SLIDE 1
Outline:
- What is charge homogeneity, and why is it
interesting?
- Current experimental methods for measuring
charge homogeneity, and their drawbacks.
- A new idea to tackle the problem.
- Experimental results
- Conclusions
Development of a nuclear quadrupole based technique for measuring - - PowerPoint PPT Presentation
Development of a nuclear quadrupole based technique for measuring - - PowerPoint PPT Presentation
Development of a nuclear quadrupole based technique for measuring charge homogeneity, and its application for YBCO Outline: What is charge homogeneity, and why is it interesting? Current experimental methods for measuring charge
SLIDE 2
SLIDE 3
b a c
YBCO7
O - Cu - Y - Ba -
YBCO6
Y1Ba2Cu3O7-
Planes Chains
Cu(2) Cu(1)
SLIDE 4
2
Cu
3
Cu
2
Cu
3
Cu
2
Cu
3
Cu
2
Cu
3
Cu
2
Cu
3
Cu
2
Cu
3
Cu
2
Cu
3
Cu
2
Cu
3
Cu
2
Cu
3
Cu
<15%
2
Cu
3
Cu
2
Cu
3
Cu
2
Cu
3
Cu
SLIDE 5
- The stripes theory claims that one dimensional
charge structures in the planes play a crucial role in the mechanism of superconductivity.
- Higher doping more stripes
- There is partial experimental evidence for stripes.
Motivation - Stripes
inhomogeneity higher Tc inhomogeneity Higher doping
SLIDE 6
SC
Evidence for inhomogeneity using SR
Low doping
Tg SC
6.3 6.4 6.5 6.6 6.7 6.8 6.9 100 200 300 400
AF
Temperature [K] Doping value - y
Tc
Superconducting
Orthorhombic Tetragonal
TN
20 40 60 80 100 120 140 160 180 200
Doping Value Tetragonal Orthorhombic
SLIDE 7
- This result supports the presence of some
magnetic structure (not necessarily in the form of stripes).
- Increasing the doping decreases the
inhomogeneity.
- It looks as if the structure is a remainder of
the AF phase.
SLIDE 8
K.M.Lang et al, Nature, 415, 412 (2002)
Evidence for inhomogeneity using STM
Bi2Sr2CaCu2O8+
p0.18±0.02 p0.14±0.02
Surface
560
SLIDE 9
Outline:
- Motivation: what is
charge homogeneity, and why is it interesting?
- What is the experimental
evidence for homogeneity , and what are the drawbacks?
- Our new idea how to
deal with this problem.
- Results
- Conclusions
TIME TO FALL ASLEEP
Summary of the introduction
- Some theories are based on structures
in the planes.
- There is incomplete experimental
evidence for such structures. A new technique, based on the nuclear quadrupole interaction. Solution
SLIDE 10
SLIDE 11
Electric quadrupole interaction
Nucleus
z y x
I I I
1 2 1 2 1 q
Vij= V(r)
zz yy xx
V V V
j i ij
r r V V
2
) ˆ ˆ ( ˆ ˆ 3 6 ˆ
2 2 2 2 y x z q q
I I I I H
2 2 2
y
1
zz yy xx zz q
V V V V
x
SLIDE 12
- The quadrupole interaction is sensitive to
the symmetry of the charge distribution, and can be a useful tool for our purpose.
- determines the homogeneity of the charge
distribution: =0 – Homogenous charge distribution =1 – Inhomogenous charge distribution
SLIDE 13
SLIDE 14
SLIDE 15
The NQR Hamiltonian for spin 3/2
3 3 3 3 6 3 ˆ q
q
H
1 1 1 1 3 1 2 ˆ
2
q
q
H
3 1
2
q
SLIDE 16
NQR experimental setup
SLIDE 17
26 27 28 29 30 31 32
Cu(1)
63Cu(2)
Frequency [MHz]
Y=6.675 T=100K
Intensity/f
2 [a.u.]
63Cu(2) 65Cu(2)
Y=7 T=100K
NQR Spectrum of YBCO
<> Vzz||c
? <> is known only for optimal doping
6.3 6.4 6.5 6.6 6.7 6.8 6.9 100 200 300 400
AF
Temperature [K] Doping value - y
Tc
Superconducting
Orthorhombic Tetragonal
TN
20 40 60 80 100 120 140 160 180 200
Doping Value Tetragonal Orthorhombic
65Cu(2) 63Cu(2)
Cu(1)
63Cu(2)
SLIDE 18
The EFG tensor for Cu(2) in YBCO7
b a c Vzz Vyy Vxx Vxx<Vyy<Vzz Vzz Vzz || c
SLIDE 19
YBCO in a magnetic field
Bo
Bo || c || Vzz z b a c
SLIDE 20
X Z
Bo
Orientation
SLIDE 21
Orientation quality
X-ray diffraction
Unoriented Sample
SLIDE 22
X Z
) ( ) ( ) ( ) ( ) ( 3
1
Sin Sin Sin Sin t Cos B 1 1 1 1 2
q
=0
1 1 1 1 3 1 2
2
q ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 2
1
Sin g Cos f Sin g Cos f Cos f Sin g Cos f Sin g t Cos B
0
Sample Vzz
SLIDE 23
Echo Intensity vs. - Theoretical Result
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity[a.u]
[degree]
SLIDE 24
Intensity (=90)/Intensity (=0)
<>=0 < || >0
||
Intensity(=90)\Intensity(=0)
SLIDE 25
NQR Spectrum of YBCO
26 27 28 29 30 31 32
Cu(1)
63Cu(2)
Frequency [MHz]
Y=6.675 T=100K
Intensity/f
2 [a.u.]
63Cu(2) 65Cu(2)
Y=7 T=100K
YBCO6.675 YBCO7- YBCO7 <> Vzz||c
?
63Cu(2) 65Cu(2)
Cu(1)
63Cu(2)
SLIDE 26
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
[degree] Intensity [a.u.]
YBCO7
SLIDE 27
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 28
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 29
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 30
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 31
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 32
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 33
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 34
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 35
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 36
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 37
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 38
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 39
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 40
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 41
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 42
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 43
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 44
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 45
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 46
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0 50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 47
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 48
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 49
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 50
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 51
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 52
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 53
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 54
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 55
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 56
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 57
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 58
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 59
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 60
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 61
H1
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u.] [degree]
YBCO7
SLIDE 62
50 100 150 200 250 300 350 0.0 0.2 0.4 0.6 0.8 1.0
H1
Intensity [a.u.] [degree]
YBCO7
SLIDE 63
SLIDE 64
Intermediate Conclusions:
- ADNQR can be applied successfully to
measure .
- For YBCO7 we obtained =0 ±0.1. This
agrees with the known result.
- Since we measure || we can further
conclude that there is no spatial fluctuation in the charge distribution.
<>=0 < || >0
SLIDE 65
20 40 60 80 100 0.0 0.2 0.4 0.6 0.8 1.0
Intensity [a.u]
[degree]
YBCO6.675 27.501MHz YBCO7- 30.53MHz YBCO7 31.15MHz
20 40 60 80 100
Results of ADNQR for different samples
=0.6 ± 0.1 =1 ± 0.1 =0 ± 0.1 YBCO6.675 YBCO7- YBCO7
Higher doping Higher homogeneity
SLIDE 66
- The stripes theory claims that one dimensional
charge structures in the planes play a crucial role in the mechanism of superconductivity.
- Higher doping more stripes
- There are experimental evidences for stripes.
Motivation - Stripes
inhomogeneity higher Tc inhomogeneity Higher doping
SLIDE 67
6.0 6.2 6.4 6.6 6.8 7.0 3.82 3.84 3.86 3.88 3.90 3.92 3.94
T=300K
Orthorhombic Tetragonal
b a c/3
Lattice Constants [Angstrom] Doping value - y
b a c
a=b =0 a b 0 Theory
The effect is due to charges and not to lattice structure
- J. D. Jorgensen et al, PRB , 41, 1863
(1990)
Is it a structural or a charge effect?
6.675 < 7 Experiment 6.675 > 7
SLIDE 68
Summary:
- ADNQR can be applied successfully to measure .
- For YBCO7 we obtained =0 (high homogeneity).
- We found the first evidence for charge
inhomogeneity in the bulk of highly doped YBCO (YBCO6.675 ).
- We can safely say that YBCO6.675 is less homogenous
than YBCO7. There is an anticorrelation between Tc and homogeneity
SLIDE 69
Acknowledgements
- Prof. Amit Keren
- Prof. Emil Polturak
Galina Bazalitsky Mordehai Ayalon Shmuel Hoida Leonid Iomin Rinat Assa, Ariel Maniv, Oshri Peleg, Eva Segal, Oren Shafir, Meni Shay, Lior Shkedy
Amit Kanigel
SLIDE 70
Electric quadrupole interaction
Nucleus
z y x
I I I
1 2 1 2 1 q
Vij= V(r)
zz yy xx
V V V
j i ij
r r V V
2
1
zz yy xx zz q
V V V e V
) ˆ ˆ ( ˆ ˆ 3 6 ˆ
2 2 2 2 y x z q q
I I I I H
2 2 2
SLIDE 71
< || >=0.01
20 40 60 80 100
- 1.0
- 0.8
- 0.6
- 0.4
- 0.2
0.0 0.2 0.4 0.6 0.8 1.0
Location [unit cell]
< || >=0.15 < || >=0.47
SLIDE 72
20 40 60 80 100
- 1.0
- 0.8
- 0.6
- 0.4
- 0.2
0.0 0.2 0.4 0.6 0.8 1.0
Location [unit cell]