Peter HIRSCHFELD: Accidental order parameter nodes in Fe-pnictide superconductors

OUTLINE:
(I) FeAs experiments in SC state
(II) spin fluctuation theory of FeAs superconductors
(III) phenomenology: qp transport in 122 systems

Started with the overview of DFT-calculated band structure.
LOFP(1111): Lebegue 2007 (Tc=6K)
LOFA : Singh & Du 2008 (Tc=26K)



(I) FeAs experiments in SC state
Phase diagram shows diversity from one compound to another: e.g. Ce-1111 has no AF-SC coexistence, whereas La-1111 does.
Inconsistency in early measurements: NMR T1~T^3, whereas penetration depth and ARPES showed full-gapped superconductor (not unlike the early days of the cuprates).

Possible symmetries of OP, classified by symmetry representations:
A1g (s-wave)
A2g (g-wave): xy(x^2-y^2)
B1g (d-wave): x^2-y^2
...
Nodes or no nodes?

*PENETRATION DEPTH
Assuming line nodes,
\lambda(w) ~ T^2 (dirty limit) or ~T (clean limit)
Experimental data all over the place, e.g.:
*Sm-1111 (SOFFA): exp-l dependence, i.e. full gap!
*La-1111: ~T^2 dependence (Ames group)

*THERMAL CONDUCTIVITY
LaFePO: \kappa/T -> const as T->0 (nodes)
K-doped Ba-122: \kappa/T ~ T

(II) Spin-fluctuation theory of FeAs superconductors
History: Berk & Schrieffer (1961)
RPA: SC pairing proportional to spin susceptibility
Implications: Peak in spin fluctuations at (pi,pi) is taken advantage of by d-wave order parameter, even with repulsive interactions.

Graser (2009): pairing functions display gap nodes
Also: Kuroki '08, '09; Ikeda '09,'10

What is origin of gap anisotropy? [Maier et al PRB'09]

1. Orbital character on Fermi sheets
2. scattering between beta-1 and beta-2 sheets
3. intraband Colulomb repulsion

Kuroki et al. discovered a hole-like \gamma-pocket at (pi,pi), which grows upon hole-doping. It is d-xy in character and turns out important for the symmetry of the OP. This pocket helps overcome frustration by intraband Coulomb repulsion and beta-beta pocket scattering.

Large inter-orbital pairing stabilizes s+- state on xz, yz portions of Fermi surface.
This extended s-wave state may still develop (accidental) nodes: depends on the details of the model.

(III) 3D superconductivity in 122 systems
Ni-doped 122: penetration depth measured by Prozorov's group (Ames): Martin et al. 2010

Co-doped Ba122: \kappa/T as T->0 by Tanatar et al (Ames, Sherbrooke), PRB (2009)
undoped material: no nodes
doped: either finite value of \kappa/T (i.e. nodes), or roughly linear in T (deep minima)

Co-Ba122: Reid et al, 2010: depending on the direction J||a or J||b, \kappa/T either shows a finite value (nodes) or zero (isotropic gap) - how is it possible??

Hirschfeld's group calculations (Mishra et al, 2009): nodes near k_z=pi, so that \kappa/T is finite as T->0.
Playing with possible node structures: lambda(T) behaves as non-universal power-law, e.g. T^1.3, T^2.16 etc, and qualitatively describes the anisotropy seen by Reid et al. (2010).

CONCLUSIONS:

• the symmetry of the OP is always A1g (extended s-wave), and generically is not required to have nodes
• nodes may appear accidentally, as a consequence of orbital anisotropy on the Fermi surface and intra-band repulsion
• various experiments (penetration depth, thermal conductivity) can be explained, qualitatively, by playing with the gap structure.

QUESTIONS:
Q: H. Alloul
Asking whether any ARPES experiments were able to observe the \gamma pocket at (pi,pi).
A: not aware of a clear exp-tal signature of all 3 hole pockets.

Q: A. Chubukov
Witihin RPA approach, does one always get a gap with nodes, if one neglects the extra hole pocket at (pi,pi)?
A: In this case, we always find a strongly anisotropic order parameter, with nodes or near nodes.

Q: Y. Grin
1) Are As-p states near Fermi level important?
2) In 1111- and 122- compounds, is the orbital contribution on the Fermi surface the same?
A: 1) the effective interactions between Fe-orbitals are mediated by As atoms, so they contribute indirectly
2) in kz=0 cut, the 1111 and 122 have identical orbital composition; at kz=pi, one expects them to differ, but detailed calculations haven't been carried out yet.

Q: P. Coleman:
Is the effect of repulsive \mu* component included in the calculations? Can it be that pure s-wave is favoured alongside s+-?
A: (with comment by Chubukov): The bare repulsive intra-band U is likely to suppress s-wave pairings. But in the spirit of RG (see previous talk by Z. Tesanovic), a situation can occur where the renormalized pair-hopping value is stronger than the intraband repulsion, making SC possible.