Zlatko Tesanovic: What is the theory of the Fe-pnictides?

Outline of the talk:

1) Fe-pnictides: semimetals turned superconductors
2) pairing states
3) minimal model
4) multiband magnetism and superconductivity

Zlatko started his talk by providing some background information on the Fe-pnictides: The Fe-pnictides were discovered by the group of H. Hosono in 2008 with a Tc of 26K. Currently, the highest Tc in the Fe-pnictides is approximately 57K. The pnictides, whose name comes from Greek meaning "choking, suffocating", are made of elements from group V of the periodic table. The 1111-materials exhibit a larger Tc than the 122-materials, though the later are easier to fabricate. The Fe-pnictides are layered, quasi-2D materials.

Zlatko then discussed similarities and differences between the cuprate superconductors and the Fe-pnictides:
Similarities:
1) both class of materials have d-electrons (Cu vs. Fe)
2) both materials are layered and quasi-2D
3) the phase diagrams of both materials exhibit superconductivity and antiferromagnetism in
close proximity

Differences:
Fe2+ has an electronic 3d6 configuration, while Cu2+ has a 3d9 configuration. Therefore, the electronic structure of the CuO2 layers is described by a single hole in a filled 3d orbital, and a one band model might be sufficient to describe the physics of these materials. In contrast, in FeAs one has a large and even number of electrons in the 3d orbital, implying that a multiband model is necessary for their description.

Zlatko then reminded us that in the cuprate superconductors, the Mott insulating state of the undoped parent compounds evolves into a superconducting state upon doping. In the undoped cuprate compounds, the effective Coulomb interaction is much larger than the electronic hopping, resulting in a Mott insulator and a Neel AFM. The greatest challenge in the cuprate superconductors is a microscopic understanding of the pseudo-gap region in the underdoped compounds.

Zlatko then presented a schematic phase diagram (ZT, Nature 4, 408 (2008)) to explain how a correlated superconductors can evolve into a Mott insulator. At weak interactions, the superconducting state is destroyed by thermal fluctuations, while at large interactions, it is destroyed by quantum fluctuations. There are many different theoretical proposals to describe this transition.

Question by P. Coleman: is there a convergence of theories?
Answer: proposed theories seem to converge towards gauge theories for the description of the underdoped cuprates.

Zlatko then presented a schematic band structure of the Fe-pnictides to show that in these materials, the bands are either almost full or empty leading to a semi-metal and implying that these materials are far away from the Mott limit of one electron/hole per site. As a result, all regions of the FeAs phase diagram are (bad) metals, in contrast to the cuprate superconductors. Zlatko therefore argued that the appropriate starting point for the description of the Fe-pnictides is an itinerant picture. This is also supported by ARPES and dHvA experiments that seem to observe coherent propagating quasi-particles.

Zltako argued that a minimal model for the FeAs layers should be an effective 2D model that includes all 5 d-orbitals. While the As bands are below the Fermi level, they contribute to the minimal model, and one therefore should start with a minimal model that include all 5 Fe orbitals and 3 As orbitals. This gives rise to a much more complicated band structure than in the cuprate superconductors, with the hybridization between the orbitals as well as the renormalization of the band parameters being crucial. Zlatko argued that there is no Hund's rule coupling in the Fe-pnictides.

Question: is this assumption not in conflict with LDA calculations.
Answer by Zlatko: I want to give a happy talk, and therefore will not comment on these calculations.

Zlatko next discussed nesting properties and valley-density-wave (VDW) states in the pnictides. He argued that valley-density-wave states arise due to nesting enhancement of electron-hole excitations, where the latter give rise to moderate interaction strengths. Here, a VDW state refers to an itinerant multiband CDW, SDW or orbital-order-wave (ODW) state. Zlatko then presented a "bare-bone" model for the Hamiltonian that includes the electronic band structure as well as intra- and inter-band interactions. Zlatko showed that by using a particle-hole transformation for one of the electronic bands, one arrives at the negative-U Hubbard model.

This model can be solved on the mean-field level by using the Hartree-Fock approximation, where self-consistency is crucial in obtaining the correct BCS ground state of the model. Zlatko then described how the Cooper instability is obtained by summing up an infinite series of ladder diagrams. Zlatko mentioned that the relevant effective interactions should be obtained from an RG analysis. By reversing the particle-hole transformation, one then arrives at an SDW, CDW or ODW state in the Fe-pnictides.

Zlatko then turned to the question of real superconductivity in the Fe-pnictides. He pointed out that there is strong mixing of odd and even d-orbitals around the Fermi surface, and that the effective interactions at the Fermi surface need to be divided into flavor conserving and mixing vertices. This gives rise to interband superconductivity. Of great importance in the emergence of the superconducting state is that the effective interaction in the particle-particle channel is sufficiently large. An RG analysis has shown that due to the proximity of an SDW state, the pairing interaction is enhanced and thus stabilizes the superconducting state.

Blogged by Dirk Morr.