‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2- x Na x CuO 2 Cl 2

1. ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca2-xNaxCuO2Cl2 Tetsuo Hanaguri Yuhki Kohsaka Hidenori Takagi Tokyo/RIKEN M. Azuma M. Takano Kyoto Christian Lupien Université de Sherbrooke Yuhki Kohsaka Curry Taylor J.C. Séamus Davis Cornell

2. OUTLINE • Ca2-xNaxCuO2Cl2 • Zero-temperature Pseudogap Spectrum • Spectroscopic Imaging

3. Cuprate High-Tc superconductors CuO2 Ca CuO2 CuO2 Y Sr Bi O Ba La(Sr) CuO YBa2Cu3Oy La2-xSrxCuO4 Bi2Sr2CaCu2Oy Ca2-xNaxCuO2Cl2

4. ZTPG Identity of Electronic Ground States zero-temperature ‘pseudogap’ regime: identity of electronic ground state?

5. Possible orders in the pseudogap • 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. So many!

6. Ca2-xNaxCuO2Cl2 (Na-CCOC) Prof. Hidenori Takagi University of Tokyo

7. ZTPG Complications in high-p high-T pseudogap regime. T>Tc • Bi-2212 • but DE~3.5kBTc~35meV @ T=100K • and Bi-2212 is strongly disordered

8. ZTPG Advantages of low-p zero-temperature pseudogap regime. T=0 PG • Na-CCOC • excellent energy resolution • access the ZTPG ground state -> MI

9. Ca2CuO2Cl2 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.

10. Crystal growth under pressure (~GPa) • Flux method (Ca2CuO2Cl2(poly)+0.2NaClO4+0.2NaCl) • Cubic anvil type high-pressure apparatus @Takano Lab. Kyoto Univ. Y. Kohsaka et al., J. Am. Chem. Soc., 124, 12275 (2002).

11. Characterization of Ca2-xNaxCuO2Cl2 crystals K. Waku et al., Insulating at x~1/16 Current Maximum doping for single crystals Y. Kohsaka, et al, J. Am Chem. Soc. 124, 12275 (2002)

12. ARPES on Ca2CuO2Cl2 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).

13. ARPES on Ca2-xNaxCuO2Cl2 F. Ronning et al, PRB 67, 165101 (2003) Y. Kohsaka et al., J. Phys. Soc. Jpn., 72, 1018 (2003).

14. ARPES on Ca2-xNaxCuO2Cl2 • Supports a Fermi-arc at x>0.05 • Gapped by SC D<10meV at x>0.10 • Four fold symmetric pseudogap at (p,0) Coherent states on Fermi-arc ~200meV pseudogap & incoherent states at antinodes. F. Ronning et al, PRB 67, 165101 (2003)

15. STM/STS Technique

16. STM technique

17. Cleaver Stud Sample Rod

18. NaCCOC data

19. Topo image of CaCl plane of Ca1.9Na0.1CuO2Cl2 CuO2 CaCl CaCl CuO2 CaCl CaCl CuO2 200 mV / 50 pA Nature 430, 1001 (Aug. 26 2004)

20. dI/dV|+24mV 5 nm Three energy ranges Electronic phase diagram Intermediate energy (<150 mV): ‘Checkerboard’ pattern (V shape) H igh energy (>150 mV): Mottness mapping (asymmetry) Low energy (<10 mV): Superconductivity V-shaped spectum T. Hanaguri et al., Nature430, 1001 (2004)

21. Intermediate energies: checkerboard

22. dI/dV|+24mV T < 250 mK Vsample = 200 mV It = 100 pA Topograph T < 250 mK Vsample = 200 mV It = 50 pA 1 Å 0.47 nS Spectroscopic imaging within pseudogap 5 nm 200 Å Nature 430, 1001 (Aug. 26 2004)

23. Maps 10% doping -150 mV

24. -48 mV

25. -24 mV

26. -8 mV

27. +8 mV

28. +24 mV

29. +48 mV

30. +150 mV

31. Topo. Spectroscopic imaging 200 Å×200 ÅT < 250 mKVsample = 200mV (400mV for 150mV data)It = 100 pA +8mV +24mV +48mV +150mV -8mV -24mV -48mV -150mV

32. FFT from Topograph Atoms

33. FFT from Maps -150 mV

34. -48 mV

35. -24 mV

36. -8 mV

37. 8 mV

38. 24 mV

39. 48 mV

40. 150 mV

41. Non-dispersive LDOS(E) Modulations Wavevectors: (1/4,0) and unexpected (¾,0) Nature 430, 1001 (2004).

42. Examine spatial structure directly at the atomic scale 0.53 nS 0.06 10% +24mV dI/dV map

43. dI/dV|+25mV T < 250 mK Vsample = 200 mVIt = 100 pA Topograph T < 250 mK Vsample = 200 mVIt = 50 pA 1 Å 0.87 nS Examine spatial structure directly at the atomic scale Nature 430, 1001 (Aug. 26 2004)

44. Point Spectra

45. Line cuts: Map vs Topo

46. Simulation z = 33 cos(1/4) + 34 sin(3/4) z = 33 cos(1/4) – 34 cos(3/4) z = 33 cos(1/4) + 34 cos(3/4) Differences z = 33 cos(1/4) + 34 cos(3/4) - 11 cos(1)

47. Bias symmetry/asymmetry inside gap +8mV +24mV +48mV -8mV -24mV -48mV Certainly not a simple situation of bias symmetric checkerboard: Some Fourier components exhibit bias symmetry and some do not.

48. Zone-face ‘nesting vector’ q=2p/4a independent of doping: Checkerboard state is constructed from scattering of the zone-face states ARPES: Scattering between parallel FS elements q=2p(3/4a) Z.-X. Shen Group Stanford University Kyle Shen et al Science 307, 901 (2005)

49. AF Conclusions ZTPG • First STS imaging of a cuprate in zero temp. pseudogap regime. • Discovery of a ‘checkerboard’ electronic crystal state in Na-CCOC • Spatial structure ~ exactly commensurate 4X4 electronic entity • Characteristic and strongly asymmetric tunneling spectrum

50. Prof. J.C. Séamus Davis Cornell University Curry Taylor Cornell University Dr. Masaki Azuma Kyoto University Prof. Mikio Takano Kyoto University Prof. Hidenori Takagi University of Tokyo Prof. Dung-Hai Lee UC Berkeley Dr. Yuhki Kohsaka Cornell University Prof. Tetsuo Hanaguri RIKEN