Markus Hücker

1. What Pins Stripes in La2-xBaxCuO4? Markus Hücker Neutron Scattering Group Electronic Liquid-Crystal Nature of Stripes Doping Phase Diagram of LBCO at Ambient Pressure Pressure Phase Diagram of LBCO at x=1/8 CMPMS (Brookhaven) DESY M. v. Zimmermann J. M. Tranquada G. D. Gu C. C. Homes Z. J. Xu J. S. Wen Washington University M. Debessai J. S. Schilling

2. Mathur et al. Nature 1998 CePd2Si2 Competing Order in Strongly Correlated Electron Systems heavy fermion superconductor

3. Competing Order in Strongly Correlated Electron Systems La2-xBaxCuO4 1/8-problem La2-xSrxCuO4 HTT LTO 3D AF LTT stripes Tc SC SG

4. Cu O HTT La,Ba LTO LTT [001] [010] [100] Common Conception: LTT Phase Pins Stripes LTO phase Cu-O-Cu LTT phase Stripe Order

5. Stripe Order in LBCO magnetism charge Tranquada et al. Nature (1995) Fujita et al. PRB (2004) Stripes: detected with neutrons, x-rays in LBCO, LNSCO

6. Electronic Liquid-Crystal Kivelson et al. Nature (1998) Hinkov et al., Science (2008) Ando et al., PRL (2002) Evidence in YBa2Cu3O6.45 Symmetry broken by orthorhombic structure Stripe phase of La2-xBaxCuO4: At ambient pressure symmetry broken by LTT structure

7. SO Stripe Order in LBCO at Ambient Pressure p = 0 GPa

8. Pressure Dependence of Tc 2 GPa x=1/8 Tc~18K Tc 0 GPa 0.125 SC 0.12 0.125 0.13 Ido et al. Physica C (1991)

9. 1 mm LBCO CGO High Energy Single-Crystal X-ray Diffraction under Pressure sample 100 keV photons BW5 @ DESY, Hamburg Review of Scientific Instruments 79, 33906 (2008)

10. Tuning the Structure with Pressure p = 0 GPa SO

11.  LTO [110] LTT [100] [010] Stripes in Tetragonal High Pressure Regime (2, 0, 0)/(0, 2, 0) T~TLT T~TLT b c T~10K a LTT HTT (2+2, 0, 5.5) pc (1, 0, 0)

12. Charge Stripes on Square Lattice • High pressure: 4-fold symmetric planes • Charge stripes still develop • Stripes spontaneously break Symmetry • What pins stripes PDF, XAFS • PDF: Tilted Octahedra even in the HTT Phase • XAFS: Local Tilts around Dopants Billinge et al., PRL (1994) Haskel et al., PRB (2000)

13. Diffuse scattering in High Pressure Regime (3/2 3/2 2) 20Å 40Å 80Å

14. LBCO

15. Nematic Patches in High Pressure Regime • Commensurate patches of stripes and octahedral tilts • Quenched disorder always a relevant pertubation • Dopant disorder leads to finite size domains nematic patches E. Carlson et al., PRL (2006)

16. Tc SO SC Summary • Stripes spontaneously break symmetry in HTT phase • Pinned by quenched dopant disorder • Supports electronic liquid-crystal picture of HTSC Outlook • c-axis correlations • What happens for x1/8 Ba • What happens at higher pressures

17. supplemental slides

18. High Energy Single-Crystal X-ray Diffraction under Pressure

19. Different Models for the Stripe Phase Electronic micro phase separation J. Zaanen et al. PRB 40, 7391 (1989) V. Emery et al., PRL 64, 475 (1990) S.R. White et al., PRL 80, 1272 (1998) Fermi surface nesting; SDW/CDW Mason et al. PRL 77, 1604 (1996) Spiral spin order B. Shraiman, E.D. Siggia, PRL 62, 1564 (1989) Hasselmann et al. PRB 69, 14424 (2004) Shushkov et al. PRB 70, 245023 (2004)

20. Question of Dimensionality (1D Stripes, 2D Pattern) “Checkerboard” electronic state in Ca2-xNaxCuO2Cl2 T. Hanaguri et al., Nature 430, 1001 (2004) Magnetic excitations in detwinned YBa2Cu3O6+x V. Hinkov et al., Nature 450, 650 (2004)

21. Competing order in La2-xBaxCuO4 Ba – doping Maeno et al. PRB, 7753 (1991) hole concentration of 1/8 crucial

22. SC Competing order in La1.875Ba0.125CuO4 100% Ba 100% Sr Tc=31K CO Kimura et al., PRB 70, 134512 (2004) Ba-doping is crucial

23.  LTO [110] LTT [100] [010] Doping dependence average structure local distortions electronic correlations

24. Average Structure and Cation Size Variance La1.85-yNdySr0.15CuO4 L1.85-yMyCuO4 Büchner et al. (1992) Wagener et al. PRB (1997) McAllisten et al. PRB (2002)

25. Detection of Charge and Spin Stripe Transition La1.875Ba0.125CuO4 charge peak LTO TSO LTT H||c spin TSO spin H||ab TCO WFM

26. SO Stripe Order in LBCO at High Pressure? I ? charge ? spin T SC pressure 

27. Traveling-Solvent Floating-Zone Technique feed rod 0.5mm/h liquid zone crystal La2-xBaxCuO4 with x=1/8 (G.D. Gu)

28. Charge correlations along the c-axis (0, 2+2, L) 1D charge stripes 2D charge grid c c c k h M. Vojta et al., cond-mat/0408461 similar result: La1.48Nd0.4Sr0.12CuO4 , x-rays, T. Niemoeller et al., EPL (1998) La1.875Ba0.075Sr0.05CuO4 , neutrons, H. Kimura et al., PRB (2003)

29. + + + + + + Search for non-1D-Correlations magnetism charge (0 2 ½) + + + (½ ½ 0) Results for LBCO consistent with 1D-stripe model

30. [001] a LTO b Cu O HTT [110] La,Ba LTT [010] [100] [010] [100] [110] c d LTT-phase LTO-phase k k L=0 L=0 2 2 L=2 L=2 1 1 L=5.5 L=0 L=6 1 2 1 2 h h

31. (1.5, 1.5, 2) T~10K (1, 0, 0) T~10K (2+2, 0, 5.5) T~10K a b c

32. Temperature dependence

33. Detection of Charge and Spin Stripe Transition La1.875Ba0.125CuO4 charge peak LTO TSO LTT H||c spin TSO spin H||ab TCO WFM

34. Pressure and Superconductivity Hg-1223 bulk LSCO bulk LSCO thin film buckled flat Bozovic et al. PRL (2002) Gao et al. PRB (1994) Yamada et al. JSSC (1989) Pressure: affects crystal structure and electronic band structure

36. ARPES

37. Stripes vs. CDW T. Valla et al., Science (2007)

38. ARPES T. Valla et al., Science (2007)