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Zheng-Yu Weng Institute for Advanced Study Tsinghua University, Beijing

Mott Physics, Sign Structure, and High- Tc Superconductivity. Zheng-Yu Weng Institute for Advanced Study Tsinghua University, Beijing. Newton Institute, Cambridge 2013.9.16. Outline . Introduction to basic experimental phenomenology of high - T c cuprates

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Zheng-Yu Weng Institute for Advanced Study Tsinghua University, Beijing

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  1. Mott Physics, Sign Structure, and High-Tc Superconductivity Zheng-Yu Weng Institute for Advanced Study Tsinghua University, Beijing Newton Institute, Cambridge 2013.9.16

  2. Outline • Introduction to basic experimental phenomenology of high-Tccuprates • High-Tccuprates as doped Mott insulators /doped antiferromagnets • Basic principles: Mott physics and sign structure • Nontrivial examples: (1) one-hole case (2) finite doping and global phase diagram (3) ground state wavefunction • Summary and conclusion

  3. Discovery of high-Tc superconductors Mueller Bednorz 1986

  4. Landau paradigm ARPES Fermi sea Fermi surface of copper typical Fermi liquid behavior: Fermi degenerate temperature Sommerfeld constant Pauli susceptibility Korringa behavior

  5. La2-xSrxCuO4 Spin susceptibility (T. Nakano, et al. (1994)) Specific heat (Loram et al. 2001) Fermi liquid behavior: Sommerfeld constant Pauli susceptibility Korringa behavior NMR spin-lattice relaxation rate (T. Imai et al. (1993))

  6. Uniform spin susceptibility Fermi liquid Heisenberg model no indication of Pauli susc. T. Nakano, et al. PRB49, 16000(1994) J

  7. uniform susceptibility, resistivity NMR 1/T1 Optical measurement Nernst effect Photoemission

  8. Underdoped phase diagram T ~ J/kB strange metal: maximal scattering Pseudogap: New quantum state of matter? A non-Fermi-liquid T0 strong AF correlations TN lower pseudogap phase T* Tv strong SC fluctuations Tc FL 0 x QCP antiferromagnetic order d-wave superconducting order

  9. Outline • Introduction to basic experimental phenomenology of high-Tccuprates • High-Tccuprates as doped Mott insulators /doped antiferromagnets • Basic principles: Mott physics and sign structure • Nontrivial examples: (1) one-hole case (2) finite doping and global phase diagram (3) ground state wavefunction • Summary and conclusion

  10. Cuprates = doped Mott Insulator T Anderson, Science 1987 ~ J/kB one-band large-U Hubbard model: T0 TN T* Tv Tc Half-filling: Mott insulator x=0 QCP x

  11. Mott Insulator/ antiferromagnet Mott insulator doped Mott insulator t-J model Heisenberg model

  12. A minimal model for doped Mott insulators: t-J model hoppingsuperexchange

  13. Pure CuO2 plane H = JSi·Sj large J = 135 meV quantum spin S =1/2 Half-filling: Low-energy physics is described by Heisenberg model

  14. charge localization at low doping ARPES result: A broad peak at x=0 Ando et al, PRL 87, 017001 (2001) K. M. Shen et al, PRL 93, 267002 (2004)

  15. Doping the Mott Insulator/ antiferromagnet La-Sr-Cu-O La-Bi2201 Peng, et al., arXiv:1302.3017 (2013) Sebastian, et al., Reports on progress in physics75, 102501 (2012)

  16. Doping the Mott Insulator/ antiferromagnet charge localization La-Sr-Cu-O La-Bi2201 Peng, et al., arXiv:1302.3017 (2013) Sebastian, et al., Reports on progress in physics75, 102501 (2012)

  17. Questions • If charge localization is intrinsic in a doped Mott insulator • with AFLRO? • If charge delocalization (superconductivity) arises by • destroying the AFLRO? • Is localization-delocalization the underlying driving force • or the T=0 phase diagram of the underdopedcuprates?

  18. Outline • Introduction to basic experimental phenomenology of high-Tccupratesand high-Tccuprates as doped Mott insulators /doped antiferromagnets • Basic principles: Mott physics and sign structure • Nontrivial examples: (1) one-hole case (2) finite doping and global phase diagram (3) ground state wavefunction • Summary and conclusion

  19. Statistical sign structure for Fermion systems Fermion signs Landau Fermi Liquid

  20. interacting fermions: fractal nodes F. Kruger and J. Zaanen, (2008) nodalhypersurface Pauli hypersurface Nodalhypersurface Test particle d=2

  21. Fermi liquid: Fermion signs Off Diagonal Long Rang Order (ODLRO): compensating the Fermion signs Bose condensation Cooper pairing in SC state CDW (“exciton” condensation) SDW (weak coupling) normal state: Fermi liquid Antiferromagnetic order (strong coupling) Complete disappearance of Fermion signs!

  22. (3) Single-hole doped Heiserberg model: ＋ － Phase string effect D.N. Sheng, Y.C. Chen, ZYW, PRL (1996)

  23. (4) Exact sign structure of the t-J model at arbitrary doping, dimensions, temperature = total steps of hole hoppings = total number of spin exchange processes = total number of opposite spin encounters Wu, Weng, Zaanen, PRB (2008)

  24. For a given path c: + - - + + + + + - - + - (-)3 - (-) + - - - - - + + + - + + K. Wu, ZYW, J. Zaanen, PRB (2008)

  25. Emergent gauge force in doped Mott insulators! Mutual Chern-Simons gauge theory ZYW et al (1997) (1998) Kou, Qi, ZYW PRB (2005); Ye, Tian, Qi, ZYW, PRL (2011); Nucl. Phys. B (2012) B Nonintegrablephase factor: “An intrinsic and complete description of electromagnetism” A “Gauge symmetry dictates the form of the fundamental forces in nature” C. N. Yang (1974) , Wu and Yang (1975)

  26. “smooth” paths good for mean-field treatment singular quantum phase interference New guiding principles: • Mott physics = phase string sign structure replacing the Fermion signs • Strong correlations = charge and spin are long-range entangled • Sign structure + restricted Hilbert space = unique fractionalization

  27. Outline • Introduction to basic experimental phenomenology of high-Tccupratesand high-Tccuprates as doped Mott insulators /doped antiferromagnets • Basic principles: Sign structure and Mott physics • Nontrivial examples: (1) one-hole case (2) finite doping and global phase diagram (3) ground state wavefunction • Summary and conclusion

  28. DMRG numerical study Z. Zhu, H-C Jiang, Y. Qi, C.S. Tian, ZYW, Scientific Report 3, 2586 (2013） t-J ladder systems

  29. Effect of phase string effect no phase string effect Self-localization of the hole! σ

  30. Removing the phase string: A sign-free model σ no phase string effect!

  31. Momentum distribution Quasiparticle picture restored! without phase string effect

  32. localization-delocalization transition t’ t

  33. Theoretical understading of self-localization of the one-hole in 2D - + + - - - + - - + + - + + destructive quantum phase interference leads to self-localization D.N. Sheng, et al. PRL (1996); ZYW, et al. PRB (2001) Holon localization at low doping: S.P. Kou, ZYW, PRL (2003) T.-P. Choy and Philip Phillips, PRL (2005) P. Ye and Q.R. Wang, Nucl. Phys. B (2013)

  34. Outline • Introduction to basic experimental phenomenology of high-Tccupratesand high-Tccuprates as doped Mott insulators /doped antiferromagnets • Basic principles: Sign structure and Mott physics • Nontrivial examples: (1) one-hole case (2) finite doping and global phase diagram (3) ground state wavefunction • Summary and conclusion

  35. Example II: Delocalization and superconductivity - + + - + + - - - - - + + - - - - + + + - + + + - - + localization/AFLRO delocalization/SC spin liquid/RVB! AF spin liquid doping localization SC

  36. Non-BCS elementary excitation in SC state - - + + + + - - - - + + - - - - + + + - - - + + spin-roton - + + - - + Superconducting transition - - spinon confinement-deconfinement transition + spinon-vortex + -

  37. Global phase diagram charge-spin long-range entanglement by phase string effect T “strange metal” T0 pseudogap AF FL SC δ localization AF = long-range RVB

  38. Outline • Introduction to basic experimental phenomenology of high-Tccupratesand high-Tccuprates as doped Mott insulators /doped antiferromagnets • Basic principles: Sign structure and Mott physics • Nontrivial examples: (1) one-hole case (2) finite doping and global phase diagram (3) ground state wavefunction • Summary and conclusion

  39. Example III : “Parent” ground state ZYW, New J. Phys. (2011) lh iu jd AFM state: Superconducting state: short-ranged emergent (ghost) spin liquid

  40. Summary and Conclusion • Cuprates are doped Mott insulators with strong Coulomb interaction • New organizing principles of Mott physics: • An altered fermion sign structure due to large-U • Consequences: • (1) Intrinsic charge localization in a lightly doped antiferromagnet • (2) Charge delocalization (superconductivity) arises by destroying • the AFLRO • (3) Localization-delocalization is the underlying driving force for the • T=0 phase diagram of the underdopedcuprates • Non-BCS-like ground state wavefunction

  41. Thank you For your attention!

  42. Fermionic RVB theories P. W. Anderson: Resonating valence bond (RVB) theory (1987) Slave-boson mean-field theory: Baskaran, Zou, Anderson (1988) Kotliar, Liu (1988) … Gauge theory description: U(1) P.A. Lee, N. Nagaosa, A. Larkin, … SU(2) X.G. Wen, P. A. Lee, … Z2 Sentil, Fisher …….. Variational wave function: Gros, Anderson, Lee, Randeria, Rice, Trivedi, Zhang; T.K. Lee; Tao Li, … Anderson, et al., J. Phys.: Condens. Mater (2004) Lee, Nagaosa, Wen, RMP (2006)

  43. (5) Hubbard model on bipartite lattices: A general sign structure (Long Zhang & ZYW, 2013 ) Hilbert space: spinonsholon (h) doublon (d) Basic hopping processes in the Hubbard model

  44. Partition function： t U J + - - + + + half-filling: + + - - + （-）

  45. Spin-charge separation three-leg ladder:

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