A new iron age (of superconductivity)

Yesterday, Ilya Eremin (MPI, Dresden) gave a really nice talk on the new Ferropnictide superconductors. It was a model of clarity. Here are a few brief notes with a few comments of mine interspersed in parentheses.

Bednorz and Muller changed the landscape of condensed matter physics!
[RHM: Strongly correlated electron materials moved from the peripheral to the centre of the field. ]

Current highest Tc=55 K SmFeAsO1-xFx

Surprising this is a superconductor since it contains iron has a large Hund's rule coupling

Pnictides vs. cuprates: similarities and differences

Similarities
Both are layered (CuO2 vs. FeAs), have d-electrons in a key role, and have AF and SC in close proximity in phase diagram

Differences
FeAs is always metallic, i.e., no Mott insulator in phase diagram
In pnictides d-bands are far from half filling, i.e., almost full (fermi surface close to gamma point) or empty (compensated metal)
EVEN number of electrons (close to 3d6) per iron atom in parent material vs.
one electron per copper atom in cuprate parent

(J. Zhao et al., Nature Materials 2008)

Claims
interactions are smaller than the bandwidth
interesting physis is due to proximity to perfect nesting
whole band is nested, not just the Fermi surface

[RHM: is a key signature of cuprate vs. pnictide difference the size of the magnetic moment in the SDW phase? it turns out to me more subtle than this see below]

For perfect nesting SDW instability occurs for small U

Nesting leads to two competing logarithmic diverges: both in SDW and SC channel
(T.M. Rice for Cr, ) so they must be considered on equal footing and worry about interference effects [this is quite different to the cuprates, where one tends to think in terms of a doped Mott insulator]

[RHM: Similar issues concerning the interference between the particle-hole and particle-particle channels occur in one dimension: cf., Solyom, 1980]

"Toy model":
[I prefer the term "minimal model", perhaps for marketing reasons?]

This has two parabolic bands (alpha and beta band) with identical dispersion and circular Fermi surfaces. One is centred at Gamma point and the other at the corner of the Brillouin zone.
4 types of interactions: both intra-band and inter-band.
There are then 4 possible instabilities:
SDW,
CDW,
s-wave superconductivity
s-wave superconductivity (pi phase shift between bands)

Derives RG equations for the four interactions u1, u2, u3, and u4
[PRB, 2008, Chubukov, Efremov, Eremin]

Strongest instability is SDW then CDW, then extended s-wave. The growth rate of the latter coupling constant changes sign with increasing rescaling (i.e., RG flow) resulting from the interfering logarithms.

Similar results are obtained from functional RG [Visawanath et al, PRL 09]

Can we understand real space magnetism in terms of an itinerant SDW picture?
Two inequivalent As positions leads to ambiguity in Fe sublattice order
Experiment shows (0,pi) order with respect to Fe lattice (stripe like AFM structure)

An alternative picture is that of localised spins in frustrated J1-J2 model. [Uhrig, Holt, Hamer, Oitmaa, and Singh, PRB 2009]. Then the reduced magnetic moment comes from proximity to a quantum phase transition rather than itinerancy.

Look at Fermi surface in unfolded Brillouin zone
Now four pockets alone BZ boundary (i.e., one hole and two electron pockets)
mean-field equations do not specify relative size and magnitude of two
pocket order parameter amplitudes
ground state degeneracy is larger than in J1-J2 model
O(6) degeneracy = 5 goldstone modes

But electron pockets are elliptic, no need for quantum fluctuations in itinerant picture
charge fluctuations are crucial,

Questions:
seems cant get the SDW to SC transition with doping, i.e., moving away from perfect nesting does dominant interaction changes

not clear answer, seems may end up with nodes on fermi surface.