1 / 107

Colloquium article in Reviews of Modern Physics 75 , 913 (2003)

Quantum phase transitions: from Mott insulators to the cuprate superconductors. Colloquium article in Reviews of Modern Physics 75 , 913 (2003).

Download Presentation

Colloquium article in Reviews of Modern Physics 75 , 913 (2003)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Quantum phase transitions: from Mott insulators to the cuprate superconductors Colloquium article in Reviews of Modern Physics75, 913 (2003) Leon Balents (UCSB) Eugene Demler (Harvard) Matthew Fisher (UCSB) Kwon Park (Maryland) Anatoli Polkovnikov (Harvard) T. Senthil (MIT) Ashvin Vishwanath (MIT) Matthias Vojta (Karlsruhe) Ying Zhang (Maryland)

  2. Band theory k Half-filled band of Cu 3d orbitals – ground state is predicted by band theory to be a metal. Parent compound of the high temperature superconductors: La O However, La2CuO4 is a very good insulator Cu

  3. Parent compound of the high temperature superconductors: A Mott insulator Ground state has long-range spin density wave (Néel) order at wavevector K= (p,p)

  4. Parent compound of the high temperature superconductors: A Mott insulator Ground state has long-range spin density wave (Néel) order at wavevector K= (p,p)

  5. Parent compound of the high temperature superconductors: A Mott insulator Ground state has long-range spin density wave (Néel) order at wavevector K= (p,p)

  6. Introduce mobile carriers of density d by substitutional doping of out-of-plane ions e.g. First study magnetic transition in Mott insulators………….

  7. Outline • Magnetic quantum phase transitions in “dimerized” Mott insulators Landau-Ginzburg-Wilson (LGW) theory • Mott insulators with spin S=1/2 per unit cell Berry phases, bond order, and the breakdown of the LGW paradigm • Cuprate Superconductors Competing orders and recent experiments

  8. A. Magnetic quantum phase tranitions in “dimerized” Mott insulators: Landau-Ginzburg-Wilson (LGW) theory: Second-order phase transitions described by fluctuations of an order parameter associated with a broken symmetry

  9. TlCuCl3 M. Matsumoto, B. Normand, T.M. Rice, and M. Sigrist, cond-mat/0309440.

  10. Coupled Dimer Antiferromagnet M. P. Gelfand, R. R. P. Singh, and D. A. Huse, Phys. Rev. B40, 10801-10809 (1989). N. Katoh and M. Imada, J. Phys. Soc. Jpn.63, 4529 (1994). J. Tworzydlo, O. Y. Osman, C. N. A. van Duin, J. Zaanen, Phys. Rev. B 59, 115 (1999). M. Matsumoto, C. Yasuda, S. Todo, and H. Takayama, Phys. Rev. B 65, 014407 (2002). S=1/2 spins on coupled dimers

  11. Weakly coupled dimers

  12. Weakly coupled dimers Paramagnetic ground state

  13. Weakly coupled dimers Excitation: S=1 triplon

  14. Weakly coupled dimers Excitation: S=1 triplon

  15. Weakly coupled dimers Excitation: S=1 triplon

  16. Weakly coupled dimers Excitation: S=1 triplon

  17. Weakly coupled dimers Excitation: S=1 triplon

  18. Weakly coupled dimers Excitation: S=1 triplon (exciton, spin collective mode) Energy dispersion away from antiferromagnetic wavevector

  19. TlCuCl3 “triplon” N. Cavadini, G. Heigold, W. Henggeler, A. Furrer, H.-U. Güdel, K. Krämer and H. Mutka, Phys. Rev. B 63 172414 (2001). K. Damle and S. Sachdev, Phys. Rev. B 57, 8307 (1998) This result is in good agreement with observations in CsNiCl3 (M. Kenzelmann, R. A. Cowley, W. J. L. Buyers, R. Coldea, M. Enderle, and D. F. McMorrow Phys. Rev. B 66, 174412 (2002)) and Y2NiBaO5 (G. Xu, C. Broholm, G. Aeppli, J. F. DiTusa, T.Ito, K. Oka, and H. Takagi, preprint).

  20. Coupled Dimer Antiferromagnet

  21. l close to 1 Weakly dimerized square lattice

  22. l Weakly dimerized square lattice close to 1 Excitations: 2 spin waves (magnons) Ground state has long-range spin density wave (Néel) order at wavevector K= (p,p)

  23. TlCuCl3 J. Phys. Soc. Jpn72, 1026 (2003)

  24. lc = 0.52337(3)M. Matsumoto, C. Yasuda, S. Todo, and H. Takayama, Phys. Rev. B 65, 014407 (2002) Pressure in TlCuCl3 T=0 Quantum paramagnet Néel state 1 The method of bond operators (S. Sachdev and R.N. Bhatt, Phys. Rev. B 41, 9323 (1990)) provides a quantitative description of spin excitations in TlCuCl3 across the quantum phase transition (M. Matsumoto, B. Normand, T.M. Rice, and M. Sigrist, Phys. Rev. Lett.89, 077203 (2002))

  25. lc = 0.52337(3)M. Matsumoto, C. Yasuda, S. Todo, and H. Takayama, Phys. Rev. B 65, 014407 (2002) • d in • cuprates ? T=0 Quantum paramagnet Néel state Magnetic order as in La2CuO4 Electrons in charge-localized Cooper pairs 1 The method of bond operators (S. Sachdev and R.N. Bhatt, Phys. Rev. B 41, 9323 (1990)) provides a quantitative description of spin excitations in TlCuCl3 across the quantum phase transition (M. Matsumoto, B. Normand, T.M. Rice, and M. Sigrist, Phys. Rev. Lett.89, 077203 (2002))

  26. LGW theory for quantum criticality S. Chakravarty, B.I. Halperin, and D.R. Nelson, Phys. Rev. B 39, 2344 (1989)

  27. LGW theory for quantum criticality S. Chakravarty, B.I. Halperin, and D.R. Nelson, Phys. Rev. B 39, 2344 (1989) A.V. Chubukov, S. Sachdev, and J.Ye, Phys. Rev. B 49, 11919 (1994)

  28. B. Mott insulators with spin S=1/2 per unit cell: Berry phases, bond order, and the breakdown of the LGW paradigm

  29. Mott insulator with two S=1/2 spins per unit cell

  30. Mott insulator with one S=1/2 spin per unit cell

  31. Mott insulator with one S=1/2 spin per unit cell

  32. Mott insulator with one S=1/2 spin per unit cell Destroy Neel order by perturbations which preserve full square lattice symmetry e.g. second-neighbor or ring exchange. The strength of this perturbation is measured by a coupling g.

  33. Mott insulator with one S=1/2 spin per unit cell Destroy Neel order by perturbations which preserve full square lattice symmetry e.g. second-neighbor or ring exchange. The strength of this perturbation is measured by a coupling g.

  34. Mott insulator with one S=1/2 spin per unit cell

  35. Mott insulator with one S=1/2 spin per unit cell

  36. Mott insulator with one S=1/2 spin per unit cell

  37. Mott insulator with one S=1/2 spin per unit cell

  38. Mott insulator with one S=1/2 spin per unit cell

  39. Mott insulator with one S=1/2 spin per unit cell

  40. Mott insulator with one S=1/2 spin per unit cell

  41. Mott insulator with one S=1/2 spin per unit cell

  42. Mott insulator with one S=1/2 spin per unit cell

  43. Mott insulator with one S=1/2 spin per unit cell

  44. Mott insulator with one S=1/2 spin per unit cell

  45. Resonating valence bonds P. Fazekas and P.W. Anderson, Phil Mag30, 23 (1974); P.W. Anderson 1987 Such states are associated with non-collinear spin correlations, Z2 gauge theory, and topological order. Resonance in benzene leads to a symmetric configuration of valence bonds (F. Kekulé, L. Pauling) N. Read and S. Sachdev, Phys. Rev. Lett. 66, 1773 (1991); X. G. Wen, Phys. Rev. B 44, 2664 (1991).

  46. Excitations of the paramagnet with non-zero spin

  47. Excitations of the paramagnet with non-zero spin

  48. Excitations of the paramagnet with non-zero spin

  49. Excitations of the paramagnet with non-zero spin

More Related