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Charge Density Waves in High Temperature Superconductors
Elizabeth Blackburn
School of Physics and Astronomy
University of Birmingham
ECRYS 2014 - Cargese – 12 August 2014
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Acknowledgements Alex Holmes
Ted Forgan
Anke Watenphul Martin von Zimmerman Uta Rütt Olof Gutowski Stephen Hayden
Niels Christensen Jacob Larsen
Johan Chang Joel Mesot
Ruixing Liang Doug Bonn Walter Hardy
Markus Hücker
Laurence Bouchenoire Simon Brown Paul Thompson
Ayman Said Bogdan Leu
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(as the Pauli Exclusion
Principle says it must)
CDWs Superconductors
Monceau, Advances in Physics 61, 325 (2012).
x
each electron in a pair does its own thing …
… but the CENTRES OF MASS of ALL the pairs do exactly the SAME thing –
like in a laser or a BEC
… but what force holds the electrons together?
( ~ a “coherence length” ξ apart)
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Conventional ‘s-wave’
electron pairs
not circulating …
Unconventional: ‘p-wave’
e.g. Sr2RuO4
circulating: = 1
Cooper pairs in superconductors
Unconventional ‘d-wave’
e.g. High-Tc , CeCoIn5
circulating both ways - = 2
+
+
- = 2 order
parameter -
energy gap
node in energy
gap
Fermi surface
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Conventional ‘s-wave’
electron pairs
not circulating …
Unconventional: ‘p-wave’
e.g. Sr2RuO4
circulating: = 1
The type of pairing controls the symmetry of the superconducting
gap function, which, amongst other things, affects flux line and Josephson tunnelling properties
How does the pairing arise??
Cooper pairs in superconductors
Unconventional ‘d-wave’
e.g. High-Tc , CeCoIn5
circulating both ways - = 2
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The Copper-Oxygen Planes
Barisic et al., PNAS 110, 12235 (2013) Mark Winter,
http://www.shef.ac.uk/chemistry/orbitron/
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The cuprate superconductor phase diagram
Wahl , Nature Physics (2012)
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The pseudogap – loss of DOS at Fermi Level, well above Tc
• Pre-formed pairs?
• Competing order? Bi2212
Wahl , Nature Physics (2012) Kondo et al., Nature Physics (2011)
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‘pseudogap’
Tc ‘plateau’
Fermi Liquid
Phase diagram of YBa2Cu3O7-x versus doping
What changes as we cross the ‘dome’?
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Overdoped – all holes visible - obeys Luttinger theorem
Underdoped – tiny number of electrons not holes
B. Vignolle et al. Comptes Rendus Physique (2011)
N.B. QOs give the area of the electron pocket
The Fermi surface – quantum oscillation data
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Superconductivity in YBCO6+x
Superconductivity mainly resides in the CuO2 bi-layered planes
Ghiringhelli et al., Science (2012) Andersen et al., Physica C (1999) v. Zimmerman et al., Phys.Rev.B (2003)
Oxygen content is varied from O7 to O6 by
removing O from the chains running along b
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Oxygen ordering in YBCO6+x
Ghiringhelli et al., Science (2012) Andersen et al., Physica C (1999) v. Zimmerman et al., Phys.Rev.B (2003)
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Signs of something changing inside the PG region
• Transport measurements
LeBoeuf et al., Nature (2007), Phys. Rev. B (2011)
This suggests that the Fermi surface changes topology below THall
Hall effect
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Signs of something changing inside the PG region
• Transport measurements
Barisic et al., PNAS 110, 12235 (2013)
Sheet resistance
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Signs of something changing inside the PG region
• Transport measurements
• NMR/NQR
Wu et al., Nature 477, 7363 (2011) – picture is ortho-VIII.
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63Cu NQR shows signs of charge order in o-II YBCO
Wu et al., Nature (2011) (& Nature Comms .2013)
They suggested a charge modulation along a with period 4a…
Splitting in a Cu line appears at high field and low temperature.
15 T
28.5 T
… beware: NMR/NQR is a ‘local’ probe
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Signs of something changing inside the PG region
• Transport measurements
• NMR/NQR
• Quantum oscillations
all holes visible small e- pocket
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Signs of something changing inside the PG region
• Transport measurements
• NMR/NQR
• Quantum oscillations
• Kerr effect
Xia et al., Phys. Rev. Lett. 100, 127002 (2008).
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Signs of something changing inside the PG region
• Transport measurements
• NMR/NQR
• Quantum oscillations
• Kerr effect
• Ultrasound
LeBoeuf et al., Nat. Phys. 9, 79 (2012).
c66
Magnetic field (T)
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Signs of something changing inside the PG region
• Transport measurements
• NMR/NQR
• Quantum oscillations
• Kerr effect
• Ultrasound
• Polarized neutron diffraction
HgBCO - Li et al., Phys. Rev. B 84, 224508 (2011).
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Signs of something changing inside the PG region
• Transport measurements
• NMR/NQR
• Quantum oscillations
• Kerr effect
• Ultrasound
• Polarized neutron diffraction
Li et al., Nature 455, 372 (2008).
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Signs of something changing inside the PG region
• Transport measurements
• NMR/NQR
• Quantum oscillations
• Kerr effect
• Ultrasound
• Polarized neutron diffraction
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What is changing? The YBa2Cu3Oy family shows charge density wave order which competes with superconductivity
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– Using high energy x-ray diffraction
• Chang et al., Nature Physics (2012)
• Blackburn et al., Phys. Rev. Lett. (2013)
What is changing? The YBa2Cu3Oy family shows charge density wave order which competes with superconductivity
– Using soft x-ray resonant scattering
• Ghiringhelli et al., Science (2012)
• Achkar et al., Phys. Rev. Lett. (2012)
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Direct Observations of CDWs - two techniques:
Our Collaboration: ‘Hard’ X-ray (100 keV) diffraction up to B = 17 T
Resonant Elastic X-ray Scattering: mainly 930 eV Cu L3 edge
Similar results seen over a range of (under) dopings and for different Cu-O chain orderings (ortho-II, -III & -VIII)
Diffraction signal arises from displacements of all
atoms in the unit cell…
Large volume of Q-space accessible – extra info.
Diffraction signal arises from spatial variation of Cu L-resonance energy
Small volume of Q-space accessible – but site-specific
Chang et al., Nat. Phys. 8, 871 (2012). - o-VIII Blackburn et al., PRL 110, 137004 (2013). - o-II and o-III
Ghiringhelli et al., Science 337, 821 (2012). Achkar et al., PRL 109, 167001 (2012). - o-III + origin of contrast discussion Blanco-Canosa et al., PRL 110, 187001 (2013). - o-II
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CDWs (and other lattice instabilities) are also seen in other cuprates!
A general feature of the underdoped cuprates - can we link it to the other observations?
• YBCO • Bi2201 – Comin et al., Science 343, 390 (2014). • Hg1201 – Tabis et al., arXiv 1404.7658 (2014). • Eu-LSCO – Ghiringhelli et al., Science 337, 821 (2012) • LSCO – Christensen et al., arXiv 1404.3192 (2014) • ….
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Let’s start with one compound, YBCO o-VIII
Similar but unequal q-vectors along the a & b directions
q1 = (0.305, 0, 0.5) q2 = (0, 0.314, 0.5)
J. C
han
g et
al.
, Nat
ure
Ph
ysic
s (2
01
2)
In YBCO6.67
Tc
Adjacent cells along c in antiphase
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Achkar et al.,Phys. Rev. Lett. (2012).
Energy dependence in ortho-III YBCO
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Comin et al., arXiv 1402.5415 (2014)
A bond density wave?
O-2p charge modulations
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ξa = 95±5 Å ξc ≈ 0.6 c
Lattice parameters: a = 3.81 Å, b = 3.87 Å, c = 11.72 Å
Correlation lengths:
(Gaussian sigmas)
Ortho-VIII example
J. C
han
g et
al.
, Nat
ure
Ph
ysic
s (2
01
2)
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Origin of this scattering atomic displacements vs charge modulation
measured u/a ~ 7 x 10-4 estimated: u/a ~ 8 x 10-4
net charge / unit cell (CDW amplitude) is ~ 10-3 e, => not a Cu valence modulation
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spin
charge
Spin and charge wavevectors
Blackburn et al, PRL (2013).
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Open points: spin order or strong spin fluctuations at (½ + δspin, ½) Closed points: CDW peaks at (δcharge,0)
Spin and charge wavevectors – updated a little…
T. P. Croft et al, Phys Rev B 89, 224513 (2014).
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Open points: spin order or strong spin fluctuations at (½ + δspin, ½) Closed points: CDW peaks at (δcharge,0)
Spin and charge wavevectors – updated a little…
T. P. Croft et al, Phys Rev B 89, 224513 (2014).
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Modelling the CDW
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Modelling the CDW
Blackburn et al., Phys. Rev. Lett. (2013)
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increasing p
d
d
Modelling the CDW
Blackburn et al., Phys. Rev. Lett. (2013)
→Fermi surface effects
DW wavevector
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Links to the Fermi surface
Tabis et al., arXiv: 1404.7658
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2D suggestions for Fermi surface reconstruction
“Antiferromagnetic” Charge Density Wave
gives an electron pocket (N.B. this is a 2d picture of 3d reconstruction by CDW)
gives a hole pocket –
disagrees with Hall data
looks a bit like the ARPES/STM signals
Sach
dev
et
al.,
J. P
hys
.: C
on
den
s. M
atte
r (2
01
2)
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The Fermi surface – quantum oscillation data
S. E. Sebastian et al, Nature (advance online) (2014).
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Modelling the CDW
Is it single-q or double-q?
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Ultrasound Studies
LeBoeuf et al., Nature Physics (2012).
ortho-II
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LeBoeuf et al., Nature Physics (2012).
c66
c44 c11
c55
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Modelling the CDW
Is it single-q or double-q?
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Differences between qa and qb
Blackburn et al, PRL (2013).
It is therefore likely that the lattice response is driven by the CuO2 planes, which determine the q.
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Blanco-Canosa et al. arXiv 1406.1595 (2014).
Differences between qa and qb
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Crossover temperature as f(B)
TVL and TVS from LeBoeuf et al., PRB 83, 054506 (2011).
TKerr
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Examining the doping dependence
Huecker et al, arXiv:1405.7001 (2014).
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Examining the doping dependence
Huecker et al, arXiv:1405.7001 (2014).
T† = broad maximum in 1/(T1T) from planar 63Cu NQR/NMR
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Studying the critical field in YBCO
• Two superconducting domes?
Grissonnanche et al., Nature Comms (2014)
CDW
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Signs of something changing inside the PG region
• Transport measurements
• NMR/NQR
• Quantum oscillations
• Kerr effect
• Ultrasound
• Polarized neutron diffraction
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Time/Energy Scales of CDW
LeBoeuf et al., Nat. Phys. (2012).
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Energy at which the charge response is probed.
Can we improve these measurements with using inelastic x-ray scattering?
Blackburn et al., PRB 88, 054506 (2013).
Lifetime
Energy resolution of the instrument.
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What about phonons?
Raichle et al., Phys. Rev. Lett. 107, 177004 (2011).
Cu-O bond bending phonon @ ~ 40 meV (YBCO7)
Softens at k = 0.3, but not at h = 0.3
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Associated Phonon Anomalies – ortho-VIII
Le Tacon et al., Nature Physics 10, 52 (2013).
Almost purely transverse acoustic mode
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Associated Phonon Anomalies – ortho-VIII
Le Tacon et al., Nature Physics 10, 52 (2013).
Mode Energy
Phonon Linewidth
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Associated Phonon Anomalies – ortho-II
Blackburn et al., Phys. Rev. B 88, 054506 (2013).
Measured at a mixed mode, thought to be primarily transverse acoustic
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BUT – does this match the NMR data?
T. Wu et al., arXiv:1404.1617 (2014).
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BUT – does this match the NMR data?
T. Wu et al., arXiv:1404.1617 (2014).
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Summary
Fradkin & Kivelson Nature Physics (2012)
• The CuO2 planes are prone to an instability before becoming superconducting.
• The CDW appears to be able to motivate the FS reconstruction.
• What does it have to do with the pseudogap?