The Mott transition across the actinide series and the double life of delta Plutonium.

1. The Mott transition across the actinide series and the double life of delta Plutonium. Gabriel Kotliar and Center for Materials Theory

2. OUTLINE The challenge of strongly correlated electron systems. Late actinides: experimental overview Introduction to Dynamical Mean Field Theory (DMFT). Theory of delta Pu Theory of Am and Cm Conclusions

3. Electrons in a Solid:the Standard Model Framework is reiigorous and predictive. BANDS AT THE FERMI LEVEL--? Metal No bands at the fermi level insulator. Wave metals are NOT very resistive. Thermodynamics, cv chi hall coefficient etc.. As free electrons. KEY Framework is reiigorous and predictive. BANDS AT THE FERMI LEVEL--? Metal No bands at the fermi level insulator. Wave metals are NOT very resistive. Thermodynamics, cv chi hall coefficient etc.. As free electrons. KEY

4. Spectral Function Photoemission and correlations Probability of removing an electron and transfering energy w=Ei-Ef, and momentum k f(w) A(w, K) M2

5. Strong Correlation Problem:where the standard model fails Fermi Liquid Theory works but parameters can�t be computed in perturbation theory. Fermi Liquid Theory does NOT work . Need new concepts to replace of rigid bands ! Partially filled d and f shells. Competition between kinetic and Coulomb interactions. Breakdown of the wave picture. Need to incorporate a real space perspective (Mott). Non perturbative problem.

6. Strongly correlated systems Copper Oxides. High Temperature Superconductivity. Cobaltates Anomalous thermoelectricity. Manganites . Colossal magnetoresistance. Heavy Fermions. Huge quasiparticle masses. 2d Electron gases. Metal to insulator transitions. Lanthanides, Transition Metal Oxides, Multiferroics������.. Get tokura osgawara PRL, and the science express, and ando prl , and formula units. Theory will play an important role in optimizing their physical properties Ando et. Al. Phys. Rev. B 60, 10580-10583 (1999). Ogasawara Phys. Rev. Lett. 85, 2204 (2000) Get tokura osgawara PRL, and the science express, and ando prl , and formula units. Theory will play an important role in optimizing their physical properties Ando et. Al. Phys. Rev. B 60, 10580-10583 (1999). Ogasawara Phys. Rev. Lett. 85, 2204 (2000)

8. Localization Delocalization in Actinides

9. Basic Questions How does the electron go from being localized to itinerant. How do the physical properties evolve. How to bridge between the microscopic information (atomic positions) and experimental measurements. New concepts, new techniques

10. Phases of Pu (A. Lawson LANL) The main characters alpha, ground state monoclinic. Delta fcc negative thermal expansion. Epsilon bcc smaller than delta. Contracts in the liquid. Gigantic volume changes. < Volume collapse, bigger than cerium>The main characters alpha, ground state monoclinic. Delta fcc negative thermal expansion. Epsilon bcc smaller than delta. Contracts in the liquid. Gigantic volume changes. < Volume collapse, bigger than cerium>

12. Small amounts of Ga stabilize the d phase (A. Lawson LANL) Extraordinary sensitivity to impurities. Focus on delta mostly. Important for applications, ductile, stable. Any element (except Np stabilizes it) bigger or smaller.Extraordinary sensitivity to impurities. Focus on delta mostly. Important for applications, ductile, stable. Any element (except Np stabilizes it) bigger or smaller.

13. Anomalous Resistivity Apply the standard model to Pu, runs into problems. Certainly for delta.Apply the standard model to Pu, runs into problems. Certainly for delta.

14. Specific heat and susceptibility. Pu is non magnetic Localized picture, starting point for f electrons in UBe 13. Heavy fermion behavior. Combining the two models. High temperature localized. Low temperature band like. Difficult crossover. Pu is heavy but NOT magnetic. Discuss susceptiblity puzzle. Polarized neutron scattering. No magnetic scattering. Localized picture, starting point for f electrons in UBe 13. Heavy fermion behavior. Combining the two models. High temperature localized. Low temperature band like. Difficult crossover. Pu is heavy but NOT magnetic. Discuss susceptiblity puzzle. Polarized neutron scattering. No magnetic scattering.

15. Standard model fails for the late actinides Predicts all the phases of Pu and Am to be magnetic, with a large moment. (about 5 mB) Imposing paramagnetism, DFT fails to describe the volume of delta Pu by 25 % Many modfications have been attempted, to explain why Pu is non magnetic. Mixed level model (Wills et. al. ) Pu has (5f)4 conf. LDA+U amf (Shick, Anisimov) Pu has (5f)5 Cannot account for anomalous elastic properties, transport and thermodynamics

16. DMFT A. Georges and G. Kotliar PRB 45, 6479 (1992). Happy marriage of atomic and band physics. Extremize functional of A(w)

17. Dynamical Mean Field Theory Weiss field is a function. Multiple scales in strongly correlated materials. Exact large coordination (Metzner and Vollhardt 89) , kinetic vs interaction energy Immediate extension to real materials DFT+DMFT Functionals of density and spectra. Review Kotliar et. al. RMP (2006)

18. Different way of thinking was generated by the study of the Mott transition at integer filling. Universality and system specificity. . Bridge atomic physic and band physics. Crossovers with changing degrees of freedom. Different way of thinking was generated by the study of the Mott transition at integer filling. Universality and system specificity. . Bridge atomic physic and band physics. Crossovers with changing degrees of freedom.

19. Volume Collapse Transitions: relaxing the lattice positions. Savrasov et. al.

20. Phonon freq (THz) vs q in delta Pu X. Dai et. al. Science vol 300, 953, 2003

21. Inelastic X Ray. Phonon energy 10 mev, photon energy 10 Kev.

22. Notice the agreement. Usefulness of theory. Notice the discreapancy. Scientfici opportunity. Notice the agreement. Usefulness of theory. Notice the discreapancy. Scientfici opportunity.

23. The �DMFT-valence� in the late actinides.

25. 2/3<l.s> in the late actinides [DMFT results: K. Haule and J. Shim ]

27. Photoemission Spectra[ Shim. Haule,GK Nature (2007)]

28. Photoemission and Mixed valence in Pu

29. Conclusions Unique properties of Pu and Am under pressure result from a proximity of a localization delocalization transition. Rare form of mixed valence. DMFT provides a good start. Qualitative insights, some quantitative predictions into delta Pu. Other Pu phases. Meaningful interplay of theory and experiment. Key in condensed matter physics.

30. Conclusions Pu is a unique strongly correlated element. It is one among many strongly correlated electron system, materials for which neither the standard model of solids, works well. They require, new concepts, new computational methods, new algorithms, DMFT provides all of the above, and is being used in many other problems. Many applications to othe problems exist, others are in progress, research opportunity in correlated materials.

33. Am equation of state. LDA+DMFT.New acceleration technique for solving DMFT equations S. Savrasov K. Haule G. Kotliar cond-mat. 0507552 (2005)

34. Mott transition in open (right) and closed (left) shell systems. Superconductivity ? Localized (5f)6 in L.S coupling or jj coupling ?

36. Photoemission spectra using Hubbard I solver and Sunca . [Savrasov Haule and Kotliar cond-mat 0507552 PRL (2006)] Hubbard bands width is determined by multiplet splittings.

38. Photomission Spectra of Am under pressure. Sunca. Onset of mixed valence. Savrasov Haule Kotliar (2005) PRL (2006)

39. Conclusion Am Americium undergoes Mott transition under pressure. [AmIII-AmIV] boundary. Unusual superconductivity and resistivities. Theoretical clue mixed valent due to admixture of (5f) upon application of pressure. Realizes Mott transition from the insulating side, towards a close shell configuration..

43. K.Haule and J. Shim Trends in Actinides

44. Conclusion DMFT conceptual framework to think about electrons in solids. Finite T Mott transition in 3d . Single site DMFT worked well! Ab-initio many body electronic structure of solids. Building theoretical spectroscopies. Frontier, cuprates, lower T, two dimensionality is a plaquette in a medium enough? Inhomogenous structure in correlated materials New renormalizaton group methods built around DMFT ?

45. Conclusion A Few References �� A.Georges, G. K., W. Krauth and M. J. Rozenberg, Reviews of . Modern Physics 68, 13 (1996). G. K, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, C.A. Marianetti, RMP 78, 865-951, (2006). G. K and D. Vollhardt Physics Today, Vol 57, 53 (2004).

46. Conclusions Constant interplay between theory and experiment has lead to new advances. General anomalies of correlated electrons and anomalous system specific studies, need for a flexible approach. (DMFT). New understanding of Pu. Methodology applicable to a large number of other problems, involving correlated electrions, thermoelectrics, batteries, optical devices, memories, high temperature superconductors, ��..

47. Conclusions DMFT produces non magnetic state, around a fluctuating (5f)^5 configuraton with correct volume the qualitative features of the photoemission spectra, and a double minima structure in the E vs V curve. Correlated view of the alpha and delta phases of Pu. Interplay of correlations and electron phonon interactions (delta-epsilon). Calculations can be refined in many ways, electronic structure calculations for correlated electrons research program, MINDLAB, �.

48. What do we want from materials theory? New concepts , qualitative ideas Understanding, explanation of existent experiments, and predictions of new ones. Quantitative capabilities with predictive power. Notoriously difficult to achieve in strongly correlated materials.

49. Some new insights into the funny properties of Pu Physical anomalies, are the result of the unique position of Pu in the periodic table, where the f electrons are near a localization delocalization transition. We learned how to think about this unusual situation using spectral functions. Delta and Alpha Pu are both strongly correlated, the DMFT mean field free energy has a double well structure, for the same value of U. One where the f electron is a bit more localized (delta) than in the other (alpha). Negative thermal expansion, multitude of phases.

50. Quantitative calculations Photoemission spectra,equilibrium volume, and vibration spectra of delta. Good agreement with experiments given the approximations made.Many systematic improvements are needed. Work is at the early stages, only a few quantities in one phase have been considered. Other phases? Metastability ? Effects of impurities? What else, do electrons at the edge of a localization localization do ? [ See epsilon Pu spectra ]

51. Collaborators, Acknowledgements References Collaborators: S. Savrasov ( Rutgers-NJIT) X. Dai ( Rutgers), E. Abrahams (Rutgers), A. Migliori (LANL),H Ledbeter(LANL). Acknowledgements: G Lander (ITU) J Thompson(LANL) Funding: NSF, DOE, LANL.

52. Cluster DMFT: removes limitations of single site DMFT

53. Two Site Cellular DMFT (G.. Kotliar et.al. PRL (2001)) in the 1D Hubbard model M.Capone M.Civelli V. Kancharla C.Castellani and GK PRB 69,195105 (2004)T. D Stanescu and GK PRB (2006) Edit. LISA.Edit. LISA.

54. Framework is reiigorous and predictive. BANDS AT THE FERMI LEVEL--? Metal No bands at the fermi level insulator. Wave metals are NOT very resistive. Thermodynamics, cv chi hall coefficient etc.. As free electrons. KEY Framework is reiigorous and predictive. BANDS AT THE FERMI LEVEL--? Metal No bands at the fermi level insulator. Wave metals are NOT very resistive. Thermodynamics, cv chi hall coefficient etc.. As free electrons. KEY

55. Smith Kmeko Phase diagram. Minimum in melting curve and divergence of the compressibility at the Mott endpoint

56. The enhancement of the specific heat, further evidence for an open shell configuration, presence of electronic entropy.

57. Double well structure and d Pu Qualitative explanation of negative thermal expansion[Lawson, A. C., Roberts J. A., Martinez, B., and Richardson, J. W., Jr. Phil. Mag. B, 82, 1837,(2002). G. Kotliar J.Low Temp. Physvol.126, 1009 27. (2002)]

58. �Invar model � for Pu-Ga. Lawson et. Mag. Vol. 86, Nos. 17�18, 11�21 June 2006, 2713�2733(2006) Data fits if the excited state has zero stiffness.

59. Dynamical Mean Field Theory. Cavity Construction. A. Georges and G. Kotliar PRB 45, 6479 (1992).

60. Animate, and expand.Animate, and expand.

61. Expt. Wong et. al.

62. Elastic Deformations 1 Pa= 10 dyn/cm^2 , others gamma Ce c44/c�=2.8, La = 4.1, Th 3.6 find out about alpha cerium. From Kittel U=1/2 C11 ( exx^2 + eyy^2 +ezz^2)+ � c44 (eyz^2 +ezx^2+exy^2)+ C12(eyy ezz+ ezz exx +exx eyy). And exx=dux/dx and exy=duy/dx+dux/dy B= 1/3(c11+2 c12) C�= c11-c121 Pa= 10 dyn/cm^2 , others gamma Ce c44/c�=2.8, La = 4.1, Th 3.6 find out about alpha cerium. From Kittel U=1/2 C11 ( exx^2 + eyy^2 +ezz^2)+ � c44 (eyz^2 +ezx^2+exy^2)+ C12(eyy ezz+ ezz exx +exx eyy). And exx=dux/dx and exy=duy/dx+dux/dy B= 1/3(c11+2 c12) C�= c11-c12

64. Localization Delocalization in Actinides

66. Spectral Function and Photoemission Probability of removing an electron and transfering energy w=Ei-Ef, and momentum k f(w) A(w, K) M2

67. Framework is reiigorous and predictive. BANDS AT THE FERMI LEVEL--? Metal No bands at the fermi level insulator. Wave metals are NOT very resistive. Thermodynamics, cv chi hall coefficient etc.. As free electrons. KEY Framework is reiigorous and predictive. BANDS AT THE FERMI LEVEL--? Metal No bands at the fermi level insulator. Wave metals are NOT very resistive. Thermodynamics, cv chi hall coefficient etc.. As free electrons. KEY

68. W110 =2/3<l.s> and banching ratio