Markus Hücker
What Pins Stripes in La2-xBaxCuO4?
Neutron Scattering Group
Electronic Liquid-Crystal Nature of Stripes Electronic Liquid-Crystal Nature of Stripes
Doping Phase Diagram of LBCO at Ambient PressureDoping Phase Diagram of LBCO at Ambient Pressure
Pressure Phase Diagram of LBCO at x=1/8Pressure Phase Diagram of LBCO at x=1/8
CMPMS (Brookhaven)
J. M. TranquadaG. D. GuC. C. Homes Z. J. XuJ. S. Wen
DESYM. v. Zimmermann
Washington University
M. DebessaiJ. S. Schilling
Competing Order in Strongly Correlated Electron Systems
CePd2Si2
Mathur et al. Nature 1998
heavy fermion superconductor
La2-xSrxCuO4
3DAF LTT
LTO
0.05 0.10 0.15 0.200
20
40
60
80
100
hole density (x)
T (
K)
SC
Tc
1/8-problem
Competing Order in Strongly Correlated Electron Systems
La2-xBaxCuO4
SG
stripes
HTT
Common Conception: LTT Phase Pins Stripes
La,Ba
Cu
OHTT
[010]
[100]
[001]
LTO
LTT
LTO phase
LTT phase
Cu-O-Cu
Stripe Order
Stripes: detected with neutrons, x-rays in LBCO, LNSCO
Stripe Order in LBCO
1.8 2.0 2.2
0
200
400
600
k (r.l.u.)
Int
(co
un
ts/m
in)
0.4 0.5 0.6100
200
300
400
500
k (r.l.u.)
Int
(co
un
ts/1
0se
c)
Tranquada et al. Nature (1995)
magnetism charge
Fujita et al. PRB (2004)
Electronic Liquid-Crystal
Kivelson et al. Nature (1998)
At ambient pressure symmetry broken by LTT structureAt ambient pressure symmetry broken by LTT structure
Hinkov et al., Science (2008)Ando et al., PRL (2002)Evidence in YBa2Cu3O6.45
Stripe phase of La2-xBaxCuO4:
Symmetry broken by orthorhombic structureSymmetry broken by orthorhombic structure
Stripe Order in LBCO at Ambient Pressure
p = 0 GPa
SO
0.100 0.125 0.1500
10
20
30
40
50
60
70
CO
SC
LTO
Tc
TLT
SCLTT
Tem
pera
ture
(K
)
hole doping (x)
Pressure Dependence of Tc
Ido et al. Physica C (1991)
0 GPa
2 GPa
0.120.1250.13
0.125SC
Tc
x=1/8
Tc~18K
sample
High Energy Single-Crystal X-ray Diffraction under Pressure
100 keVphotons
BW5 @ DESY, Hamburg
Review of Scientific Instruments 79, 33906 (2008)
LBCO
CGO
1 mm
p = 0 GPa
SO
0.0 0.5 1.0 1.5 2.0 2.5 3.00
50
100
150
200
250
LBCO (x=1/8)
pressure (GPa)
Tc
CO + DS
LTO
LTT + CO
HTT
Tem
pera
ture
(K
)
Tuning the Structure with Pressure
0.100 0.125 0.1500
10
20
30
40
50
60
70
CO
SC
LTO
Tc
TLT
SC
LTT
Tem
pera
ture
(K
)
hole doping (x)
Stripes in Tetragonal High Pressure Regime
c
(2, 0, 0)/(0, 2, 0) T~TLT
b
-0.01 0.00 0.010
1
2
3
4
5
6
7
8
9
1.72GPa
1.77GPa
0
0.6
0.77
1.15GPa
1.45GPa
p=2.7GPa
Inte
nsity
(ar
b. u
nits
)
q (r.l.u.)
T~TLT
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Tilt a
ng
le
(de
gre
e)
HTT
0 1 2 30.0
0.1
0.2
0.3
0.4
0.5
0.6
LTO
Pressure (GPa)
2(b-
a)/(
a+b)
at
TL
T (
%)
pc
T~10Ka
(1, 0, 0)
(2+2, 0, 5.5)
LTT HTT
LTO
[110]
0.0 0.5 1.0 1.5 2.0 2.5 3.00.00
0.10
0.20
0.30
0.40
Pressure (GPa)
Inte
grat
ed In
tens
ity I C
O (
coun
ts/s
ec)
0
1
2
3
4
Integrated Intensity I(100) (counts/sec)
LTT
[100][010]
High pressure: 4-fold symmetric planesHigh pressure: 4-fold symmetric planes
Charge stripes still develop Charge stripes still develop
Stripes spontaneously break SymmetryStripes spontaneously break Symmetry
What pins stripesWhat pins stripes
Charge Stripes on Square Lattice
PDF: Tilted Octahedra even in the HTT PhasePDF: Tilted Octahedra even in the HTT Phase
XAFS: Local Tilts around DopantsXAFS: Local Tilts around Dopants
PDF, XAFS
Haskel et al., PRB (2000)
Billinge et al., PRL (1994)
-0.01 0.00 0.01
0
25
50
75
100
2.7GPa
1.77GPa (x 0.1)
p=0GPa (x 0.01)
Inte
nsi
ty (
10
3 co
un
ts/s
ec)
q (r.l.u.)
(3/2 3/2 2)
0.0 0.5 1.0 1.5 2.0 2.5 3.00
50
100
pressure (GPa)
Tc
CO + DS
LTO
LTT + CO
HTT
Tem
pera
ture
(K
)
Diffuse scattering in High Pressure Regime
80Å
40Å
20Å
LBCO
-0.02 0.00 0.02
0
5
10
15
20
25
30
q (r.l.u) q (r.l.u)
p=1.77GPa
-0.02 0.00 0.02
0
5
10
15
p=2.7GPa
q (r.l.u)-0.02 0.00 0.02
0
10
20
30
40
(2+2,0,5.5)
p=0GPa
In
ten
sity
IC
O (
cou
nts
/sec
)
-0.02 0.00 0.02
0
5
10
15
20
25
30
q (r.l.u) q (r.l.u)
p=1.77GPa
-0.02 0.00 0.02
0
5
10
15
p=2.7GPa
q (r.l.u)-0.02 0.00 0.02
0
10
20
30
40
(2+2,0,5.5)
p=0GPa
In
ten
sity
IC
O (
cou
nts
/sec
)
0
50
100
0
2
4
6
0.00
0.05
0.10
0.15
0.20
0.25(1.5,1.5,2)
Inten
sity I(1.5 1.5 2) (105 co
un
ts/sec)
0.0 0.5 1.0 1.5 2.0 2.5 3.00
50
100
pressure (GPa)
Tc
CO + DS
LTO
LTT + CO
HTT
Tem
pera
ture
(K
)
Nematic Patches in High Pressure Regime
Commensurate patches of stripes and octahedral tilts Commensurate patches of stripes and octahedral tilts
Quenched disorder always a relevant pertubationQuenched disorder always a relevant pertubation
Dopant disorder leads to finite size domainsDopant disorder leads to finite size domains
E. Carlson et al., PRL (2006)
nematic patches
Summary
Stripes spontaneously break symmetry in HTT Stripes spontaneously break symmetry in HTT phase phase
Pinned by quenched dopant disorderPinned by quenched dopant disorder
Supports electronic liquid-crystal picture of Supports electronic liquid-crystal picture of HTSCHTSC
Outlook
c-axis correlationsc-axis correlations
What happens for xWhat happens for x1/8 Ba1/8 Ba
What happens at higher pressuresWhat happens at higher pressures
SO0.100 0.125 0.150
0
10
20
30
40
50
60
70
CO
SC
LTO
Tc
TLT
SCLTT
Tem
pera
ture
(K
)hole doping (x)
SC
Tc
supplemental slides
High Energy Single-Crystal X-ray Diffraction under Pressure
Different Models for the Stripe Phase
Fermi surface nesting; SDW/CDW
B. Shraiman, E.D. Siggia, PRL 62, 1564 (1989) Hasselmann et al. PRB 69, 14424 (2004)Shushkov et al. PRB 70, 245023 (2004)
Spiral spin order
Mason et al. PRL 77, 1604 (1996)
Electronic micro phase separationJ. Zaanen et al. PRB 40, 7391 (1989)V. Emery et al., PRL 64, 475 (1990)S.R. White et al., PRL 80, 1272 (1998)
Question of Dimensionality (1D Stripes, 2D Pattern)
V. Hinkov et al., Nature 450, 650 (2004)
Magnetic excitations in detwinned YBa2Cu3O6+x
“Checkerboard” electronic state in Ca2-xNaxCuO2Cl2T. Hanaguri et al., Nature 430, 1001 (2004)
hole concentration of 1/8 crucialhole concentration of 1/8 crucial
Maeno et al. PRB, 7753 (1991)Maeno et al. PRB, 7753 (1991)
Competing order in La2-xBaxCuO4
Ba – doping
Kimura et al., PRB 70, 134512 (2004)
SCCO
Tc=31K
100% Ba 100% Sr
Competing order in La1.875Ba0.125CuO4
Ba-doping is crucial
Doping dependence
LTO
[110]
LTT
[100][010]
average structure
local distortions
electronic correlations
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
100
200
300
400
LTT
LTO
HTT
Tem
pera
ture
(K
)
Nd - content (y)
1.216 1.212 1.208 1.204 1.200 1.196 1.192
<rave
> (A)
0.0045 0.0050 0.0055 0.0060
o
o
(A2)
Average Structure and Cation Size Variance
McAllisten et al. PRB (2002)
La1.85-yNdySr0.15CuO4
Büchner et al. (1992)Wagener et al. PRB (1997)
L1.85-yMyCuO4
0.0
0.5
1.0(1, 0, 0)
(2.24, 0, 5.5)
Inte
grat
ed I
nten
sity
1.20
1.25
1.30
ab
T (K)0 10 20 30 40 50 60 70
1.25
1.30
1.35
1.40
c
Detection of Charge and Spin Stripe Transition
TSO
WFM
TSO
H||ab
H||c
spin
spin
La1.875Ba0.125CuO4
TCO
charge peak
LTOLTT
charge
spin
SCpressure
?
?
T
I
SO
0.100 0.125 0.1500
10
20
30
40
50
60
70
CO
SC
LTO
Tc
TLT
SCLTT
Tem
pera
ture
(K
)
hole doping (x)
Stripe Order in LBCO at High Pressure?
Traveling-Solvent Floating-Zone Technique
feedrod
crystal
liquidzone
0.5mm/h
La2-xBaxCuO4 with x=1/8(G.D. Gu)
Charge correlations along the c-axis
c
-1.0 -0.5 0.0 0.5 1.0
0
50
100
150
200
L (r.l.u.)
Int
(co
un
ts/m
in)
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)
1D charge stripes
2D charge grid
(0, 2+2, L)
c
c
M. Vojta et al., cond-mat/0408461
h
k
(0 2 ½)
Results for LBCO consistent with 1D-stripe model
0.4 0.5 0.6100
200
300
400
500
k (r.l.u.)
Int (
cou
nts
/10
sec)
0.55 0.60 0.65100
200
300
400
500
h (r.l.u.)
Int (
cou
nts
/10
sec)
0.4 0.5 0.6100
200
300
400
500
h (r.l.u.)
Int (
cou
nts
/10
sec)
+++
+++
+++
(½ ½ 0)
1.7 1.8 1.9 2.0 2.1 2.2 2.3
0
200
400
600
k (r.l.u.)
Int (
cou
nts
/min
)0.20 0.25 0.30
-100
0
100
200
300
400
500
600
h (r.l.u.)
Int (
cou
nts
/min
)
2.1 2.2 2.3
0
200
400
600
k (r.l.u.)
Int (
cou
nts
/min
)
magnetism charge
Search for non-1D-Correlations
[100]
La,Ba
[010]
[110]
Cu
O
[001]
h
k
L=0
L=0
21
L=5.5
HTT
LTO
LTT
LTT-phase LTO-phase
k
L=2
a b
c d
L=6
1
2
h
2
1
1 2
L=0
L=2
[110]
[100][010]
a c
(1, 0, 0) T~10K (1.5, 1.5, 2) T~10K(2+2, 0, 5.5) T~10Kb
-0.002 -0.001 0.000 0.001 0.002
0
100
200
300
400
2.7GPa
1.77GPa
1.72GPa
p=0GPa (x 0.1)
1.64GPa
Inte
nsity
(co
unts
/sec
)
k (r.l.u.)-0.02 -0.01 0.00 0.01 0.02
-5
0
5
10
15
20
25
30
35
2.7GPa
1.77GPa
p=0GPa
Inte
nsity
(co
unts
/sec
)
k (r.l.u.)-0.01 0.00 0.01
0
25
50
75
100
2.7GPa
1.77GPa (x 0.1)
p=0GPa (x 0.01)
Inte
nsi
ty (
103 c
ou
nts
/se
c)
q (r.l.u.)
0 20 40 60 80 100
0.0
0.1
0.2
e
2.7GPa1.77GPa
1.72GPa
1.62GPa
p=1.45GPa
2(b-
a)/(
a+b)
(%
)
Temperature (K)
0 10 20 30 40 50 60 70
0.00
0.05
0.10
0.15
0.20
0.25
1.15GPa (x0.2)
2.7GPa
1.77GPa
p=0GPa (x0.1)
Inte
grat
ed In
tens
ity (
coun
ts/s
ec)
Temperature (K)0 10 20 30 40 50 60 70
0.0
0.5
1.0
1.5
2.0
dc
ba
(1.5, 1.5, 2)
(2+2, 0, 5.5)(1, 0, 0)
2.7GPa
1.77GPa
1.15GPap=0GPa
Inte
nsity
I CO (
coun
ts/s
ec)
Temperature (K)
0 20 40 60 80 1000.00
0.01
0.02
0.03
TDS p=0GPa
2.7GPa
1.77GPa
(1.5, 1.5, 2)
FW
HM
(r.
l.u.)
Temperature (K)0 20 40 60 80 100
0
2
4
6
8
10
12
THT
=235K
TLT
THT
TLT
2.7GPa
1.77GPa
p=0GPa (x0.1)
Pea
k In
tens
ity (
105 c
ount
s/se
c)
Temperature (K)
Temperature dependence
0.0
0.5
1.0(1, 0, 0)
(2.24, 0, 5.5)
Inte
grat
ed I
nten
sity
1.20
1.25
1.30
ab
T (K)0 10 20 30 40 50 60 70
1.25
1.30
1.35
1.40
c
Detection of Charge and Spin Stripe Transition
TSO
WFM
TSO
H||ab
H||c
spin
spin
La1.875Ba0.125CuO4
TCO
charge peak
LTOLTT
Yamada et al. JSSC (1989)
Bozovic et al. PRL (2002)
LSCO thin filmLSCO bulk
Gao et al. PRB (1994)
Hg-1223 bulk
Pressure and Superconductivity
Pressure: affects crystal structure and electronic band structure
buckled
flat
0 2 4 6 8 10 12 140
5
10
15
20
25
30
35
0.125
0.12
x=0.14
T
C
(K)
pressure (GPa)
ARPES
Stripes vs. CDW
T. Valla et al., Science (2007)
ARPES
T. Valla et al., Science (2007)
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