Transcript A numerical renormalization group study of a two band

AFM correlation and the pairing mechanism in the
iron pnictides and the (overdoped) cuprates
Collaborators
Fa Wang (Berkeley)
Hui Zhai (Berkeley)
Ying Ran (Berkeley)
A. Vishwanath (Berkeley)
Fa Wang
Fa Wang et al, PRL 102, 047005 (2009)
Fa Wang, Hui Zhai & DHL, EPL 85, 37005 (2009)
Hui Zhai, Fa Wang & DHL, Phy. Rev. B (in press)
Hui Zhai
Systems with superconductivity near antiferromagnetic order
BEDNORZ, MULLER, Z. PHYSIK B-COND MAT 64 189 (86).
M.K. WU et al PHYS. REV. LETT. 58 908 (87).
• Heavy fermion compounds, e.g., CeCoIn5,
CeRhIn5, YbPd2Sn, CePd2Si2, CeIn3
Mathur et al, Nature, 394, 39 (‘98)
• Organic Compounds, e.g., -(BETS)2FeBr4,
-(BEDT-TTF)2Cu[N(CN)2]Br
The Question
Does the AFM correlation have anything to do
with the pairing mechanism in these materials?
Let’s focus on the iron pnictides and the cuprates.
Method: Functional Renormalization Group (FRG)
There is a lack of an ideal `ab initio' method for (strongly) correlated systems.
• Exact diagonalization, Quantum Monte-Carlo,DMFT, Mean-field,
Variational method, LDA, each has its own limitation.
• FRG: Unbiased, applicable to infinite system, but lacks a
small parameter (such as the  in 4-) to justify it rigorously.
Results for the (overdoped) Cuprates
Approach from the
overdoped side
k1
k3
k2
k4
Pairing mechanism
Dual scattering processes !
B
A
AFM driven correlations
Note that SDW correlation grow over a very wide
energy scale. It is not due to nesting.
FRG results for the iron pnictides
Recent FRG results
C. Platt, C. Honerkamp, W. Hanke, arXiv: 0903.1963
FeAs trilayer
k1+k2=k3+k4
k1
k3
k2
k4
2 x 106 scattering vortices
have to be re-evalueated at
each step of RG
I. I. Mazin, et al. PRL 101, 057003 (2008) (LDA)
K. Kuroki et al PRL 101, 087004 (2008). (LDA)
Z.J. Yao et al, New J. Phys. 11, 025009 (2009) (FLEX)
K. Seo et al, PRL 101, 206404 (2008). (Exchange model)
• Order parameter has opposite sign on
electron and hole FS.
• The gap function has large variations.
• Large variation of the order parameter
around some FS.
Gap variation
• The degree of gap anisotropy depends on microscopic parameters.
• It originates from the orbital dependence of pairing.
• It should be considered when fitting NMR and heat transport measurements.
Subleading pairing channels
SDW and orbital current order
Two types of Pomeranchuk instability
•This is a band version of “orbital
ordering”.
•Expect this type of distortion to
couple strongly with AFM.
• Give rise to Lattice distortion.
• Brings in magnetic anisotropy in
the AFM ordered state.
Pairing Mechanism
Dual scattering processes !
A
B
AFM driven correlations
Current order
PI
AFM
SC
AF correlation grow over a very wide energy range hence it is not
due to nesting.
However whether the AFM will be surpassed by SC does depend on how
well the FS are nested.
Pnictide Ladder RG results
Gap function
Conclusion
Thank You !