Sri Raghu

Stuart reviewed two talks on organics: one by Bourbonnais, which discussed the quasi-1D TMTSF, and one by Kanoda on quasi2D ET systems. Stuart first began with the description of the Fermi surface and electronic structure of these two classes of organic superconductors. He described their phase diagrams, which are rich with insulting metallic and superconducting phases. He reviewed the crossover from metal to insulator in the P-T phase diagram (Kanoda). He then went on to describe the results of RG calculations for the quasi-1d salts (Bourbonnais). Evidence for spin fluctuation mediated pairing. Stuart mentioned that the coefficient of the linear-in-temperature resistivity vanished at the critical point. He mentioned the “extended” region of quantum criticality due to SDW instability, which affects normal state properties (e.g. linear resistivity). It was not clear how the calculation of linear resistivity was performed. Stuart then mentioned Kanoda’s scaling of resistivity for ETs near the critical endpoint, which occurred in his system at T=40K.

After his brief presentation, the following discussion resulted.

Andriy Nevidomsky: wanted to clarify the definition of T-linear resistivity coefficient. Andrey Chubukov: reminded that the RG Bourbonnais used is perturbative in character, and cannot be taken to T=0. According to Andrey, the methods of Bourbonnais can only describe behavior at intermediate energy scales. Jan Zaanen: asked about (z*nu) and predictions based on DMFT vs. classical Ising exponents. Steve Kivelson: asked why is it meaningful to talk about a QCP at T=40K? Stuart Brown: mentioned that the issue was never resolved. Sri Raghu: maybe there’s another axis which you imagine tuning close to a T=0 transition. Otherwise, there is not much meaning in invoking dynamic scaling of thermodynamic quantities in the vicinity of a finite temperature transition.
There was much discussion about this point. Most people found it strange that a transition at 40K was used to invoke dynamic scaling of even thermodynamic quantities, which cannot be the case for finite temperature phase transitions. Steve Kivelson: He invoked observation of critical points in the lambda transition of He. Correction to scaling from irrelevant operators dominate scaling fits. This was a cautionary note against scaling experimental data.

Questions, Insights and Developments in Heavy Fermions

Presenter: Piers Coleman

Blog by Andriy Nevidomskyy

Talks by Thompson, Paschen, Lohneysen, Campuzano, Flint, Schuberth, Lonzarich

5 questions picked by Piers:

volume changing QCP

co-existence of AFM/Kondo/SC

role of frustration, “global” phase diagram?

delocalizing QCP – 2-dimensionality not important? (Paschen)

composite pairing

1. volume changing QCP and 2. co-existence of AFM/Kondo/SC.

CeRhIn5: coexistence of AFM and SC (under pressure)
under pressure (and field) dHvA show discontinuity of the Fermi surface at P~2.3GPa

CePt2In7 very similar to CeRhIn5: Fermi surface change at pressure P1 where AFM and SC meet

3. Can some heavy fermions be understood as lying on a “global” phase diagram as function of magnetic frustration and Doniach parameter?
Example: CePdAl (von Lohneysen) – example of a kagome lattice, heavily frustrated. Is there a spin liquid not quenched by Kondo effect down to low temperatures? (1/3 of Ce moments remain disordered)

4. delocalizing QCP – 2-dimensionality not important (Paschen)
Ce3Pd20Si6: expect resistivity \rho~ T3/2 for AFM in d=3, but instead see \rho ~ T

5. composite pairs
work by Rebecca Flint

YbRh2Si2: work by Erwin Schuberth
SC at Tc~2 mK (!) Measured C/T, which shows huge entropy ~0.3Rln2 released at SC Tc.
But where can the entropy come from? All spin entropy is already quenched, therefore the only possibility – from nuclei.
Exciting possibility of the nuclear Kondo effect (in which case superconductivity would almost certainly involve composite pairing).

Questions/comments:

Q: Andrey Chubukov: if SDW QCP is approached, would one also see a jump in the Fermi surface volume (as one sees in YRS, attributed due to Kondo breakdown)? A: There appears to be a smooth evolution of the Hall coefficient (not a jump), although yes, one would naively expect such a jump because the Fermi surface reconstruct at the SDW transition

Remark by Steve Kivelson: as you move off of \nu=1 in Quantum Hall, there’s a 10^6 fold increase in specific heat because of the formation of skyrmion lattice which has Goldstone modes. Those gapless excitations are then picked up by C/T.
Could it be that something similar happens in YRS, when the nuclei are disordered but once SC sets in, they couple strongly to the SC quasi-Goldstone mode resulting in a huge increase in C/T?

Q: Steve Kivelson. Are there structural measurements to confirm if the transition is 1st order in CeRhIn5 at the same pressure when the Fermi surface volume jumps? A: No such measurements exist at this time.

## Big Issues, Questions and Insights from the conference. Weds, 1st October 2014.

Strong Correlations and Unconventional Superconductivity:Towards a Conceptual FrameworkEdited by Piers ColemanFollowing the excitement of last weeks conference, we decided to devote this week's discussion session to the highlights, questions, insights and

major issues arising out of the meeting. We divided the meeting into five areas, iron based, cuprate, organic, heavy fermion and triplet-based superfluids,

The presenter outlined in five minutes what she or he thought were the key issues, and we then had about 15 minutes of discussion. Each section was blogged, and you can read the blogs below.

Questions, Insights and Developments inIron-based superconductors.Presenter: Catherine PepinBlogger: Andrey ChubukovThe summary on the cuprates was given by Catherine Pepin from CEA, Saclay. In view of the blogger, she did an excellent job and presented the summary in an elegant and simple, yet fully physically sound manner.

Catherine briefly described cuprate talks at the conference, starting with the talk by M. Rice, who argued that pseudogap is the crossover region in which the system shows simultaneously tendencies towards magnetism and superconductivity. She then described talks by P. Lee and D. Agterberg on finite-momentum pairing state (pair-density-wave), which provides good explanation of the ARPES data and can potentially break time-reversal symmetry. She then discussed the talk on S. Kivelson on intertwined orders, vestigial nematic order, and enhancement of Tc by nematic fluctuations, and the talk by T. Maier on the interplay between the role of charge and spin fluctuations for superconductivity near a CDW instability. She finally discussed the talk by S. Sachdev on (i) predominantly d-wave form-factor of CDW order parameter and (ii) on the development of CDW with required momentum (Q,0/(0,Q) from pre-existing state of matter FL*.

Catherine made a observation that the prevailing leitmotiv of the discussions on pseudogap in the cuprates is that competing order alone does not explain the physics and, most likely, emerges from already pre-existing pseudogap state. She cited earlier works by A. Kampf and co-authors in this regard. She also discussed four other scenarios for pseudogap/competing order, not presented at the conference.

She listed several fundamental unresolved issues

“mother state”from which all ordered states emergeThe discussion followed.

S. Kivelsonmade a remark that Amperian pairing discussed by Lee/Agterberg and pair-density-wave (PDW) discussed earlier by him and co-authors break the same symmetries and are essentially the same orders.D. Scalapinoelaborated on the discussion about his work with T. Maier on the contributions from charge and spin fluctuations to superconductivity near CDW instability.A. Nevidomskyyasked about the number of QCP’s in the cuprates.J. Zaanencommented on the absence of information of \omega/T scaling in the strange metal phase andJ. Tranquadabriefly discussed optical data above T*.There were numerous remarks and brief arguments from many participants.

Questions, Insights and Developments inIron-based superconductors.Presenter: Luca de MediciBlogger: Leni BosconesAfter solving problems with the computers, with the help of Piers Coleman. Luca de Medici starts to tell us about the main highlights in iron superconductors. He has singled out three themes

Single-layer FeSe:(@ Zhou’ s talk). Grown first on graphene and then on STO. He reminds us the phase diagram as a function of annealing how it goes from normal phase then N+S, then Superconducting . There are claims of SC close to 100 K. He mentions that in this system the topology of the Fermi surface is different to that in the 122 systems. There is no pocket at the Gamma point. He wonders whether the interpocket nesting has to be replaced by intrapocket nesting. In @Hong Ding’s talk we saw how the Fermi surface in LiFeAs doped with cobalt, evolves from being nested to non- nesting situation. This questions the relevance of Fermi surface nesting for superconductivity.Role of local Mott vs Hund’s coupling. Mostly from @Kotliar and @MingYi. Luca highlights the results presented regarding the strength of correlations by Gabi Kotliar and MingYi. In particular Kotliar pointed that Tc is maximized at intermediate correlation strength. Ming Yi showed many experimental results on the strength on correlations, including evidence of a temperature induced orbital-selective Mott transitions in chalcogenides which was explained theoretically by Rong YuNematic correlations. There were many talks about nematic fluctuations, among them those given by experimentalists Anna Boehmer, Ian Fisher and Pencheng Dai. It was pointed that 122 and FeSe have the same nematic susceptibility but different magnetism. The shear modulus measurements are highlighted. Anna Boehmer made a point on the fact that magnetic fluctuations and nematic seem connected in some materials but not in others.Discussion starts:Piers emphasizes his interest on the fact that there is no hole pocket at Gamma. He considers that this means that the proposal of s+- gap symmetry fails. Andrey Chubukov says that there is in principle no problem with that. According to Piers what fails it is the coskx+cosky dependence. Andrey says that there are several scenarios, one can have s+- between electron pockets, it could also be d-wave.

The main point is that the band at the Gamma point does not cross the Fermi level, it is close, 80 meV below. Andrey Chubukov points that Hong Ding’s sees it 60 meV below but it seems that there is another band which is not seen in ARPES, but that it crosses the Fermi level. Zhou says that these data are not convincing. There are some doubts on which material we are talking about, finally it is clarified that it is about alkaline doped chalcogenides. Zhou points that they see a flat band, very strong band below Fermi level.

Zaanen and Scalapino question whether it is possible that an xy band is not seen. This question remains open. According to Piers the main issue if the band is finally not there the question is how Coulomb interaction is avoided and sc appears.

The discussion moves to Hund’s issue. It is pointed that Hunds coupling is maybe important but not necessarily the driver.

Jan Zaanenasks whether the nematicity can be understood in DMFT and similar techniques?, i.e. whether there is a connection between Hund’s coupling and nematicity. So far the studies have been done in the paramagnetic state, so there is no answer to this question.Andrey Chubkovasks about experimental evidence that the band narrows? Luca says that in some series one sees how it happens with doping, in the chalcogenides it is with temperature.It is also stated that contrary to Kotliar’s argument, calculations confirm that Mott physics plays an important role

Are nematic correlations uncorrelated with superconductivity?

Piers Colemanseems to remember that some experimentalists raised this question, maybe Anna Boehmer. Other people remember that she pointed out that based on NMR measurements in FeSe the nematicity is not connected to magnetic fluctuations. It does not seem to be so clear whether anybody said that nematicity was not related with superconductivity.Questions, Insights and Developments in Organic SuperconductorsPresenter: Stuart BrownBlogger: Sri RaghuStuart reviewed two talks on organics: one by Bourbonnais, which discussed the quasi-1D TMTSF, and one by Kanoda on quasi2D ET systems. Stuart first began with the description of the Fermi surface and electronic structure of these two classes of organic superconductors. He described their phase diagrams, which are rich with insulting metallic and superconducting phases. He reviewed the crossover from metal to insulator in the P-T phase diagram (Kanoda). He then went on to describe the results of RG calculations for the quasi-1d salts (Bourbonnais). Evidence for spin fluctuation mediated pairing. Stuart mentioned that the coefficient of the linear-in-temperature resistivity vanished at the critical point. He mentioned the “extended” region of quantum criticality due to SDW instability, which affects normal state properties (e.g. linear resistivity). It was not clear how the calculation of linear resistivity was performed. Stuart then mentioned Kanoda’s scaling of resistivity for ETs near the critical endpoint, which occurred in his system at T=40K.

After his brief presentation, the following discussion resulted.

Andriy Nevidomsky:wanted to clarify the definition of T-linear resistivity coefficient.Andrey Chubukov:reminded that the RG Bourbonnais used is perturbative in character, and cannot be taken to T=0. According to Andrey, the methods of Bourbonnais can only describe behavior at intermediate energy scales.Jan Zaanen:asked about (z*nu) and predictions based on DMFT vs. classical Ising exponents.Steve Kivelson:asked why is it meaningful to talk about a QCP at T=40K?Stuart Brown:mentioned that the issue was never resolved.Sri Raghu:maybe there’s another axis which you imagine tuning close to a T=0 transition. Otherwise, there is not much meaning in invoking dynamic scaling of thermodynamic quantities in the vicinity of a finite temperature transition.There was much discussion about this point. Most people found it strange that a transition at 40K was used to invoke dynamic scaling of even thermodynamic quantities, which cannot be the case for finite temperature phase transitions.

Steve Kivelson:He invoked observation of critical points in the lambda transition of He. Correction to scaling from irrelevant operators dominate scaling fits. This was a cautionary note against scaling experimental data.Questions, Insights and Developments in Heavy FermionsPresenter: Piers ColemanBlog by Andriy NevidomskyyTalks by Thompson, Paschen, Lohneysen, Campuzano, Flint, Schuberth, Lonzarich

5 questions picked by Piers:

1. volume changing QCP and 2. co-existence of AFM/Kondo/SC.CeRhIn5: coexistence of AFM and SC (under pressure)

under pressure (and field) dHvA show discontinuity of the Fermi surface at P~2.3GPa

CePt2In7 very similar to CeRhIn5: Fermi surface change at pressure P1 where AFM and SC meet

3. Can some heavy fermions be understood as lying on a “global” phase diagram as function of magnetic frustration and Doniach parameter?Example: CePdAl (von Lohneysen) – example of a kagome lattice, heavily frustrated. Is there a spin liquid not quenched by Kondo effect down to low temperatures? (1/3 of Ce moments remain disordered)

4. delocalizing QCP – 2-dimensionality not important (Paschen)Ce3Pd20Si6: expect resistivity \rho~ T3/2 for AFM in d=3, but instead see \rho ~ T

5. composite pairswork by Rebecca Flint

YbRh2Si2: work by Erwin SchuberthSC at Tc~2 mK (!) Measured C/T, which shows huge entropy ~0.3Rln2 released at SC Tc.

But where can the entropy come from? All spin entropy is already quenched, therefore the only possibility – from nuclei.

Exciting possibility of the nuclear Kondo effect (in which case superconductivity would almost certainly involve composite pairing).

Questions/comments:Q: Andrey Chubukov:if SDW QCP is approached, would one also see a jump in the Fermi surface volume (as one sees in YRS, attributed due to Kondo breakdown)?A:There appears to be a smooth evolution of the Hall coefficient (not a jump), although yes, one would naively expect such a jump because the Fermi surface reconstruct at the SDW transitionRemarkbySteve Kivelson:as you move off of \nu=1 in Quantum Hall, there’s a 10^6 fold increase in specific heat because of the formation of skyrmion lattice which has Goldstone modes. Those gapless excitations are then picked up by C/T.Could it be that something similar happens in YRS, when the nuclei are disordered but once SC sets in, they couple strongly to the SC quasi-Goldstone mode resulting in a huge increase in C/T?

Q: Steve Kivelson.Are there structural measurements to confirm if the transition is 1st order in CeRhIn5 at the same pressure when the Fermi surface volume jumps?A:No such measurements exist at this time.