![Page 1: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/1.jpg)
‘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
![Page 2: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/2.jpg)
OUTLINE
• Ca2-xNaxCuO2Cl2
• Zero-temperature Pseudogap Spectrum
• Spectroscopic Imaging
![Page 3: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/3.jpg)
La2-xSrxCuO4 YBa2Cu3Oy Bi2Sr2CaCu2Oy
Cuprate High-Tc superconductors
La(Sr)
CuO2CuO2
Y
Ba
CuO
CuO2
Ca
SrBiO
Ca2-xNaxCuO2Cl2
![Page 4: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/4.jpg)
Identity of Electronic Ground States
zero-temperature ‘pseudogap’ regime:identity of electronic ground state?
ZTPG
![Page 5: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/5.jpg)
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.
![Page 6: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/6.jpg)
Ca2-xNaxCuO2Cl2 (Na-CCOC)
Prof. Hidenori TakagiUniversity of Tokyo
![Page 7: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/7.jpg)
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
![Page 8: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/8.jpg)
T=0PG
• Na-CCOC • excellent energy resolution• access the ZTPG ground state -> MI
Advantages of low-p zero-temperature pseudogap regime.
ZTPG
![Page 9: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/9.jpg)
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
![Page 10: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/10.jpg)
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)
![Page 11: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/11.jpg)
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
![Page 12: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/12.jpg)
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
![Page 13: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/13.jpg)
ARPES on Ca2-xNaxCuO2Cl2
Y. Kohsaka et al., J. Phys. Soc. Jpn., 72, 1018 (2003).
F. Ronning et al, PRB 67, 165101 (2003)
![Page 14: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/14.jpg)
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.
![Page 15: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/15.jpg)
STM/STS Technique
![Page 16: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/16.jpg)
Tip
Sample
Sample
Bias
Amp
XY Scan Control
XY
Z
Data-Acquisition
FeedbackControl
0zzeI -µ
STM technique
![Page 17: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/17.jpg)
Cleaver
StudSample
RodRod
![Page 18: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/18.jpg)
NaCCOC data
![Page 19: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/19.jpg)
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)
![Page 20: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/20.jpg)
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
![Page 21: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/21.jpg)
Intermediate energies: checkerboard
![Page 22: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/22.jpg)
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)
![Page 23: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/23.jpg)
-150 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
Maps 10% doping
![Page 24: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/24.jpg)
-48 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
![Page 25: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/25.jpg)
-24 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
![Page 26: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/26.jpg)
-8 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
![Page 27: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/27.jpg)
+8 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
![Page 28: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/28.jpg)
+24 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
![Page 29: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/29.jpg)
+48 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
![Page 30: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/30.jpg)
+150 mV
-400 -200 0 200 4000
1
2
3
4
Co
nd
uct
an
ce (
nS
)
Bias Voltage (mV)
![Page 31: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/31.jpg)
+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
![Page 32: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/32.jpg)
FFT from Topograph
Atoms
![Page 33: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/33.jpg)
-150 mV
FFT from Maps
![Page 34: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/34.jpg)
-48 mV
![Page 35: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/35.jpg)
-24 mV
![Page 36: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/36.jpg)
-8 mV
![Page 37: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/37.jpg)
8 mV
![Page 38: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/38.jpg)
24 mV
![Page 39: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/39.jpg)
48 mV
![Page 40: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/40.jpg)
150 mV
![Page 41: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/41.jpg)
Non-dispersive LDOS(E) Modulations
Nature 430, 1001 (2004).
Wavevectors: (1/4,0) and unexpected (¾,0)
![Page 42: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/42.jpg)
10% +24mV dI/dV map
0.06
0.53 nS
Examine spatial structure directly at the atomic scale
![Page 43: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/43.jpg)
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)
![Page 44: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/44.jpg)
Point Spectra
![Page 45: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/45.jpg)
Line cuts: Map vs Topo
![Page 46: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/46.jpg)
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)
![Page 47: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/47.jpg)
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
![Page 48: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/48.jpg)
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
![Page 49: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/49.jpg)
• 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
![Page 50: ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2](https://reader036.vdocuments.net/reader036/viewer/2022062809/5681581b550346895dc57fc9/html5/thumbnails/50.jpg)
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