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‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2. Tetsuo Hanaguri Yuhki Kohsaka Hidenori Takagi Tokyo/RIKEN M. Azuma M. Takano Kyoto. Christian Lupien Université de Sherbrooke. Yuhki Kohsaka Curry Taylor J.C. S é amus Davis Cornell. OUTLINE. - PowerPoint PPT Presentation
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‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca2-xNaxCuO2Cl2
Yuhki KohsakaCurry TaylorJ.C. Séamus DavisCornell
Tetsuo HanaguriYuhki KohsakaHidenori TakagiTokyo/RIKEN
M. AzumaM. TakanoKyoto
Christian LupienUniversité de Sherbrooke
OUTLINE
• Ca2-xNaxCuO2Cl2
• Zero-temperature Pseudogap Spectrum
• Spectroscopic Imaging
La2-xSrxCuO4 YBa2Cu3Oy Bi2Sr2CaCu2Oy
Cuprate High-Tc superconductors
La(Sr)
CuO2CuO2
Y
Ba
CuO
CuO2
Ca
SrBiO
Ca2-xNaxCuO2Cl2
Identity of Electronic Ground States
zero-temperature ‘pseudogap’ regime:identity of electronic ground state?
ZTPG
Possible orders in the pseudogap
So many!
•Orbital-Current Phases - broken time-reversal symmetry- d-Density Wave :
S. Chakravarty, R. B. Laughlin, et al.,PRB 63, 094503 (2001).
- Intra Unit Cell Orbital Current :C. M. Varma, PRB 55, 14554 (1997).
- Staggered Flux Phase :I. Affleck & J. B. Marsdon, PRB 37, 3774 (1988).J. Kishine, P. A. Lee & X. –G. Wen, PRL 86, 5365 (2000).
•Electronic Crystals - broken translational/rotational symmetry
- Stripes :J. Zaanen & O. Gunnarsson PRB 40, 7391 (1989).K. Machida, Physica C 158, 192 (1989).S. A. Kivelson, E. Fradkin & V. J. Emery, Nature 393, 550 (1999).E. Demler, S. Sachdev, et al., PRL 87, 067202 (2002).
- Checkerboards / Wigner Crystals :M. Vojta, PRB 66, 104505 (2002).J. Zaanen & O. Gunnarsson PRB 40, 7391 (1989).H.-D. Chen et al., PRL 89 137004 (2002).H. C. Fu, J. C. Davis and D.-H. Lee, cond-mat/0403001.
- Charge Order Embedded in an SC State:P. W. Anderson, cond-mat/0406038.A. Melikyan & Z. Tesanovic, cond-mat/0408344.M. Takigawa, M. Ichioka & K. Machida, private commun.
Ca2-xNaxCuO2Cl2 (Na-CCOC)
Prof. Hidenori TakagiUniversity of Tokyo
Complications in high-p high-T pseudogap regime.
T>Tc
• Bi-2212 • but E~3.5kBTc~35meV @ T=100K• and Bi-2212 is strongly disordered
ZTPG
T=0PG
• Na-CCOC • excellent energy resolution• access the ZTPG ground state -> MI
Advantages of low-p zero-temperature pseudogap regime.
ZTPG
Cl atom replaces apical
O of La2CuO4
Single CuO2 layer, easily cleavable @ CaCl, highly insulating cleave surface, no supermodulation, can be doped from p~0 to p~0.25.
Ca2CuO2Cl2
1m m@Takano Lab. Kyoto Univ.
• Flux method (Ca2CuO2Cl2(poly)+0.2NaClO4+0.2NaCl)
• Cubic anvil type high-pressure apparatus
Y. Kohsaka et al., J. Am. Chem. Soc., 124, 12275 (2002).
Crystal growth under pressure (~GPa)
Characterization of Ca2-xNaxCuO2Cl2 crystals
-1.0
-0.8
-0.6
-0.4
-0.2
0.0M
/H /
10-2
emu·
g-1
403020100
T / K
H = 10 OeFC
x = 0.12
x = 0.10
x = 0.08
x = 0.06
0.10
0.05
0.00x in
Ca 2-
xNa xC
uO2C
l 2
420P / GPa
10
8
6
4
2
0
Res
isti
vity
(m
cm)
300250200150100500Temperature(K)
x = 0.06
x = 0.08
x = 0.10
K. Waku et al.,
Y. Kohsaka, et al, J. Am Chem. Soc. 124, 12275 (2002)
Insulating at x~1/16
Current Maximum dopingfor single crystals
Undoped compound Ca2CuO2Cl2 is similar to La2CuO4.
It is well characterized by ARPES.
Neutron measurement observed the AF order
TN=270K
F. Ronning et al, Science 282, 2067 (1998) and PRB 67, 035113 (2003).
ARPES on Ca2CuO2Cl2
ARPES on Ca2-xNaxCuO2Cl2
Y. Kohsaka et al., J. Phys. Soc. Jpn., 72, 1018 (2003).
F. Ronning et al, PRB 67, 165101 (2003)
F. Ronning et al, PRB 67, 165101 (2003)
• Supports a Fermi-arc at x>0.05• Gapped by SC <10meV at x>0.10• Four fold symmetric pseudogap at (,0)
ARPES on Ca2-xNaxCuO2Cl2
Coherent states on Fermi-arc
~200meV pseudogap
& incoherent
states at antinodes.
STM/STS Technique
Tip
Sample
Sample
Bias
Amp
XY Scan Control
XY
Z
Data-Acquisition
FeedbackControl
0zzeI -µ
STM technique
Cleaver
StudSample
RodRod
NaCCOC data
200 mV / 50 pA
Topo image of CaCl plane of Ca1.9Na0.1CuO2Cl2
CuO2
CuO2
CaCl
CaCl
CuO2
CaCl
CaCl
Nature 430, 1001 (Aug. 26 2004)
Three energy ranges
T. Hanaguri et al., Nature 430, 1001 (2004)
Electronic phase diagram
Intermediate energy (<150 mV): ‘Checkerboard’ pattern (V
shape)
V-shaped spectumH igh energy (>150 mV):
Mottness mapping (asymmetry)
Low energy (<10 mV): Superconductivity
dI/dV|+24mV
5 nm
Intermediate energies: checkerboard
dI/dV|+24mV
T < 250 mK
Vsample = 200 mV
It = 100 pA
0.47 nS
Topograph
T < 250 mK
Vsample = 200 mV
It = 50 pA
1 Å
Spectroscopic imaging within pseudogap
5 nm
200 Å
Nature 430, 1001 (Aug. 26 2004)
-150 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
Maps 10% doping
-48 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
-24 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
-8 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
+8 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
+24 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
+48 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
+150 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
+8mV
-8mV
+24mV
-24mV
+48mV
-48mV
+150mV
-150mV
Topo.
200 Å×200 ÅT < 250 mKVsample = 200mV (400mV for 150mV data)
It = 100 pA
Spectroscopic imaging
FFT from Topograph
Atoms
-150 mV
FFT from Maps
-48 mV
-24 mV
-8 mV
8 mV
24 mV
48 mV
150 mV
Non-dispersive LDOS(E) Modulations
Nature 430, 1001 (2004).
Wavevectors: (1/4,0) and unexpected (¾,0)
10% +24mV dI/dV map
0.06
0.53 nS
Examine spatial structure directly at the atomic scale
dI/dV|+25mV
T < 250 mK
Vsample = 200 mVIt = 100 pA 0.87
nS
Topograph
T < 250 mK
Vsample = 200 mVIt = 50 pA 1 Å
Examine spatial structure directly at the atomic scale
Nature 430, 1001 (Aug. 26 2004)
Point Spectra
Line cuts: Map vs Topo
Simulation
z = 33 cos(1/4) – 34 cos(3/4) z = 33 cos(1/4) + 34 cos(3/4) z = 33 cos(1/4) + 34 sin(3/4)
Differences
z = 33 cos(1/4) + 34 cos(3/4) - 11 cos(1)
Bias symmetry/asymmetry inside gap
Certainly not a simple situation of bias symmetric checkerboard: Some Fourier components exhibit bias
symmetry and some do not.
+8mV
-8mV
+24mV
-24mV
+48mV
-48mV
q=2(3/4a)
Kyle Shen et al Science 307, 901 (2005)Z.-X. Shen Group
Stanford University
Checkerboard state is
constructed from
scattering of the zone-face states
Zone-face ‘nesting vector’
q=2/4a independent
of doping:
ARPES: Scattering between parallel FS elements
• First STS imaging of a cuprate in zero temp. pseudogap regime.
AF
Conclusions
ZTPG
• Characteristic and strongly asymmetric tunneling spectrum
• Discovery of a ‘checkerboard’ electronic crystal state in Na-CCOC
• Spatial structure ~ exactly commensurate 4X4 electronic entity
Prof. Tetsuo HanaguriRIKEN
Prof. Hidenori TakagiUniversity of Tokyo
Dr. Yuhki KohsakaCornell University
Prof. Dung-Hai LeeUC Berkeley
Prof. Mikio TakanoKyoto University
Dr. Masaki AzumaKyoto University
Curry TaylorCornell University
Prof. J.C. Séamus DavisCornell University