1. U Si Ru Hidden Order in URu2Si2: can we now solve this riddle ? Gabriel Kotliar Work in collaboration with Kristjan Haule K. Haule and G. Kotliar EPL 89 57006(2010) K. Haule and G. Kotliar Nat Phys 5:637‐641(2009) Recent work with A. Toth 1 At the Informal Seminaire Physique Quantique Hors Equilibrium Paris Tuesday Sept 21 (2010)

2. URu2Si2: a typical problem in the theory of correlated electron materials A non-historical review of some important experimental facts about URu2Si2. URu2Si2 a good test of the LDA+ DMFT strategy. New insights into a very old problem. Comparison with some experiments Revisiting experiments in dilute systems. Outlook and Conclusions : key open questions and some more general perspectives on strongly correlated materials. 2

3. Dynamical Mean Field Theory. Cavity Construction. A. Georges and G. Kotliar PRB 45, 6479 (1992). A(  ) 10

4. 8 atomic levels Quantifying the degree of localization/delocalization Impurity Solver Machine for summing all local diagrams in PT in U to all orders.

5. 12 DMFT picture. Atom in a medium obeying a self consistency condition, Impurity Model. Simplified reference frame for describing correlated solids New concepts, more precise language to quantify the degree of itineracy. Generalizations to cluster and to realistic modelling of materials Many technical advances over the past decade. Dynamical Mean Field Picture A. Georges and G. Kotliar PRB 45, 6479 (1992).

6. Determine energy and and  self consistently from extremizing a functional : the spectral density functional. Chitra and Kotliar (2001). Savrasov and Kotliar (2001) Full self consistent implementation. Review: Kotliar et.al. RMP (2006) Determine energy and and  self consistently from extremizing a functional : the spectral density functional. Chitra and Kotliar (2001). Savrasov and Kotliar (2001) Full self consistent implementation. Review: Kotliar et.al. RMP (2006) 12 Spectra=- Im G(k,  ) LDA+DMFT. V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). Lichtenstein and Katsnelson (1998) LDA++

7. Main DMFT Concepts in electronic structure. Valence Histograms. Describes the Probability of finding the correlated site in the solid in a given atomic state J. H. Shim, K. Haule, and G. Kotliar, Nature London 446, 513 (2007). Weiss Weiss field, collective hybridization function, quantifies the degree of localization Functionals of density and spectra, total energies: spectral density functional. Local Self Energies and Correlated Bands Orbitally Resolved Spectral Functions Transfer of spectral weight. Review: Realistic DMFT. Rev. Mod. Phys. G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, and C. A. Marianetti Rev. Mod. Phys. 78,865 (2006). 13

8. Tunnelling: Orbitally resolved DOS High temperature. Fano-shapes first observed by S. Davis group spd DOS small changes only f DOS is gapped [no Kondo peak!!] Kondo effect arrested by the splitting of the two singlets (which is the consequence of the bare small crystal field and the hexadecapolar order ). Single particle gap~7 mev Just like T 0, it should decrease with increasing magnetic field. [ prediction] Notice BCS-like coherence peaks in f DOS when hidden order gap forms. K. Haule and G. Kotliar Nat Phys 5:637‐641(2009) 14

9. URu2Si2: DMFT allows two broken translational symmetry states at low T Moment free phase: Large moment phase: tetragonal symmetry broken-> these terms nonzero Density matrix for U 5f state the J=5/2 subspace J=5/2 15

10. f 2, “Kondo “ limit, Hunds. S=1, L=5, J=4. Crystal fields two low lying singlets Therefore there are two singlets relevant at low energies but they are not non Kramer doublets. Conspiracy between cubic crystal field splittings and tetragonal splittings bring these two states close. This is why only URu2Si2 is different from thousands of U based heavy fermions. Does not arise in one particle crystal field scheme. It is not forced by symmetry.. URu2Si2 Valence histogram. Under reflections x  -x or y  -y (x+iy) 4  (x-iy) 4 [0>  - [0> (odd ) and [1>  [1> (even) J=4 16

11. Order parameter: Different orientation gives different phases: “adiabatic continuity” explained! In the atomic limit: DMFT order parameter. Approximate X-Y symmetry Does not break the time reversal, nor C4 symmetry. It breaks inversion symmetry. Moment only in z-direction! X 01 =[0><1] 17

12. XY-Ising crystal field: z direction Magnetic moment: y-direction Hexadecapole: x-direction A toy model The two broken symmetry states 18

13. Mean field Exp. by E. Hassinger et.al. PRL 77, 115117 (2008) HO & AFM in magnetic field Only four fitting parameters: J eff 1, J eff 2 determined by exp. transition temperature, and pressure dependence. Notice that T 0 decreases with Increasing magnetic field but mangetic field stabilizes hidden order. 19

14. Key experiment: Neutron scattering The low energy resonance A.Villaume, F. Bourdarot, E. Hassinger, S. Raymond, V. Taufour, D. Aoki, and J. Flouquet, PRB 78, 012504 (2008) 20

15. hexadecapole Goldstone mode Symmetry is approximate “Pseudo-Goldstone” mode Fluctuation of m - finite mass The exchange constants J are slightly different in the two phases (~6%) AFM moment AFM moment “Pseudo Goldstone” mode Interpretation of Neutron scattering experiments K. Haule and G. Kotliar EPL 89 57006(2010) 21

16. Contrast this with the tunnelling gap, or the optical gap or the gap in the neutron scattering at (1.4,0,0) which decreases with incresing magnetic field. 22

17. Fermi surface nesting, Reconstruction below Tc 2 incommensurate peaks (0.6,0,0), (1.4,0,0) Nesting 0.6a* and 1.4a* T>T 0 T<T 0 Wiebe et.al. 2008 Fermi surface reconstruction 23

18. 24

19. Visualizing the Formation of the Kondo Lattice and the Hidden Order in URu2Si2 Pegor Aynajian, Eduardo H. da Silva Neto, Colin V. Parker, Yingkai Huang, Abhay Pasupathy, John Mydosh, Ali Yazdani Pegor AynajianEduardo H. da Silva NetoColin V. ParkerYingkai HuangAbhay Pasupathy John MydoshAli Yazdani arXiv:1003.5259arXiv:1003.5259 [pdf]pdf 25

24. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Functional formulation. Chitra and Kotliar Phys. Rev. B 63, 115110 (2001) Ambladah et. al Int. Jour Mod. Phys. B 13, 535 (1999). Ir>=|R,  > Double loop in Gloc and Wloc

25. Full implementation in the context of a a one orbital lattice model. P Sun and G. Kotliar Phys. Rev. B 66, 85120 (2002). After finishing the loop one can treat the graphs involving Gnonloc Wnonloc in perturbation theory.. Phys. Rev. Lett. 92, 196402 (2004) Limiting case (perturbation theory as solvers) Zeyn and Antropov. N. E. Zein and V. P. Antropov, J. Appl. Phys. 89, 7314 (2001), Phys. Rev. Lett. 89, 126402 (2002) Application to semiconductors N. Zeyn S. Savrasov and G. Kotliar PRL 96, 226403, 2006 EDMFT loop Chitra and Kotliar Phys. Rev. B 63, 115110 (2001). G. Kotliar and S. Savrasov in New Theoretical Approaches to Strongly Correlated Systems, A. M. Tsvelik Ed. 2001 Kluwer Academic Publishers. 259-301. cond-mat/0208241 S. Y. Savrasov, G. Kotliar, Phys. Rev. B 69, 245101 (2004)

26. Determine energy and and  self consistently from extremizing a functional : the spectral density functional. Chitra and Kotliar (2001). Determine energy and and  self consistently from extremizing a functional : the spectral density functional. Chitra and Kotliar (2001). R. Chitra and G. Kotliar, Phys. Rev. B 63, 115110 Savrasov and Kotliar (2001) Full self consistent implementation. Review: Kotliar et.al. RMP (2006) (2001). Savrasov and Kotliar (2001) Full self consistent implementation. Review: Kotliar et.al. RMP (2006) 12 LDA+DMFT. V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). U is parametrized in terms of Slater integrals F0 F2 F4 ….

27. Effective interaction among electrons. Constrained RPA (cRPA) Ferdi Ariasetiwan,A, M Imada, A Georges, G Kotliar, S Biermann, AI Lichtenstein, PRB 70, 195104 (2004) energy-dependent effective interaction between the 3d electrons Can be used to extract a screened U Identity:

28. J.H.Shim, KHaule, G.Kotliar,Science 318, 1615 (2007) ‏ Protracted screening and multiple hybridization Gaps in Ce115’s. K. Burch et.al. Quasiparticle multiplets in Plutonium and its Compounds. J.H.Shim, KHaule, G.Kotliar, Nature 446, 513 (2007). Hidden Order in URu2Si2, Kondo effect and hexadecapole order. KHaule,andG. Kotliar, Nature Physics 5, 796 - 799 (2009). Strong Correlations without high energy satellites in Ba Fe2As2 Origin of the particle-hole assymetry between LaSrCuO4 and NdCuO4 C. Weber K Haule and G. Kotliar submitted to Nature Physics A. Kutepov K. Haule S. Savrasov and G. Kotliar to be submitted to PRL 36