Transcript Slide 1

What Pins Stripes in La2-xBaxCuO4?
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
CMPMS (Brookhaven)
J. M. Tranquada
G. D. Gu
C. C. Homes
Z. J. Xu
J. S. Wen
DESY
M. v. Zimmermann
Washington University
M. Debessai
J. S. Schilling
Competing Order in Strongly Correlated Electron Systems
heavy fermion superconductor
Mathur et al. Nature 1998
CePd2Si2
Competing Order in Strongly Correlated Electron Systems
La2-xBaxCuO4
La2-xSrxCuO4
1/8-problem
100
T (K)
HTT
LTO
80
60
40
3D
AF
LTT
Tc
stripes
20
SC
SG
0
0.05
0.10
0.15
hole density (x)
0.20
Common Conception: LTT Phase Pins Stripes
Cu
LTO
O
LTO phase
HTT
La,Ba
LTT
Cu-O-Cu
[001]
[010]
LTT phase
[100]
Stripe Order
Stripe Order in LBCO
500
400
300
200
100
charge
Int (counts/min)
Int (counts/10sec)
magnetism
0.4
0.5
k (r.l.u.)
0.6
600
400
200
0
1.8
2.0
k (r.l.u.)
2.2
Tranquada et al. Nature (1995)
Fujita et al. PRB (2004)
Stripes: detected with neutrons, x-rays in LBCO, LNSCO
Electronic Liquid-Crystal
Kivelson et al. Nature (1998)
Evidence in YBa2Cu3O6.45
Hinkov et al., Science (2008)
Ando et al., PRL (2002)
Symmetry broken by orthorhombic structure
Stripe phase of La2-xBaxCuO4:
At ambient pressure symmetry broken by LTT structure
Stripe Order in LBCO at Ambient Pressure
p = 0 GPa
Temperature (K)Temperature (K)
350
300
La2-xBaxCuO4
250
HTT
LTO
200
150
70
LTO
60
TLT
50
CO
40
30
SO
20
10
0
Tc
LTT
SC
0.100
SC
0.125
hole doping (x)
0.150
Pressure Dependence of Tc
2 GPa
x=1/8
20
0.125
0.12
0.125
0.13
15
TC (K)
0 GPa
Tc~18K
Tc
10
SC
5
0
0
2
4
6
8
10
pressure (GPa)
Ido et al. Physica C (1991)
12
14
High Energy Single-Crystal X-ray Diffraction under Pressure
sample
1 mm
LBCO
100 keV
photons
CGO
BW5 @ DESY, Hamburg
Review of Scientific Instruments 79, 33906 (2008)
Tuning the Structure with Pressure
p = 0 GPa
LBCO (x=1/8)
350
La2-xBaxCuO4
250
250
HTT
200
LTO
200
Temperature (K)
T (K)
300
150
70
LTO
Temperature (K)
60
TLT
50
CO
40
30
10
0
100
LTO
50
LTT
SC
150
Tc
SO
20
HTT
LTT + CO
SC
0.100
0.125
0.150
hole doping (x)
0
0.0
0.5
1.0
CO + DS
Tc
1.5
2.0
pressure (GPa)
2.5
3.0
Stripes in Tetragonal High Pressure Regime
b
p=2.7GPa
6 1.72GPa
5 1.45GPa
4 1.15GPa
0.77
2
0.6
0
0.5
2.5
0.4
2.0
0.3
1.5
0.2
HTT
LTO
1.0
0.1
0.5
LTO
[110]
0
-0.01
0.00
q (r.l.u.)
0.01
0.0
0
1
2
3
0.0
Pressure (GPa)
[100]
[010]
T~10K
a
4
LTT
0.40
HTT
(2+2, 0, 5.5)
3
0.30
pc
2
0.20
0.10
0.00
1
(1, 0, 0)
0.0
0.5
1.0
1.5
2.0
Pressure (GPa)
2.5
0
3.0
Integrated Intensity I(100) (counts/sec)
LTT
Integrated Intensity ICO (counts/sec)
1

3.0
c
7 1.77GPa
3
T~TLT
0.6
Tilt angle  (degree)
Intensity (arb. units)
8
(2, 0, 0)/(0, 2, 0) T~TLT
2(b-a)/(a+b) at TLT (%)
9
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
Billinge et al., PRL (1994)
 XAFS: Local Tilts around Dopants
Haskel et al., PRB (2000)
0
10
20
30
40
50
60
70
0
10
20
30
40
50
60
70
Temperature (K)
High Pressure Regime
c Diffuse scattering in d
Temperature (K)
(1.5, 1.5, 2)
100
10
p=0GPa (x0.1)
p=0GPa (x 0.01)
(3/2 3/2 2)
FWHM (r.l.u.)
3
6
50
1.77GPa
1.77GPa (x 0.1)
4
25
2
2.7GPa
2.7GPa
0.03
40Å
0.02
TLT
TLT
0-0.01 20
Temperature (K)
20Å
0.04
75
8
0
0
(1.5, 1.5, 2)
0.05
5
Intensity
counts/sec)
(10(10
Peak
counts/sec)
Intensity
12
2.7GPa
THT=235K
1.77GPa
0.01
TDS
THT
0.00 60
40
800.01 100
q (r.l.u.) (K)
Temperature
80Å
0.00
0
p=0GPa
20
40
60
80
100
Temperature (K)
100
HTT
LTO
50
LTT + CO
0
0.0
0.5
CO + DS
Tc
1.0
1.5
pressure (GPa)
2.0
2.5
3.0
LBCO
15
15
25
30
100
0.20
4
20
0.15
10
10
20
15
50
10
0.10
2
10
55
0.05
5
0
0
0
-0.02 0.00 0.02
q (r.l.u)
Temperature (K)
0.25
6
30
(1.5,1.5,2)
(2+2,0,5.5)
p=2.7GPa
5
Intensity ICO (counts/sec)
40
p=1.77GPa
00
0
-0.02 0.00 0.02
q (r.l.u)
0.00
-0.02 0.00
0.00 0.02
0.02
-0.02
(r.l.u)
qq (r.l.u)
100
HTT
LTO
50
LTT + CO
0
0.0
0.5
CO + DS
Tc
1.0
1.5
pressure (GPa)
2.0
Intensity I(1.5 1.5 2) (10 counts/sec)
p=0GPa
2.5
3.0
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)
Summary
 Stripes spontaneously break symmetry in HTT phase
 Pinned by quenched dopant disorder
 Supports electronic liquid-crystal picture of HTSC
Outlook
70
LTO
Tc
TLT
50
15
CO
40
Tc
10
30
C
Temperature
T (K)(K)
 c-axis correlations
20
60
 What happens for x1/8 Ba
20
SC
00
0
 What happens at higher pressures
LTT
5
10
2 0.1004
6
0.125
8
SC
SO
10
hole doping (x)
SC
0.150
pressure (GPa)
12
14
supplemental slides
High Energy Single-Crystal X-ray Diffraction under Pressure
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)
Spiral spin order
B. Shraiman, E.D. Siggia, PRL 62, 1564 (1989)
Hasselmann et al. PRB 69, 14424 (2004)
Shushkov et al. PRB 70, 245023 (2004)
Question of Dimensionality (1D Stripes, 2D Pattern)
“Checkerboard” electronic state in Ca2-xNaxCuO2Cl2
T. Hanaguri et al., Nature 430, 1001 (2004)
Magnetic excitations in detwinned YBa2Cu3O6+x
V. Hinkov et al., Nature 450, 650 (2004)
Competing order in La2-xBaxCuO4
Ba – doping
Maeno et al. PRB, 7753 (1991)
hole concentration of 1/8 crucial
Competing order in La1.875Ba0.125CuO4
100% Ba
100% Sr
Tc=31K
SC
CO
Kimura et al., PRB 70, 134512 (2004)
Ba-doping is crucial
Doping dependence
300
4.0
250
3.5
200
3.0
150
2.5
0.06
0.08
0.10
0.12
0.14
0.16
TLT (K)
1000
50
40
(1, 0, 0)
500
30
20
0.06
0.08
0.10
0.12
0.14
0.16
0
0.18
60
electronic
correlations
TCO (K)
300
40
200
(2+2, 0, 5.5)
20
0
0.06
0.08
0.10
0.12
0.14
Ba-content (x)
0.16
100
0
0.18
Intensity (counts/sec)
400
Intensity (counts/sec)
60
local
distortions
LTO
[110]
0.18
1500
70
Tilt  (degree)
average
structure
THT (K)

LTT
[100]
[010]
Average Structure and Cation Size Variance
La1.85-yNdySr0.15CuO4
L1.85-yMyCuO4
o2
 (A )
0.0045
0.0050
0.0055
0.0060
o
<rave> (A)
1.216
1.212
Temperature (K)
400
1.208
1.204
1.200
1.196
1.192
HTT
300
200
LTO
100
LTT
0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Nd - content (y)
Büchner et al. (1992)
Wagener et al. PRB (1997)
McAllisten et al. PRB (2002)
Integrated Intensity
Detection of Charge and Spin Stripe Transition
(1, 0, 0)
1.0
La1.875Ba0.125CuO4
(2.24, 0, 5.5)
charge peak
0.5
LTO
TLTT
SO
0.0
1.40
1.30
H||c
TSO
1.25
1.30
H||ab
TCO
WFM
1.20
0
10
20
30
40
T (K)
50
60
1.25
70
cspin
spin
ab
1.35
Stripe Order in LBCO at High Pressure?
I
70
?
LTO
Temperature (K)
60
charge
TLT
50
CO
40
30
SO
20
10
0
?
Tc
spin
LTT
SC
0.100
SC
0.125
T
0.150
hole doping (x)
SC

pressure
Traveling-Solvent Floating-Zone Technique
feed
rod
0.5mm/h
liquid
zone
crystal
La2-xBaxCuO4 with x=1/8
(G.D. Gu)
Int (counts/min)
Charge correlations along the c-axis
1D charge stripes
(0, 2+2, L)
200
150
100
50
0
-1.0
-0.5
0.0
0.5
1.0
L (r.l.u.)
2D charge grid
c
c
c
k
h
M. Vojta et al., cond-mat/0408461
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)
Search for non-1D-Correlations
charge
400
200
100
0.4
0.6
0.5
h (r.l.u.)
500
400
300
1.7 1.8 1.9 2.0 2.1 2.2 2.3
k (r.l.u.)
200
(½ ½ 0)
Int (counts/10sec)
+
400
200
0
0.60
2.1
0.65
h (r.l.u.)
++
600
200
0
100
0.55
+
+
+
400
(0 2 ½)
+
+
500
400
300
200
100
0.4
2.2
0.5
k (r.l.u.)
0.6
2.3
k (r.l.u.)
+
600
Int (counts/min)
300
600
Int (counts/min)
Int (counts/min)
500
Int (counts/10sec)
Int (counts/10sec)
magnetism
500
400
300
200
100
0
-100
0.20
0.25
h (r.l.u.)
Results for LBCO consistent with 1D-stripe model
0.30
[001]
a
LTO
b
Cu
O
HTT
[110]
La,Ba
LTT
[010]
[100]
[010]
[100]
c
[110]
d
LTT-phase
k
LTO-phase
k
L=0
L=0
2
2
L=2
L=2
1
1
L=5.5
L=0
1
L=6
2
h
1
2
h
(1, 0, 0) T~10K
35
a
100
p=0GPa
1.64GPa
1.72GPa
1.77GPa
20
15
3
200
2.7GPa
10
5
1.77GPa
0
0
-5
75
50
1.77GPa (x 0.1)
25
2.7GPa
0
2.7GPa
-0.002 -0.001 0.000 0.001 0.002
k (r.l.u.)
c
p=0GPa (x 0.01)
25
Intensity (counts/sec)
Intensity (counts/sec)
300
100
b
30
p=0GPa (x 0.1)
(1.5, 1.5, 2) T~10K
(2+2, 0, 5.5) T~10K
Intensity (10 counts/sec)
400
-0.02
-0.01
0.00 0.01
k (r.l.u.)
0.02
-0.01
0.00
q (r.l.u.)
0.01
Temperature dependence
b
(1, 0, 0)
p=0GPa
1.15GPa
p=0GPa (x0.1)
0.20
0.15
(2+2, 0, 5.5)
2.0
0.25
Intensity ICO (counts/sec)
1.15GPa (x0.2)
0.10
1.77GPa
0.05
1.5
1.0
1.77GPa
0.5
0.2
p=1.45GPa
2.7GPa
0.00
0.0
0
10
20
30
40
50
60
70
0
10
c
d
(1.5, 1.5, 2)
12
20
30
40
50
60
Temperature (K)
Temperature (K)
(1.5, 1.5, 2)
p=0GPa (x0.1)
70
1.62GPa
0.1
1.72GPa
10
0.03
FWHM (r.l.u.)
8
5
Peak Intensity (10 counts/sec)
e
2.7GPa
2(b-a)/(a+b) (%)
Integrated Intensity (counts/sec)
a
6
1.77GPa
4
TLT
2
THT
2.7GPa
0
0
20
TLT
40
60
2.7GPa
0.0
2.7GPa
0
1.77GPa
0.01
80
Temperature (K)
100
TDS
0.00
0
20
40
60
80
Temperature (K)
0.02
THT=235K
1.77GPa
20
p=0GPa
40
60
80
Temperature (K)
100
100
Integrated Intensity
Detection of Charge and Spin Stripe Transition
(1, 0, 0)
1.0
La1.875Ba0.125CuO4
(2.24, 0, 5.5)
charge peak
0.5
LTO
TLTT
SO
0.0
1.40
1.30
H||c
TSO
1.25
1.30
H||ab
TCO
WFM
1.20
0
10
20
30
40
T (K)
50
60
1.25
70
cspin
spin
ab
1.35
Pressure and Superconductivity
Hg-1223 bulk
LSCO bulk
LSCO thin film
buckled
flat
Bozovic et al. PRL (2002)
Gao et al. PRB (1994)
Yamada et al. JSSC (1989)
Pressure:
affects crystal structure and electronic band structure
35
x=0.14
30
25
TC (K)
0.12
20
15
0.125
10
5
0
0
2
4
6
8
10
pressure (GPa)
12
14
ARPES
Stripes vs. CDW
T. Valla et al., Science (2007)
ARPES
T. Valla et al., Science (2007)