1. ‘Checkerboard’ Electronic Crystal State in Lightly-Doped Ca 2-x Na x CuO 2 Cl 2 Yuhki Kohsaka Curry Taylor J.C. Séamus Davis Cornell Tetsuo Hanaguri Yuhki Kohsaka Hidenori Takagi Tokyo/RIKEN M. Azuma M. Takano Kyoto Christian Lupien Université de Sherbrooke

2. OUTLINE Ca 2-x Na x CuO 2 Cl 2 Zero-temperature Pseudogap Spectrum Spectroscopic Imaging

3. La 2-x Sr x CuO 4 YBa 2 Cu 3 O y Bi 2 Sr 2 CaCu 2 O y Cuprate High-T c superconductors La(Sr) CuO 2 Y Ba CuO CuO 2 Ca Sr Bi O Ca 2-x Na x CuO 2 Cl 2

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

5. 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.

6. Ca 2-x Na x CuO 2 Cl 2 (Na-CCOC) Prof. Hidenori Takagi University of Tokyo

7. Complications in high-p high-T pseudogap regime. T>Tc Bi-2212 but  E~3.5k B T c ~35meV @ T=100K and Bi-2212 is strongly disordered ZTPG

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

9. Cl atom replaces apical O of La 2 CuO 4 Single CuO 2 layer, easily cleavable @ CaCl, highly insulating cleave surface, no supermodulation, can be doped from p~0 to p~0.25. Ca 2 CuO 2 Cl 2

10. @Takano Lab. Kyoto Univ. Flux method (Ca 2 CuO 2 Cl 2 (poly)+0.2NaClO 4 +0.2NaCl) Cubic anvil type high-pressure apparatus Y. Kohsaka et al., J. Am. Chem. Soc., 124, 12275 (2002). Crystal growth under pressure (~GPa)

11. Characterization of Ca 2-x Na x CuO 2 Cl 2 crystals K. Waku et al., Y. Kohsaka, et al, J. Am Chem. Soc. 124, 12275 (2002) Insulating at x~1/16 Current Maximum doping for single crystals

12. Undoped compound Ca 2 CuO 2 Cl 2 is similar to La 2 CuO 4. It is well characterized by ARPES. Neutron measurement observed the AF order T N =270K F. Ronning et al, Science 282, 2067 (1998) and PRB 67, 035113 (2003). ARPES on Ca 2 CuO 2 Cl 2

13. ARPES on Ca 2-x Na x CuO 2 Cl 2 Y. Kohsaka et al., J. Phys. Soc. Jpn., 72, 1018 (2003). F. Ronning et al, PRB 67, 165101 (2003)

14. Supports a Fermi-arc at x>0.05 Gapped by SC  0.10 Four fold symmetric pseudogap at ( ,0) ARPES on Ca 2-x Na x CuO 2 Cl 2 Coherent states on Fermi-arc ~200meV pseudogap & incoherent states at antinodes.

15. STM/STS Technique

16. STM technique

17. Cleaver Stud Sample Rod

18. NaCCOC data

19. 200 mV / 50 pA Topo image of CaCl plane of Ca 1.9 Na 0.1 CuO 2 Cl 2 CuO 2 CaCl CuO 2 CaCl Nature 430, 1001 (Aug. 26 2004)

20. Three energy ranges T. Hanaguri et al., Nature 430, 1001 (2004) Electronic phase diagram Intermediate energy (<150 mV): ‘Checkerboard’ pattern (V shape) V-shaped spectum H igh energy (>150 mV): Mottness mapping (asymmetry) Low energy (<10 mV): Superconductivity dI/dV| +24m V 5 nm

21. Intermediate energies: checkerboard

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

23. -150 mV Maps 10% doping

24. -48 mV

25. -24 mV

26. -8 mV

27. +8 mV

28. +24 mV

29. +48 mV

30. +150 mV

31. +8mV -8mV +24mV -24mV +48mV -48mV +150mV -150mV Topo. 200 Å×200 Å T < 250 mK V sample = 200mV (400mV for 150mV data) I t = 100 pA Spectroscopic imaging

32. FFT from Topograph Atoms

33. -150 mV FFT from Maps

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 Nature 430, 1001 (2004). Wavevectors: (1/4,0) and unexpected (¾,0)

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

43. dI/dV| +25mV T < 250 mK V sample = 200 mV I t = 100 pA 0.87 nS Topograph T < 250 mK V sample = 200 mV I t = 50 pA 1 Å 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 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)

47. 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

48. 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

49. 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

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