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Cluster DMFT studies of the Mott transition of Kappa Organics and Cuprates.

Cluster DMFT studies of the Mott transition of Kappa Organics and Cuprates. G. Kotliar Physics Department and Center for Materials Theory Rutgers. La Jolla San Diego May 2005. Outline.

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Cluster DMFT studies of the Mott transition of Kappa Organics and Cuprates.

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  1. Cluster DMFT studies of the Mott transition of Kappa Organics and Cuprates. G. Kotliar Physics Department and Center for Materials Theory Rutgers La Jolla San Diego May 2005

  2. Outline • Dynamical Mean Field Theory and a cluster extension, CDMFT: G.. Kotliar,S. Savrasov, G. Palsson and G. Biroli, Phys. Rev. Lett. 87, 186401 (2001) • Model for kappa organics. [O. Parcollet, G. Biroli and G. Kotliar PRL, 92, 226402. (2004)) ] • Model for cuprates [O. Parcollet (Saclay), M. Capone (U. Rome) M. Civelli (Rutgers) V. Kancharla (Sherbrooke) GK(2005).

  3. Model Hamiltonians: Hubbard model • U/t • Doping d or chemical potential • Frustration (t’/t) • T temperature

  4. Limit of large lattice coordination Metzner Vollhardt, 89 Muller-Hartmann 89

  5. Mean-Field Classical vs Quantum Classical case Quantum case A. Georges, G. Kotliar Phys. Rev. B 45, 6497(1992) Review: G. Kotliar and D. Vollhardt Physics Today 57,(2004)

  6. COHERENCE INCOHERENCE CROSSOVER T/W Phase diagram of a Hubbard model with partial frustration at integer filling.  M. Rozenberg et.al., Phys. Rev. Lett. 75, 105-108 (1995). .

  7. Medium of free electrons : impurity model. Solve for the medium using Self Consistency G.. Kotliar,S. Savrasov, G. Palsson and G. Biroli, Phys. Rev. Lett. 87, 186401 (2001)

  8. Other cluster extensions (DCA Jarrell Krishnamurthy, M Hettler et. al. Phys. Rev. B 58, 7475 (1998)Katsnelson and Lichtenstein periodized scheme. Causality issues O. Parcollet, G. Biroli and GK Phys. Rev. B 69, 205108 (2004)

  9. Benchmark :1D Hubbard ModelM. Capone, M. Civelli, S.S. Kancharla, C. Castellani, G. Kotliar,Phys. Rev B 69, 195105 (2004) H= -t ∑jσ c†jσcj+1σ+ h.c +U ∑ nj↑ nj↓ -μ N U= 4 t Exact Bethe Ansatz (BA) VS Dynamical Mean Field Theory VS Cellular Dynamical Mean Field Theory (2 site cluster only!)

  10. Mott transition in layered organic conductors S Lefebvre et al. cond-mat/0004455, Phys. Rev. Lett. 85, 5420 (2000)

  11. modeled to triangular lattice modeled to triangular lattice t t t’ t’ k-(ET)2X are across Mott transition ET = Insulating anion layer X-1 conducting ET layer [(ET)2]+1

  12. Single-site DMFT as a zeroth order picture ?

  13. Finite T Mott tranisiton in CDMFT Parcollet Biroli and GK PRL, 92, 226402. (2004))

  14. Evolution of the spectral function at low frequency. If the k dependence of the self energy is weak, we expect to see contour lines corresponding to t(k) = const and a height increasing as we approach the Fermi surface.

  15. Evolution of the k resolved Spectral Function at zero frequency. (QMC study Parcollet Biroli and GK PRL, 92, 226402. (2004)) ) U/D=2.25 U/D=2 Uc=2.35+-.05, Tc/D=1/44. Tmott~.01 W

  16. Momentum Space Differentiation the high temperature story T/W=1/88

  17. CDMFT study of cuprates . • Allows the investigation of the normal state underlying the superconducting state, by forcing a symmetric Weiss function, we can follow the normal state near the Mott transition. • Earlier studies (Katsnelson and Lichtenstein, M. Jarrell, M Hettler et. al. Phys. Rev. B 58, 7475 (1998). T. Maier et. al. Phys. Rev. Lett 85, 1524 (2000) ) used QMC as an impurity solver and DCA as cluster scheme. • We use exact diag ( Krauth Caffarel 1995 with effective temperature 32/t=124/D ) as a solver and Cellular DMFT as the mean field scheme.

  18. Superconductivity in the Hubbard model role of the Mott transition and influence of the super-exchange. (M. Capone V. Kancharla. CDMFT+ED, 4+ 8 sites t’=0) .

  19. D wave Superconductivity and Antiferromagnetism t’=0 M. Capone V. Kancharla (see also VCPT Senechal and Tremblay ). Antiferromagnetic (left) and d wave superconductor (right) Order Parameters

  20. Follow the “normal state” with doping. Evolution of the spectral function at low frequency. 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.

  21. Hole doped case t’=-.3t, U=16 t n=.71 .93 .97 Color scale x= .37 .15 .13

  22. K.M . Shen et. al. Science (2005). For a review Damascelli et. al. RMP (2003)

  23. Approaching the Mott transition: CDMFT Picture • Qualitative effect, momentum space differentiation. Formation of hot –cold regions is an unavoidable consequence of the approach to the Mott insulating state! • D wave gapping of the single particle spectra as the Mott transition is approached. • Similar scenario was encountered in previous study of the kappa organics. O Parcollet G. Biroli and G. Kotliar PRL, 92, 226402. (2004) .

  24. CDMFT one electron spectra n=.96 t’/t=.-.3 U=16 t • i

  25. Experiments. Armitage et. al. PRL (2001).Momentum dependence of the low-energy Photoemission spectra of NCCO

  26. Approaching the Mott transition: CDMFT picture. • Qualitative effect, momentum space differentiation. Formation of hot –cold regions is an unavoidable consequence of the approach to the Mott insulating state! • General phenomena, BUT the location of the cold regions depends on parameters. • Quasiparticles are now generated from the Mott insulator at (p, 0). • Results of many numerical studies of electron hole asymmetry in t-t’ Hubbard models Tohyama Maekawa Phys. Rev. B 67, 092509 (2003) Senechal and Tremblay. PRL 92 126401 (2004) Kusko et. al. Phys. Rev 66, 140513 (2002)…………

  27. To test if the formation of the hot and cold regions is the result of the proximity to Antiferromagnetism, we studied various values of t’/t, U=16.

  28. Introduce much larger frustration: t’=.9t U=16tn=.69 .92 .96

  29. Approaching the Mott transition: • Qualitative effect, momentum space differentiation. Formation of hot –cold regions is an unavoidable consequence of the approach to the Mott insulating state! • General phenomena, but the location of the cold regions depends on parameters. • With the present resolution, t’ =.9 and .3 are similar. However it is perfectly possible that at lower energies further refinements and differentiation will result from the proximity to different ordered states.

  30. Evolution of the real part of the self energies.

  31. Fermi Surface Shape Renormalization ( teff)ij=tij+ Re(Sij(0))

  32. Fermi Surface Shape Renormalization • Photoemission measured the low energy renormalized Fermi surface. • If the high energy (bare ) parameters are doping independent, then the low energy hopping parameters are doping dependent. Another failure of the rigid band picture. • Electron doped case, the Fermi surface renormalizes TOWARDS nesting, the hole doped case the Fermi surface renormalizes AWAY from nesting. Enhanced magnetism in the electron doped side.

  33. Qualitative Difference between the hole doped and the electron doped phase diagram is due to the underlying normal state.” In the hole doped, it has nodal quasiparticles near (p/2,p/2) which are ready “to become the superconducting quasiparticles”. Therefore the superconducing state can evolve continuously to the normal state. The superconductivity can appear at very small doping. • Electron doped case, has in the underlying normal state quasiparticles leave in the (p, 0) region, there is no direct road to the superconducting state (or at least the road is tortuous) since the latter has QP at (p/2, p/2).

  34. Understanding the result in terms of cluster self energies (eigenvalues)

  35. Systematic Evolution

  36. Understanding the location of the hot and cold regions.

  37. How is the Mott insulatorapproached from the superconducting state ? Work in collaboration with M. Capone

  38. Evolution of the low energy tunneling density of state with doping. Decrease of spectral weight as the insulator is approached. Low energy particle hole symmetry.

  39. Alternative view

  40. Conclusions • DMFT is a useful mean field tool to study correlated electrons. Provide a zeroth order picture of a physical phenomena. • Provide a link between a simple system (“mean field reference frame”) and the physical system of interest. [Sites, Links, and Plaquettes] • Formulate the problem in terms of local quantities (which we can usually compute better). • Allows to perform quantitative studies and predictions . Focus on the discrepancies between experiments and mean field predictions. • Generate useful language and concepts. Follow mean field states as a function of parameters.

  41. Conclusions • Qualitative effect, momentum space differentiation. Formation of hot –cold regions is an unavoidable consequence of the approach to the Mott insulating state! • General phenomena, but the location of the cold regions depends on parameters. Study the “normal state” of the Hubbard model is useful. • On the hole doped normal and superconducting state can be connected to each other as in the RVB scenario. High Tc superconductivity may result follow from doping a Mott insulator phase but it is not necessarily follow from it. One may not be able to connect the Mott insulator to the superconductor if the nodes are in the “wrong place”.

  42. Comparison with Experiments in Cuprates: Spectral Function A(k,ω→0)= -1/π G(k, ω→0) vs k hole doped electron doped P. Armitage et.al. 2001 K.M. Shen et.al. 2004 2X2 CDMFT Civelli et.al. 2004

  43. Unfortunately the Hubbard model does not capture the trend of supra with t’. Need augmentation.

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