electronic structure of iron-based superconductors amalia...
TRANSCRIPT
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Amalia Coldea
KITP, 30 September 2014
Electronic structure of iron-based superconductors
UNIVERSITY OF OXFORD
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II. Electronic structure of bulk FeSe from ARPES and
quantum oscillations
I. Fermi surface shrinking and the effectsof electronic correlations
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Classes of Fe-based superconductors
The common features: robust Fe/(Pn=As,P) layers where Fe atoms are tetragonallycoordinated by pnictide or chalcogenide atoms.
‘1111’ type
‘122’ type
‘11’ type
‘111’ type
Tc ~ 55 KTc ~ 38 KTc~27 K Tc~18 K Tc ~ 37 K
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Generic phase diagram of isoelectronic pnictides
LiFeP
LaFePOLaFeAsO
BaFe2As2 BaFe2P2
“chemical pressure” c/a ratio
5 bands (orbitals), magnetism, structural distortions
FeSe
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Fermi surface nesting and gap symmetry
hole
electron
Superconductivity develops when the nesting / magnetism is destroyed.
Different possible scenarios for nodal and nodeless superconductivity depend on orbital character.
D. SinghP. J. Hirschfeld et al, Rep. Prog. Phys. 74, 124508 (2011)
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Quantum oscillations map out the Fermi surface
• oscillations of the density of states in magnetic field;
F=(ħ / 2π e) A(EF)
A (EF)
• ‘k-space microscopy’: 0.1% IBZ; 3D map of the Fermi surface;• bulk probe; no sensitive to surface effects like AR PES;
de Haas van Alphen effect
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Lifshitz-Kosevich formalism (LK formula)
• extracted parameters: orbitally averaged quasiparticle effective mass m*(band renormalization near the Fermi energy), •scattering times ~ττττ, spin-splitting factor g*
Temperature - low temperatures
Finite scattering time – clean samples
Superconducting state –random vortex lattice
Spin-splitting of the Fermi surface
Shoenberg, Magnetic oscillations in metals, (1984)
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Lifshitz-Kosevich formalism.The effect of electronic correlations
m*/mb=(1+λel-ph)(1+ λel-el) ~1+ λel-ph+ λel-el
Shoenberg, Magnetic oscillations in metals, (1984)
C Bergemann, PhD Thesis
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Quantum oscillations in iron pnictides
-Clean samples : mean free path > 150 Å
- End member compounds: (Ba/Sr/Ca)Fe 2As2, (Ba/Sr/Ca)Fe2P2, KFe2As2, etc
- twinning of samples is detrimental for the observation of quantum oscillations;
Disorder induced only outside the Fe plane BaFe2(As,P)2
-Doped samples: Co-doped or K-doped BaFe2As2; large upper critical fields > 60Tand large randomness in the distribution of ions on the Fe sites;
-Lighter masses and smaller frequencies usually are easier to be observed thanheavier masses and large frequencies;
ħωωωωc>kBT, ωωωωcτ>>1τ>>1τ>>1τ>>1
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Measurement techniques of quantum oscillations
50 µm
B
Low temperatures (0.3 K < T < 4 K), high magnetic fields (0 < B < 55 T) rotation in field (-900 < θ < 900);
10-12 EMU
AFM piezocantilevers micron-size crystals Capacitive levers mm-size crystals (Sebastian)
Transport measurements to de-twin crystals(Terashima)
BaFe2As2
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I. Fermi surface shrinking and the effectsof electronic correlations - LaFePO
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Superconducting order parameter with line nodes in LaFePO
• Clean superconductor with no structuraltransition.Superfluid density show lineardependence down to 100 mK suggesting the
presence of nodes in the symmetry of thesuperconducting gap;
∆λ ~ T
±
J. Fletcher, et. al., PRL 102, 147001 (2009)J. Analytis et al., arXiv:0810.5368
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10 12 14 16 18-4x10-4
-2x10-4
0
2x10-4
4x10-4
0 1000 2000 3000 4000
0
2x10-2
4x10-2
6x10-2
θ =31o
torq
ue (
Ω)
B (T)
β1 β
2
α1 α
2
FF
T (
ampl
itude
)
F (T)
de Haas-van Alphen effect in LaFePO
0 3 6 9 12 15 18
-0.25
0.00
0.25
0.50
0.75
θ =94o
θ =31oT=0.35 K
torq
ue (
Ω)
B (T)
Hc2
Hc2
Sample B
• high B: normal state; oscillations periodic in inverse field, de Haas-van Alphen effect.• τ ~ B2 –characteristic to a paramagnet;• a simple corrugation of the Fermi cylinder leads to a beat pattern in the magnetization.
τ ~ B2
A.I. Coldea et al., PRL, 101,216402 (2008)
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de Haas-van Alphen effect in LaFePOTo
rque
(a.
u.)
A.I. Coldea et al., PRL, 101,216402 (2008)
F=(ħ / 2π e) A(EF)
Different frequencies correspond to extremal areas of the Fermi surface perpendicular to the applied magnetic field for a particular orientation;
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α2
α1
β2
β1
Fermi surface warping and Yamaji angle
∆Fα/Fα ~ 4%;∆Fβ/Fβ ~23 %;
F(θ )=F(0) / cosθQuasi-two dimensionalcylinder;
K. Yamaji, J. Phys. Soc. Jpn. 58, 1520 (1989)
H H
At Yamaji angles all Fermi surfacecross sections have equal areas;their magnetization contributionsinterfere constructively=peak effect.
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-45 0 45 900.6
0.7
0.80.9
1
2
3
4
5
6
7
-45 0 45 900.6
0.7
0.80.9
1
2
3
4
5
6
7
θ (degrees)
dHvA
Fre
quen
cy F
(kT
)
h
e
band 1
band 2
band 3
band 4
band 5
θ (degrees)
dHvA
Fre
quen
cy F
(kT
)
dHvA data versus band structure calculations
• electronic branches show similar dispersion to the experimental α and β pockets; • no experimental branch matches the weak dispersion due to the 3D hole pocket;
e
e
M
-45 0 45 900.6
0.7
0.80.9
1
2
3
4
5
6
7
θ (degrees)
εδ
α1
α2
β1
γ
β2
dHvA
Fre
quen
cy F
(kT
)
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Band shifting and charge balance
Electron bands shifted by ∆E=+85 meV (band 5), +30 meV (band 4); hole bands all shifted by ∆E=-53 meV; Charge imbalance ~0.034 el/fu; ~1.7% oxygen deficiency in LaFePO.
-45 0 45 900.6
0.7
0.80.9
1
2
3
4
5
6
7
θ (degrees)
εδ
α1
α2
β1
γ
β2
dHvA
Fre
quen
cy F
(kT
)
-45 0 45 900.6
0.7
0.80.9
1
2
3
4
5
6
7
-45 0 45 900.6
0.7
0.80.9
1
2
3
4
5
6
7
θ (degrees)
dHvA
Fre
quen
cy F
(kT
)
e
h band 2
band 3
band 4
band 5
θ (degrees)
dHvA
Fre
quen
cy F
(kT
) M
Γ
e
h
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Shrinking of the Fermi surface in LaFePO
experimental observation of upward shift of the electron bands and of a downward shift of the hole band may be evidenceof dominance of interband scattering (nesting);
L. Ortenzi et al., PRL 103, 046404 (2009).
Q
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Shrinking of the Fermi surface in LaFePO
L. Ortenzi et al., PRL 103, 046404 (2009).
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Shrinking of the Fermi surface pockets
Hui Zhai, et al., Physical Review B, 80, 064517 (2009)
SDW/ Pomerachuk instability in the iron pnictide tends to shrink both the electron and hole pockets. Antiferromagnetically driven electronic correlations.
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I. Fermi surface shrinking and the effectsof electronic correlations – LiFeP and LiFeAs
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Quantum oscillations in the superconductingLiFeP and LiFeAs
LiFeP nodal superconductor TC~4K
LiFeAs nodeless superconductor TC~18K
NODES
S. Kasahara et al., Phys. Rev. B 85, 060503(R) (2012) K. Hashimoto et al., Phys. Rev. Lett. 108, 047003
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Quantum oscillations in LiFeAs and LiFeP
Torque shows quantum oscillations in LiFeP and LiFe As above Hc2. There are 5 different frequencies for LiFeP and 3 different fre quencies observed for LiFeAs.
T = 1.5K
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Quantum oscillations in LiFeAs and LiFeP
For LiFeP, small shifts of the band energies: +20 meV and +45 meV for band 4 and 5 (electron) and −65, −80, 18 meV for bands 1, 2 and 3 (hole) bring the observations and calculations into almost perfect agreement. These shifts shrink both the electron and hole FSs and likely originate from many body corrections to the DFT bandstructure.
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Fermi surface parameters in LiFeAs and LiFeP
K. Hashimoto et al., arXiv:1107.4505 (2011)
dxy
Location of nodes ?
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Effect of electronic correlations in LiFeAs
Ferber et al., Phys. Rev. B 85, 094505 (2012)
The effect of correlations on the Fermi surface manifests itself mainly in a shrinking of the middle hole pocket, and, in order to preserve the electron count, an increase of the outer hole pocket size.
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I. Fermi surface shrinking and the effectsof electronic correlations – BaFe2(As,P)
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Effect of chemical pressure: P/As substitution
S. Kasahara et al. , PRB 81, 134422 (2010)
BaFe2As2 (low T)
BaFe2P2
W. Xie, PRB 79, 115128 (2009)
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Evolution of Fermi surface in BaFe2(As1-xPx)2
H. Shishido et al. AIC, PRL 104, 057008 (2010)
oscillations observed for materials with Tc = 0 – 25 K; Tmax=30 K for x = 0.33;
l=800Å
l=150Å
Tc~25 K
Tc~30 K
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Spin fluctuations in BaFe2(As1-xPx)2
S. Kasahara et al., PRB 81, 184519 (2010)
Y. Nakai, et al.arXiv:1005.2853(2010)
H. Shishido et al., AIC, PRL 104, 057008 (2010)
Antiferromagnetic spin fluctuations close to QCP
ρ =ρ0 + ATα
1/T1T~1/(T+θ)
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0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5
710 T985 T240019201645 T1335 T
FF
T A
mpl
itude
(a.
u.)
T (K)
∆B = 35-45 T
Moderate mass enhancement in LaFePO
• the effective masses between 1.7-2.1 me for both electrons and holes; • moderate mass enhancement for the electronic bands;
(el-el + el-ph)
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Heavier quasiparticles in LiFeAs
5.2(4) me
6.0(4) me
m*/mb=(1+λel-ph)(1+ λel-el) ~ 1+ λel-ph+ λλλλel-el
Heavy effective masses in LiFeAs for the electron b ands as compared to other iron pnictides; band masses 1-1.5 me and electron-phonon coupling ~0.25;
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Correlations in iron pnictides
Nature Materials, 10, 932–935, (2011)
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The strength of electronic correlations.Electronic bands in clean superconductors
Nodal superconductors Fully gapped superconductor
PRL 108, 047002 (2012); PRL 101, 216402 (08); PRL 104, 057008 (2010);
FeSe
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Summary of quantum oscillation in iron-based superconductors
• Quantum oscillations in iron pnictides are in broad agreement with band structure.
• Fermi surface shrinking for superconducting compounds as compared with band structure calculations; local correlations or partially from long-range spin fluctuations?
• Mass enhancement in the clean and nodal superconductors correlates with the increase in Tc for isoelectronic system like BaFe2(P1-xAsx)2 and LiFeAs and LiFeP; electronic correlations are important (quantum critical point ?).
PRL 101, 216402 (08); PRL103, 026404 (09), PRL103, 076401 (2009) ; PRL 104, 057008 (2010);
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Electronic structure of bulk FeSe from ARPES and
quantum oscillations
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Unusual high Tc in a mono-layer of FeSe
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ARPES and pressure effects
FeSe
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Superconductivity and structural transition in FeSe
(0kl) (hk0)
M. Watson et al., Oxford (2014)