“Possible probes for detecting s±-wave
pairing symmetry in Iron-Pnictides:
Novel Josephson junctions and impurity effects”
Wei-Feng Tsai
Xiao-Ting Zhou, Chen Fang, Kangjun Seo,
Yan-Yang Zhang, Dao-Xin Yao, JiangPing Hu
(Purdue University)
and
B. Andrei Bernevig
(Princeton University)
Paper ref: arXiv:0812.0661, 0903.1694, 0905.0734
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Outline
Introduction
Direct phase-sensitive probe:
• Novel π-junction
Indirect probes:
• S/N/S± Josephson junction
• Impurity-induced bound states
• Quasiparticle interference patterns
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It is critical to determine pairing symmetry in
superconducting Iron Pnictides
Many aspects analogous to high-Tc cuprates:
(1) Parent compound is antiferromagnetic
albeit metallic
(possibly proximate to a Mott insulator)
(2) Quasi-2D nature (superconductivity related
to the FeAs layer)
New features: multi-orbital nature
and complex Fermi surfaces
J. Zhao et al., Nature Materials 7 (2008)
Many theoretical proposals for pairing symmetry:
For instance, triplet s-wave, nodal s-wave, d-wave, p-wave, extended swave (s±)…etc.
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X. Dai et al., PRL 101 (2008); K. Kuroki et al., PRL 101 (2008);
M. Daghofer et al., PRL 101 (2008); Q. Si and E. Abarahams, PRL 101 (2008);
P.A. Lee and X.G. Wen, PRB 78 (2008); I. Mazin et al., PRL (2008)…
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Pairing symmetry in two band-{t}-J1-J2 model
s-wave pairing
coskx+cosky
J1
d-wave pairing
coskx-cosky
+
+
+
+
+
-
Symmetry factors
+
Function peaks at
Fermi surfaces
-
s-wave pairing
coskxcosky
J2
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d wave pairing
sinkxsinky
K. Seo, B. A. Bernevig, and J.P. Hu PRL 101, 206404 (2008)
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Properties of s-wave coskxcosky Pairing Symmetry
 Order parameters have different signs at
electron and hole pockets
 If magnetic exchanges are symmetric for all
orbits, gaps should be determined by single
energy scale
 Superconducting gaps are larger in smaller
pockets.
 Fermi surfaces are generally gapped unless
heavy doping crosses gapless line.
Gapless lines
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Alas, most experiments are only sensitive to
SC gap magnitudes
Question: How to detect sign-changed s-wave
pairing symmetry?
D. Parker and I. Mazin, arXiv: 0812.4416
J. Wu and P. Phillips, PRB 79 (2009)
X.-Y. Feng and T.-K. Ng, PRB 79 (2009)
P. Ghaemi et al., PRL 102 (2009)
S. Onari and Y. Tanaka, PRB 79 (2009)
J. Linder et al., arXiv: 0901.1895
…
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Novel π-Junction (I):
why usual corner-junctions cannot work for s±?
Ic/I0
Φ/Φ0
Y.-R. Zhou et al.,
arXiv:0812.3295
for Co-doped 122
material.
Ic/I0
s±: non-trivial phase structure
of SC order parameter in k-space!
Φ/Φ0
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D. J. Van Harlingen, RMP 67 (1995)
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Novel π-Junction (II) – our proposal
p
+
-
+
p

2
ky
-
+
0
-
top s-SC
θt
Iron pnictide, s±
θm
bottom s-SC
θb
p
- 
2
+
-p
-p
Φ= θt -θb
p
- 
2
0
kx
+
p

2
p
Key assumption: momentum conserved
after tunneling between layers –
high-quality interfaces may be required
*Suggested s-SC with (1) large FS: MgB2 (a~0.3nm),
Be thin film (a~0.23nm); (2) small FS: 2H-NbSe2
(a~0.345nm). Or possibly metallic thin film with large or
small FS due to SC proximity effect.
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Φ/π
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S-N-S± Junction (I) – basic idea
∆s∆>
L 0
s-SC
(x<0)
∆1 > 0,
∆R∆2 < 0
Iron(x>0)
pnictide
[ ∆λ(x), s-SC order parameter;
λcould be a band index ]
Within WKJB approximation, the junction can be described by a continuum BdG eq.
where
Andreev bound state solutions ~ e -γ|x|
∆L = ∆R = ∆
∆L = -∆R = ∆
εbs = ± ∆
εbs = 0
T.K.Ng and N.Nagaosa, arXiv:0809.3343
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For the junction with unconventional pairing symmetries, see e.g.
S. Kashiwaya and Y. Tanaka, Rep. Prog. Phys. 72 (2000)
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within ‘N’ region)
S-N-S± Junction (II) –
QP-LDOS for various pairing symmetries
(at x=
0
(in units of |t1|)
(~ ∆ )
FeAs
*A two-orbital exchange coupling model on the lattice is used for Iron pnictides
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Detection of the (phase) sign change through
impurity effects
Questions for s±-SC:
1) Any non-trivial in-gap bound-states?
(E < ∆coh) [See also T. Zhou et al., 0904.4273; D.
Zhang, 0904.3708]
2) What does the quasi-particle interference
pattern look like? [Also suggested by Fa Wang et
al. in EPL 85 (2009)]
A. V. Balatsky et al, RMP (2006)
J. E. Hoffman et al, Science 297 (2002)
Q.H. Wang and D.H. Lee, PRB (2003)
Strategy:
“Hamiltonian” =2-orbital model + a localized single impurity
(non-magnetic/magnetic, intra-orbital/inter-orbital)
Self-consistent BdG
(on 32x32 lattice)
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+
T-matrix
Approximation
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LDOS near the non-magnetic impurity site
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BdG calculations with VI=4|t1| and ne~2.1 per site on a 32x32 lattice
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Bound state energy vs. impurity scattering strength
(non-magnetic, intra-orbital)
s±-SC, ∆coh=0.4|t1|
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[For many impurities, see for instance, Y. Bang et al., PRB 79 (2009)]
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LDOS near the magnetic impurity site
impurity site: (16,16)
JIsz/2=2
The peaks decay quickly after ~3 lattice constants
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Quantum phase transition (level-crossing) and
subtle features
(1) In-gap bound states are more robust (2) No πphase shift at the impurity site
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[For strong “inter-band” magnetic scattering, see Jian Li and Y. Wang, 0905.3883]
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Quasi-particle interference (QPI): some parameters
Pairing symmetry: ∆0 coskx cosky (∆0 / W ~ 0.01)
DOS for a clean s±-SC
∆coh ~ 0.08
(in units of |t1|)
Vimp = 4 ∆0 such that N0 Vimp < 1, i.e., in the weak scattering (perturbative) regime
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QPI: induced LDOS(q,ω) for coskx cosky s-SC
qy
qy
nonmagnetic
magnetic
ω=-0.09
qx
peaks around (±π,0)/ (0,±π)
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ω=-0.09
qx
large peaks around (0,0)
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QPI: induced DOS(q,ω) for |coskx cosky| s-SC
non-magnetic
magnetic
In sign-changed s-wave pairing states:
 The peaks around (π,0)/(0,π) show up for the case of non-magnetic
impurity
 Anti-correlation between the intensities around (0,0) and (π,0)/(0,π)
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Y.Y. Zhang et al., arXiv:0903.1694
F Wang et al., EPL 85, 37005 (2009)
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Summary
Due to the special feature of coskx cosky s-wave pairing symmetry, which
changes sign between electron and hole Fermi pockets, we have shown:
1. A novel tri-layer π-junction.
2. The presence of non-trivial in-gap bound states in the
S-N-S± Josephson junction, sharply in contrast to other
singlet pairing states.
3. A non-magnetic impurity in s±-SC can induce in-gap
bound states in sharp contrast to conventional s-wave SC.
4. The presence (absence) of (0,π) / (π,0) peaks in QPI for s±SC with non-magnetic (magnetic) impurities is a
distinguishable feature compared with conventional s-SC.
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Thank you very much for your
attention!
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Supplement
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sign-changed
s-wave
s-wave
PRL 102 (2009)
s-wave
arXiv:0812.3295
s-wave
Nature 453 (2008)
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Large FS
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Small FS
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Formula in SNS junction
With finite width d of the N region, the bound state energy appears at
With unequal magnitudes of pairing potentials,
provided
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QP spectrum in SNS± junction
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Model Hamiltonian in Iron Pnictides
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T-matrix for impurity-induced bound states
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Non-magnetic
magnetic
Sx2y2
S
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X
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SC gap: non-magnetic impurity
Sx2y2
S
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SC gap: magnetic impurity
Sx2y2
S
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Spatial distribution of Spin-resolved LDOS
at positive bound state energy
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T-Matrix approximation for induced LDOS
The single-impurity induced Green’s function is
The standard perturbation theory gives
Therefore the Fourier transform of the induced LDOS is
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Intra-orbital scattering dominates
QPI along special directions
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Two-Orbital: d wave
NON-magnetic
magnetic
ω= 0
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ω= 0.03
within the gap
ω= 0.07
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Five-Orbital: QPI
NON-magnetic
magnetic
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Five-Orbital: Profiles
NON-magnetic
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magnetic
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Five-Orbital: without sign change
NON-magnetic
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magnetic
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