Charge Inhomogeneity and Electronic Phase Separation in Layered

Charge Inhomogeneity and Electronic Phase Separation in Layered Cuprate F. C. Chou Center for Condensed Matter Sciences, National Taiwan University National Synchrotron Radiation Research Center, Taiwan

Inhomogeneous Electron Density

CDW, Dimerization and Nesting 1 d Peierls instability : q = 2 k. F CDW => MIT 2 d Fermi Surface nesting Peierls Transition

Phase Diagrams La 2 Cu. O 4+d La 2 -x. Srx. Cu. O 4

Charge Inhomogeneity: Spin and charge stripes La 2 -x-y. Ndy. Srx. Cu. O 4 • Holes segregate into AF antiphase domain walls Tranquada et al, Nature 1995

Spin/Charge Stripes and Superconductivity Yamada et al, PRB 1998

1 d domain walls in low x La 2 -x. Srx. Cu. O 4 L ~ 1/x Finite size effect: 1 -TN(x)/TN(0) ~ L-1/n Cho et al, 1993

Charge Inhomogeneity: Checkerboard Type Underdoped Ca 2 -x. Nax. Cu. O 2 Cl 2 Hanaguri et al, Nature 2004 Underdoped Bi 2 Sr 2 Ca. Cu 2 O 8+d Hashimoto et al, PRB 2006

Electrochemical oxygen intercalation La 2 Cu. O 4+d V Reference La 2 Cu. O 4 Grenier et al, Physica C 1991 Pt Na. OH/H 2 O electrolyte Li et al, PRL 1996

Macroscopic Phase Separation in La 2 Cu. O 4+d • Electrochemical oxygen intercalation • Undoped AF domain and hope-doped SC domain La 2 -x. Srx. Cu. O 4 Radaelli et al, PRB 1993; Statt et al, PRB 1995

Spinodal Decomposition

Staging: charge/oxygen segregation La 2 Cu. O 4 +d Wells et al, Science 1997

Electrochemical oxygen intercalation La 2 -x. Srx. Cu. O 4 La 2 Cu. O 4+d V Reference La 2 Cu. O 4 Grenier et al, Physica C 1991 Pt Na. OH/H 2 O electrolyte

La 2 -x. Srx. Cu. O 4+d: hole doping through Srx and Od • Identical SC onset ~40 K • SC volume fraction indep. of x or d

La 2 -x. Srx. Cu. O 4+d: magnetic phase by ZF-m. SR La 1. 91 Sr 0. 09 Cu. O 4+d • Magnetic static ordering onset near ~40 K • Magnetic volume fraction independent of x or d

Phase Separation? • Co-existing superconducting (SC) and magnetic (ISDW) phases • Identical SC and ISDW onsets • SC phase grows at the expense of ISDW phase • Chemical or Electronic origin?

Revisit LTT and ISDW La 2 -x. Ba 1/8 Cu. O 4 Non-SC La 2 -x. Srx. Cu. O 4+d SC Structure ordering LTT LTO Magnetic ordering 38 K 3. 5 MHz 40 K 3. 5 MHz • Competing SC and ISDW, not LTT and ISDW 17 Luke et al, Physica C 1991

LTT and 1/8 dip of Tc

Why Electronic Phase Separation? • t-J model by Emery and Kivelson: “Holes tend to phase separate but long-range Coulomb repulsion frustrates phase separation” • Competing AF correlation and Coulomb interaction • quantum confinement, paired electrons • Wigner crystal? Löw, Emery, Fabricius, and Kivelson, PRL 1994 Xiuqing Huang, cond-mat/0606177 19

Summary and Conclusions • Large unexplored phase space • PS of electronic origin: indep. of x or d alone, identical ISDW phase, competing SC and static magnetic phases • Competing SC and ISDW, not SC and LTT • The electronic interaction of the doped holes is the primary driver of the phase separation rather than specific chemistry of O or Sr in this compound Collaborators: Hashini Mohottala and Barry Wells (U. Conn. ) et al, Nature Materials 2006

Wigner crystals Phys. Rev. Lett. vol. 86, p. 3851 (2001)

Stripes in La 2 -x. Srx. Cu. O 4 Fujita et al, RRB 2002 Marouchkine, 2006

Staging behavior – neutron scattering PHYSICAL REVIEW B 69, 020502 (2004)