Wrap up

Wrap up
  
In a very short wrap up discussion, it was agreed that one common link between many different families of unconventional superconductors is that they appear in a dome-shape region around the extrapolated quantum critical point of another phase that appears at higher temperature. In that case, the mechanism for superconductivity is likely to be the exchange of collective modes associated with the phase that would disappear at this quantum critical point in the absence of superconductivity. Materials falling into this type of explanation include Bechgaard salts, many pnictides, heavy fermions, MnP, SrTiO3. Electron-doped cuprates may fall into this category, but this is still disputed. The most commonly encountered quantum critical point in the previous examples is antiferromagnetic, but it is not the only possibility. The case of hole-doped cuprates is still the most controversial: does the dome surround a quantum critical point, and if it does, what is its nature? Participants agreed that we must look closely at symmetry sensitive experiments and recent ARPES from China that may be sufficiently detailed and accurate to give indications of the mechanism.

Insights from new theoretical approaches

Insights from newer theoretical approaches
It is possible to design models with fermions that do not have a sign problem. It opens the way to large system studies that give results for these models that are close to exact. This kind of approach has allowed us to understand that, in a theory where antiferromagnetic hot spots are present, upon increasing the coupling constant, there is a maximum attainable superconducting Tc. The existence of such a maximum Tc as a function of a parameter seems to be quite general. It is seen in the attractive Hubbard model for example. Also, the validity of the Eliashberg approach, that neglects vertex corrections, has been tested within such a fermion-sign free model. 

Cluster dynamical mean-field calculations seem to reproduce much of the phenomenology of both cuprates and layered BEDT organics. They suggest qualitative differences between strongly correlated superconductivity and superconductivity that results from pairing through long-wavelength fluctuations.  

Pseudogap and strange metal

Pseudogap and strange metal
Defining a pseudogap as a depression in the single-particle spectral weight at the Fermi level, or in other observable quantities such as the spin susceptibility, the appearance of a pseudogap in the normal state is a rather common occurrence in correlated-electron systems. There are several broad classes of mechanism that can produce a pseudogap. In one scenario, backed by experiments that reveal broken symmetries, a phase transition occurs at the pseudogap. That phase transition is proposed to be in the Ashkin-Teller universality class so that it is essentially undetectable by thermodynamic measurements. 

Long wavelength fluctuations involving composite order parameters (charge plus superconducting for example) have been proposed as another mechanism. There seemed to be agreement amongst participants that in electron-doped cuprates, antiferromagnetic fluctuations in the two-dimensional renormalized classical regime can explain the main experimental results on the pseudogap.  

This is not the case in hole-doped cuprates. A purely d=2 doped Mott insulator mechanism vs antiferromagnetic quantum critical point are still on the line, an issue related with the 1+x vs x number of carriers discussed under the cuprate section. New related experimental results in half-filled quasi-two dimensional Mott insulating organics were first announced at this meeting, namely: A pseudogap appears in the proximity of the Mot transition to the superconducting state if the insulating phase is antiferromagnetic, but not if it is a spin liquid.

Other fluctuation scenarios were discussed, including Ising nematic fluctuations and fluctuations with various power-law spectra that can be treated within the Eliashberg formalism.    

Strange metal behavior also motivated discussions. At half-filling, DMFT seems to explain the scaling of the resistivity observed in layered organics, opening a possibility for explanation of that behavior in cuprates. It seems to be clear also that in the overdoped regime for the cuprates, a phenomenlogical anisotropic marginal Fermi liquid explains much of the behavior. Standard Fermi liquid behavior occurs just at the end of the superconducting dome, a phenomenon begging for a microscopic explanation.  

Organics and other unconventional superconductors

Organics  and other unconventional superconductors
Layered organic superconductors are primarily half-filled and, as a function of temperature and pressure, exhibit a Mott transition, as well as antiferromagnetic, superconducting and spin-liquid phases. They are thus interesting compounds to gain insights into hole-doped cuprates as well. The latest experimental results, presented at this workshop, suggest that a half-filled spin-liquid compound has the same spin dynamics as a doped version of that compound, despite the fact that one is an insulator and another one a conductor. From the point of view of theory, RVB and CDMFT phase diagrams share similarities.

Superconductiviy in the Mott insulating organics is certainly unusual, but another unusual type of superconductivity was discussed. Isotopic oxygen-enrichment (or Nb doping) of strontium titanate has revealed a paraelectric quantum critical point surrounded by a dome of superconductivity. Although electron-phonon interactions can possibly explain superconductivity in this case, calculations would need to be done in the highly unusual anti-adiabatic regime where the Fermi energy is smaller than the Debye frequency of the optical phonons apparently involved here. 

Topological superconductivity and semimetals

Topological superconductivity and topological semimetals

Sr2RuO4 is of particular interest because it is considered the best candidate for bulk topological superconductivity. Most experiments point toward triplet chiral p-wave order. One challenge to this is experiments of the upper critical field which suggest singlet order, but we discussed one theory that reconciles this with chiral p-wave order.  On the other hand, we also heard about and discussed recent thermal conductivity results (not yet published) which appear to be in direct contradiction to the behavior expected for chiral p-wave order. This is an outstanding puzzle that was thoroughly discussed, but with no resolution. In addition to topological superconductivity our workshop asked a leading researcher in predicting topological materials through material computation to give a short talk on the classification of different Weyl semimetals.

Iron-based superconductivity

Iron-based superconductivity

Since the discovery of iron-based superconductivity in 2006, the highest superconducting transition temperature (75K) is reached when a single atomic layer of iron selenide (FeSe) is deposited on SrTiO₃ or BaTiO_3. In addition to that bulk FeSe displays some of the most puzzling properties among the iron-based superconductors. Unlike all iron pnictides it exhibits 90 degree crystal rotation symmetry breaking (nematicity) without magnetic long range order. This has triggered intense debate concerning the origin of such nematicity, namely, whether it spin or orbital driven. Our workshop choose FeSe and related systems as the point for iron-based superconductors.  In a discussion session we have a participant giving a summary of the up to date development in FeSe/STO, discuss the likely role played by the substrate, and why STO is special. In addition we also have an open discussion on several competing theories for the nematicity of bulk FeSe. This important issue is directly relevant to what is the most important fluctuating degrees of freedom at the low energies, hence to the mechanism of Cooper pairing. In FeSe there is an incipient band just below the Fermi level. The effect of such incipient bands on superconductivity was also discussed in a very general context. Despite the thorough discussion no resolution is reached.  

Heavy fermions

Heavy fermions:  
In heavy fermion physics there is the widely discussed “small to large Fermi surface transition”. This is strikingly analogous to the carrier density transition in the cuprates discussed above. Because of such similarity we had a discussion session on the heavy fermion phases and phase transitions. Several candidate materials where the quantum paramagnet with small Fermi surface (analogous to the state in cuprates with x carrier concentration but no symmetry breaking) are discussed. Another focal point in heavy fermion physics is SmB₆. It is proposed by a participant of our workshop that this system is a “Kondo topological insulator”. There are several experimental evidence supporting this proposal. However the experimental result of another participant raised some doubts. The most striking observation is a state which conduct heat as a metal does but it does not conduct electricity. Moreover such state seems to have some kind of Fermi surface giving rise to the oscillation of magnetization as a function of magnetic field. These results arose the interests of many participants. We also learned of recent experiments that demonstrate the existence of a large number of phases in the vicinity of the coexistence between antiferromagnetism and superconductivity. One of the conclusions is that superconductivity seems to prefer C_2 instead of C_4 symmetry.