1. What Pins Stripes in La2-xBaxCuO4? Neutron Scattering Group
Markus Hücker
Neutron Scattering Group
Electronic Liquid-Crystal Nature of Stripes
Doping Phase Diagram of LBCO at Ambient Pressure
Pressure Phase Diagram of LBCO at x=1/8
John and I have been working on a proposal on the “Manipulation of Competing Order with Extreme Conditions”.
Understanding the often observed proximity between a superconducting phase, and other electronic or magnetic phases.
Still not clear if friend or foe.
As one can see here, the SC phase is often observed in proximity
To learn how particular forms of “competing order” may be related to the mechanisms of superconductivity
And one way to uncover these mechanism is to expose sample to extrem environment,
such as Temperature, H. E fields.
We are aiming at is a better understanding of the mechanisms involved in the in HTSC and other relevant cuprates and nickelates.
we basically have a twofold strategy how to exploit the effect of pressure on competing orders:
competing phases as locators for SC or other exotic ground states, that can be tuned in by external control parameters.
Competing order is not just a phenomenon, it also is a strategy to find new phases.
CMPMS (Brookhaven)
DESY
J. M. Tranquada
G. D. Gu
C. C. Homes
Z. J. Xu
J. S. Wen
M. v. Zimmermann
Washington University
M. Debessai
J. S. Schilling

2. Competing Order in Strongly Correlated Electron Systems
heavy fermion superconductor
CePd2Si2
Mathur et al. Nature 1998
John and I have been working on a proposal on the “Manipulation of Competing Order with Extreme Conditions”.
Understanding the often observed proximity between a superconducting phase, and other electronic or magnetic phases.
Still not clear if friend or foe.
As one can see here, the SC phase is often observed in proximity
To learn how particular forms of “competing order” may be related to the mechanisms of superconductivity
And one way to uncover these mechanism is to expose sample to extrem environment,
such as Temperature, H. E fields.
We are aiming at is a better understanding of the mechanisms involved in the in HTSC and other relevant cuprates and nickelates.
we basically have a twofold strategy how to exploit the effect of pressure on competing orders:
competing phases as locators for SC or other exotic ground states, that can be tuned in by external control parameters.
Competing order is not just a phenomenon, it also is a strategy to find new phases.

3. Competing Order in Strongly Correlated Electron Systems
La2-xBaxCuO4
1/8-problem
La2-xSrxCuO4
HTT
LTO 3D AF
LTT
stripes Tc
Schematic,
Mention additional phase (Pccn)
Regions of coexistance not well studied, except for high-x side in case of Nd,Eu compound. SC SG

4. Common Conception: LTT Phase Pins Stripes
La,Ba Cu O
HTT
[010]
[100]
[001]
LTO
LTT
LTO phase
Cu-O-Cu
LTT phase
q=0.
Stripe Order

5. Stripe Order in LBCO
magnetism
charge
Tranquada et al. Nature (1995)
Fujita et al. PRB (2004)
Stripes: detected with neutrons, x-rays in LBCO, LNSCO

6. Electronic Liquid-Crystal
Kivelson et al. Nature (1998)
Quantum analogues of classical liquid crystals.
Although there are other proposals like:
orbital currents
spiral oder
fermi surface nesting
checkerboard order
Here we focus on one proposal, that stripes form a state that breaks
Hinkov et al., Science (2008)
Ando et al., PRL (2002)
Evidence in YBa2Cu3O6.45
Symmetry broken by orthorhombic structure
Stripe phase of La2-xBaxCuO4:
At ambient pressure symmetry broken by LTT structure

7. Stripe Order in LBCO at Ambient Pressure
p = 0 GPa SO
The stripe phase in LBCO is where charge and spin stripe order competes with supercondcutivity.
In this paricular case the stripe order occurs in a particular structure, the LTT phase.
In the LTO or HTT phase Tc would describe the supercondcuting dome known for LSCO.
Pressure can be used to suppress the LTT phase, and x-ray can evolution of the stripe order.
As pressure is increased und SC comes up, we then can apply high magnetic fields to suppress
the supercondcutivity, and see what effect it has on the stripe order. This gives us unprecedented
access to the interplay between stripe order and SC and the question whether stripes are competing or
mediating SC.

8. Pressure Dependence of Tc
2 GPa
x=1/8
Tc~18K Tc
0 GPa
0.125 SC
The stripe phase in LBCO is where charge and spin stripe order competes with supercondcutivity.
In this paricular case the stripe order occurs in a particular structure, the LTT phase.
In the LTO or HTT phase Tc would describe the supercondcuting dome known for LSCO.
Pressure can be used to suppress the LTT phase, and x-ray can evolution of the stripe order.
As pressure is increased und SC comes up, we then can apply high magnetic fields to suppress
the supercondcutivity, and see what effect it has on the stripe order. This gives us unprecedented
access to the interplay between stripe order and SC and the question whether stripes are competing or
mediating SC.
0.12
0.125
0.13
Ido et al. Physica C (1991)

9. High Energy Single-Crystal X-ray Diffraction under Pressure
sample
LBCO
CGO
1 mm
100 keV
photons
DESY, Hamburg
Review of Scientific Instruments 79, (2008)

10. Tuning the Structure with Pressure
p = 0 GPa SO

11. Stripes in Tetragonal High Pressure Regime
(2, 0, 0)/(0, 2, 0) T~TLT
T~TLT
LTO
[110]  b c
T~10K a
LTT
HTT
TCO=TLT, but the low-T orderparamter are different.
(2+2, 0, 5.5)
LTT
[100]
[010] pc
(1, 0, 0)

12. Charge Stripes on Square Lattice
High pressure: 4-fold symmetric planes
Charge stripes still develop
Stripes spontaneously break Symmetry
What pins stripes
PDF, XAFS
PDF: Tilted Octahedra even in the HTT Phase
XAFS: Local Tilts around Dopants
Billinge et al., PRL (1994)
Haskel et al., PRB (2000)

13. Diffuse scattering in High Pressure Regime
(3/2 3/2 2)
20Å
40Å
80Å

14. LBCO

15. Nematic Patches in High Pressure Regime
Commensurate patches of stripes and octahedral tilts
Quenched disorder always a relevant pertubation
Dopant disorder leads to finite size domains
nematic patches
E. Carlson et al., PRL (2006)

16. Stripes spontaneously break symmetry in HTT phase
Summary
Stripes spontaneously break symmetry in HTT phase
Pinned by quenched dopant disorder
Supports electronic liquid-crystal picture of HTSC
Outlook SC Tc SO
c-axis correlations
What happens for x1/8 Ba
What happens at higher pressures

17. supplemental slides

18. High Energy Single-Crystal X-ray Diffraction under Pressure

19. Different Models for the Stripe Phase
Electronic micro phase separation
J. Zaanen et al. PRB 40, 7391 (1989)
V. Emery et al., PRL 64, 475 (1990)
S.R. White et al., PRL 80, 1272 (1998)
Fermi surface nesting; SDW/CDW
Mason et al. PRL 77, 1604 (1996)
Shraiman, and Siggia, PRL
Longitudinal modulation of the size of the moment will result in appearance of CDW as well (Assa Auerbach).
Spiral spin order
B. Shraiman, E.D. Siggia, PRL 62, 1564 (1989)
Hasselmann et al. PRB 69, (2004)
Shushkov et al. PRB 70, (2004)

20. Question of Dimensionality (1D Stripes, 2D Pattern)
“Checkerboard” electronic state in Ca2-xNaxCuO2Cl2
T. Hanaguri et al., Nature 430, 1001 (2004)
Hanaguri, Davis: Conductance Map at 24mV. (strong 4a and 4a/3 modulation).
B. Keimer study: x= 0.6 and 0.85
Simulation of y=0.85 data at 35meV. Anisotropic damped harmonic oscillator
Magnetic excitations in detwinned YBa2Cu3O6+x
V. Hinkov et al., Nature 450, 650 (2004)

21. Competing order in La2-xBaxCuO4
Ba introduces one hole; Th compensates one hole;
One has to dope as much more Ba than there is Th to obtain the same hole content.
This shows that the hole content is crucial, not the Ba content.
Ba – doping
Maeno et al. PRB, 7753 (1991)
hole concentration of 1/8 crucial

22. Competing order in La1.875Ba0.125CuO4
100% Sr SC
Tc=31K CO
Kimura et al., PRB 70, (2004)
Ba-doping is crucial

23. Doping dependence average structure local distortions electronic
LTO
[110] 
average
structure
LTT
[100]
[010]
local
distortions
electronic
correlations

24. Average Structure and Cation Size Variance
La1.85-yNdySr0.15CuO4
L1.85-yMyCuO4
Büchner et al. (1992)
Wagener et al. PRB (1997)
McAllisten et al. PRB (2002)

25. Detection of Charge and Spin Stripe Transition
La1.875Ba0.125CuO4
charge peak
TSO
LTT
LTO
H||c
spin
TSO
spin
H||ab
TCO
WFM

26. Stripe Order in LBCO at High Pressure?SO I ?
charge ?
spin T SC
pressure 

27. Traveling-Solvent Floating-Zone Technique
feed
rod
0.5mm/h
liquid
zone
crystal
q=0.
La2-xBaxCuO4 with x=1/8
(G.D. Gu)

28. Charge correlations along the c-axis
1D charge stripes
2D charge grid c
Vojta: Standard vector Landau theory c c k h
M. Vojta et al., cond-mat/
similar result:
La1.48Nd0.4Sr0.12CuO4 , x-rays, T. Niemoeller et al., EPL (1998)
La1.875Ba0.075Sr0.05CuO4 , neutrons, H. Kimura et al., PRB (2003)

29. Search for non-1D-Correlations
magnetism
charge
(0 2 ½) + + + +
(½ ½ 0)
Results for LBCO consistent with 1D-stripe model

30. a b c d k h LTO Cu HTT O La,Ba LTT LTT-phase LTO-phase [100] [010]
[110] Cu O
[001] h k
L=0 2 1
L=5.5
HTT
LTO
LTT
LTT-phase
LTO-phase
L=2 a b c d
L=6

31. (1, 0, 0) T~10K
(2+2, 0, 5.5) T~10K
(1.5, 1.5, 2) T~10K a b c

32. Temperature dependence

33. Detection of Charge and Spin Stripe Transition
La1.875Ba0.125CuO4
charge peak
TSO
LTT
LTO
H||c
spin
TSO
spin
H||ab
TCO
WFM

34. affects crystal structure and electronic band structure
Pressure and Superconductivity
Hg-1223 bulk
LSCO bulk
LSCO thin film
buckled
flat
Bozovic et al. PRL (2002)
Gao et al. PRB (1994)
Flat planes are important for SC.
However, detailed forensic work has to be done to understand the underlying mechanisms which phase kills which and are actually good.
Tc propto 1/a*b
Intraplanar pairing interaction seem to be more important.
Pressure is a basic thermodynamic parameter, like temperature.
In most SC Tc decreases with increasing pressure.
In high Tc it is often the other way round.
Yamada et al. JSSC (1989)
Pressure:
affects crystal structure and electronic band structure

36. ARPES

37. Stripes vs. CDW
T. Valla et al., Science (2007)

38. ARPES T. Valla et al., Science (2007)
However, if we apply the same nesting scenario to LBCO at
x=1/8, we obtain qCDW≈4kF (=π/2a), for charge order, instead
of 2kF nesting, suggested to be at play in CNCOC. Moreover,
the nesting of anti-nodal segments would produce a wavevector
that shortens with doping, opposite of that observed in
neutron scattering studies in terms of magnetic
incommensurability. This is illustrated in Fig. 4 where we
compile the doping dependences of several relevant
quantities.
There is another, more fundamental problem with the
‘nesting’ scenario: any order originating from nesting
(particle-hole channel) would open a gap only on nested
segments of the Fermi surface, preserving the non-nested
regions. The fact that only four gapless points (nodes) remain
in the ground state essentially rules out nesting as an origin of
pseudogap. In addition, a gap caused by conventional
spin/charge order would be pinned to the Fermi level only in
special cases. The observation that it is always pinned to the
Fermi level (independent of k-point, as measured in ARPES
and of doping level, as seen in STM on different materials)
and that it has d-wave symmetry undoubtedly points to its
pairing origin – interaction in the particle-particle singlet
channel (28).
T. Valla et al., Science (2007)