‘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