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Gabriel Kotliar Rutgers

Superconductivity near the Mott transition a Cluster Dynamical Mean Field Theory (CDMFT) perspective. Coherence and incoherence in stronly correlated systems. July 3-7 Rome Italy. Gabriel Kotliar Rutgers.

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Gabriel Kotliar Rutgers

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  1. Superconductivity near the Mott transition a Cluster Dynamical Mean Field Theory (CDMFT) perspective Coherence and incoherence in stronly correlated systems. July 3-7 Rome Italy Gabriel Kotliar Rutgers Collaborators : G. Biroli M . Capone M Civelli K. Haule O. Parcollet T.D. Stanescu V. Kancharla A.M.Tremblay B. Kyung D. Senechal A. Georges

  2. References Collaborators • M. Capone and GK PRB 74, 54513(2006) • M. Civelli M. Capone A. Georges K. Haule O Parcollet T. Stanescu and GK cond-mat 0704.1486 • M. Civelli et. al. PRL 95 106402(2005) • B. Kyung S. Kancharla D. Senechal A. Ms Tremblay M. CIvellli and GK PRB 73 165114(20060. • K. Haule and GK ( preprint) Closely related work: M. Capone M. Fabrizio C. Castellani and E. Tosatti Phys. Rev. Lett 93, 047001(2004) . Science 296 2364 (2002).

  3. Cuprates Damascelli, Shen, Hussain, RMP 75, 473 (2003)

  4. Kappa Organics F. Kagawa, K. Miyagawa, + K. Kanoda PRB 69 (2004) +Nature 436 (2005) Phase diagram of (X=Cu[N(CN)2]Cl) S. Lefebvre et al. PRL 85, 5420 (2000), P. Limelette, et al. PRL 91 (2003)

  5. Perspective U/t Doping Driven Mott Transition Pressure Driven Mott transtion d t’/t

  6. t-J Hamiltonian RVB P.W. Anderson (1987) Slave Boson Formulation: Baskaran Zhou Anderson (1987) Ruckenstein Hirschfeld and Appell (1987) b+i bi +f+si fsi = 1 Other RVB states with d wave symmetry. Flux phase or s+id G. Kotliar (1988) Affleck and Marston (1988) . Spectrum of excitation have point zeros like a a d –wave superconductor.

  7. Superexchange Mechanism: proximity to the Mott transition renormalizes down kinetic energy, but not the superexchange. Slave Boson Mean Field Theory Phase Diagram. Formation of Singlets Coherent Quasiparticles Re

  8. Problems with the approach. • Stability of the MFT. Ex. Neel order. Slave boson MFT with Neel order predicts AF AND SC. [Inui et.al. 1988] Giamarchi and L’huillier (1987). • Gauge fluctuations destablize the mean field [Ubbens and Lee] • Temperature dependence of the penetration depth [Wen and Lee , Ioffe and Millis ] . Theory:r[T]=x-T x2 , Exp: r[T]= x-T • Z= x . Mean field is too uniform on the Fermi surface, in contradiction with ARPES. • No proper description the incoherent regime and the coherent-incoherent and the incoherent regime.

  9. Dynamical Mean Field Theory • Map lattice model into quantum impurity problem in a self consistent medium. • The quantum impurity problem is used to generate local quantities, i.e. a local self energy. • From local quantities one reconstruct k dependent spectral functions, susceptibilities, etc. • Single site, DMFT k independent self energy (cumulant).] • Cluster extensions, incorporate additional k dpendence. • Follow different mean field states, AF, normal, supeconductor, etc as a function of parameters.

  10. CLUSTER EXTENSIONS: umbiased reduction of the many body problem to a plaquette in a medium. Reviews: Georges et.al. RMP(1996). Th. Maier, M. Jarrell, Th.Pruschke, M.H. Hettler RMP (2005); G. Kotliar S. Savrasov K. Haule O. Parcollet V. Udovenko and C. Marianetti RMP (2006) . Employ different impurity solvers. ED (Civelli Capone) CTQMC (Haule)NCA (Haule)

  11. Single site DMFT Qualitative Phase diagram of a frustrated Hubbard model at integer filling T/W Synthesis: Brinkman Rice Hubbard Castellani, C., C. DiCastro, D. Feinberg, and J. Ranninger, 1979, Phys. Rev. Lett. 43, 1957.

  12. Good description of the evolution of the spectra and transport, not too close to the Mott transition, at relatively high temperatures. For example V2O3 ( Rozenberg et. al. 1996) K-organics (Limelette et.al. 2002). • At lower temperatures, closer to the Mott transition, cluster description is necessary. • Study at low temperatures the doping driven Mott transition.

  13. The approach validates many crucial features of the RVB theory.

  14. Tunnelling DOS (NCA-tJ): Gap (distance between coherence peaks) increases with decreasing doping.

  15. Order Parameter and Superconducting Gap do not scale for large U ! ED study in the SC state Capone and GK PRB (2006) Kancharla et. al. cond-mat 0508205.

  16. CDMFT on a plaquette gives rise to a “Dynamical RVB “pictures which retains all the good features of the previous slave boson mft treatment

  17. The quasiparticle residue, decreases with doping but the effective mass (Fermi velocity) remains finite. [M. Grilli and GK] PRL (1990) • The gap in the tunneling density of states increases with decreasing doping. • The ph asymmetry grows with the approach to the Mott insulator. • Superconducting order parameter does not scale with the gap.

  18. But with substantial two differences!!! which have important consequencesa) nodal antinodal dichotomyb) vD decreses with decreasing doping in superconductor. [Two-gap picture]

  19. Nodal Antinodal Dichotomy and pseudogap. T. Stanescu and GK PRB (2006)

  20. Nodal Antinodal Dichotomy [Civelli et. al. (2007)]

  21. Follow the “normal state” with doping. Civelli et.al. PRL 95, 106402 (2005)Spectral Function A(k,ω→0)= -1/π G(k, ω→0) vs k U=16 t, t’=-.3 K.M. Shen et.al. 2004 If the k dependence of the self energy is weak, we expect to see contour lines corresponding to Ek = const and a height increasing as we approach the Fermi surface. 2X2 CDMFT

  22. Doping Driven Mott transiton at low temperature, in 2d (U=16 t=1, t’=-.3 ) Hubbard model Spectral Function A(k,ω→0)= -1/π G(k, ω→0) vs k K.M. Shen et.al. 2004 Antinodal Region 2X2 CDMFT Nodal Region Civelli et.al. PRL 95 (2005)

  23. Scaling of the || velocity in the superconductor with doping. M. Civelli et. al. cond-mat K. Haule and GK>

  24. Consequences for linear term coefficient of the penetration depth. . K. Haule and GK

  25. Experiments:two superconducing gaps, with opposite dependence on doping ? Antinodal gap increases towards the Mott insulator while vD decreases? • Coherence and single-particle excitations in the high-temperature superconductors. Guy Deutscher ,Nature 397, 410-412 (1999) Andreev reflection. • M. Opel et. al. PRB 61, 9752 (2000) Venturini, F. et al., Doping dependence of the electronic Raman spectra in Phys. Chem. Solids, 63, 2345 (2001). Raman scattering.

  26. LeTacon et. al. Two Energy Scales and two Quasiparticle Dynamics in the Superconducting . Nature Physics 2, 537 (2006)Raman scattering. . K. Tanaka, et. al Distinct Fermi-Momentum Dependent Energy Gaps in Deeply Underdoped Bi2212 . arXiv:cond-mat/0612048 . ARPES M. C. Boyer et. al. arXiv:0705.1731 . Imaging the Two Gaps of the High-TC Superconductor Pb-Bi2Sr2CuO6+x Tunnelling. arXiv:0705.0111 Spectroscopic distinction between the normal state pseudogap and the superconducting gap of cuprate high T_{c} superconductors Li Yu, et. al. .C- Axis Optical Spectrsocopy.

  27. Metodological advantages. We can follow well defined phases as a function of parameters , doping temperature. • Well defined (meta) stable states, in contrast to the old slave boson MFT approach. • CDMFT treats properly the incoherent state, with short ranged magnetic correlations.

  28. AF and superconductivity: M. Capone and GK PRB 74,054513 AFM blue dashed line with circles and dSC red solid line with squares order parameters as a function of doping for four values of the repulsion U/ t=4,8,12, and 16. The dSC order parameter is multiplied by a factor of 10 for graphical purposes.

  29. Can we continue the superconducting state towards the Mott insulating state ? For U > ~ 8t YES. For U ~ < 8t NO, magnetism really gets in the way.

  30. Evolution of the q integrated staggered spin susceptilibty K. Haule and GK (2006)

  31. Conclusions: CDMFT studies of superconductivity near a Mott insulator. Captures the essential RVB physics of the interplay of the Mott transition and superconductivity. Kinetic energy supression. Retains the good aspects of the slave boson MFT. • Solves many problems of the earlier slave boson . [e.g.doping dependence of T linear term in the penetration depth ] • Allows the continuation of spin liquid states as metastable states. Functional of local spectral functions. • Nodal Antinodal dichotomy, emerges naturally. • Work in progress. No full solution of the CDMFT eqs.and its lattice interpretation, (on the same level of single site DMFT), is available yet.

  32. Happy Birthday Carlo!!!!

  33. Temperature dependence of the arcs. doping=.09 (underdoped) Plaquette DMFT. K. Haule and GK

  34. Lines of Zeros and Spectral Shapes. Stanescu and GK cond-matt 0508302

  35. Interpretation in terms of lines of zeros and lines of poles of G T.D. Stanescu and G.K cond-matt 0508302

  36. Finite temperature view of the phase diagram :optimal doping in the t-J model.K. Haule and GK (2006)

  37. On the accuracy of CDMFT

  38. Two Site Cellular DMFT (G.. Kotliar et.al. PRL (2001))in the 1D Hubbard modelM.Capone M.Civelli V. Kancharla C.Castellani and GK PRB 69,195105 (2004)T. D Stanescu and GK PRB (2006) U/t=4. 24

  39. On the interpretation of CDMFT

  40. Doping Driven Mott transiton at low temperature, in 2d (U=16 t=1, t’=-.3 ) Hubbard model Spectral Function A(k,ω→0)= -1/π G(k, ω→0) vs k K.M. Shen et.al. 2004 Antinodal Region 2X2 CDMFT Senechal et.al PRL94 (2005) Nodal Region Civelli et.al. PRL 95 (2005)

  41. RVB phase diagram of the Cuprate Superconductors. Superexchange. • The approach to the Mott insulator renormalizes the kinetic energy Trvb increases. • Approach the Mott insulator , Z, charge stiffness , TBE=Tcoh goes to zero. M* finite. • Superconducting dome. Pseudogap evolves continously into the superconducting state. G. Kotliar and J. Liu Phys.Rev. B 38,5412 (1988) Related approach using wave functions:T. M. Rice group. Zhang et. al. Supercond Scie Tech 1, 36 (1998, Gross Joynt and Rice (1986) M. Randeria N. Trivedi , A. Paramenkanti PRL 87, 217002 (2001)

  42. Doping Driven Mott transiton at low temperature, in 2d (U=16 t=1, t’=-.3 ) Hubbard model Spectral Function A(k,ω→0)= -1/π G(k, ω→0) vs k K.M. Shen et.al. 2004 Antinodal Region 2X2 CDMFT Senechal et.al PRL94 (2005) Nodal Region Civelli et.al. PRL 95 (2005)

  43. Pseudoparticle picture

  44. How is the Mott insulatorapproached from the superconducting state ? Work in collaboration with M. Capone M Civelli O Parcollet

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