1.   Cluster Dynamical Mean Field Theory of the Copper Oxide Based Materials\
Gabriel Kotliar
Collaborators:
Kristjan Haule , Chuck Yee, Cedric Weber
Strongly correlate electron systems, are materials which keep suprirising our imagination. Completely
Unexpectedly, and thru an almost random search in the space of materials, fishing the Fermi sea,
Materials scientits kept discovering treasures, including heavy fermions, colossal magentio-resistance and high temperaturesupeconductors based on copper oxide and more recently iron pnictides. In this talk I will tell you about a theoreticla
Development, that helps understand and one day will help predict materials with extrordinary propretiesl
ICAM Workshop on New Frontiers in the Phyiscs of Two Diimensional Electron Systems. Buenos Aires November (2011) 1

2. Correlated Superconductivity
Order parameter transforms according to non trivial representation of the symmetry group of the crystal. K dependence.
Higher energy scales are involved. Fermi liquid state has not been reached, near Tc optimal.
Cluster DMFT, a natural generalization of the ME theory.
Model Hamiltonian: identify common features
System Specific Calculations: identify materials trends. 2

3. DMFT strategy and Correlated Superconductivity
Superconductivity in “simple” materials: Fermi liquid description of the normal state +residual interaction among quasiparticles
Correlated electron materials. NEEDED: reference frame to access incoherent (bad)metallic states
NEEDED: Bridge between atomic information and physical and spectroscopical properties. [Structure-property relation]
MFT divides the problem into two separate parts: a) obtaining different mean field solutions and b) evaluating their energies
. MFT provides useful concepts
MFT allows you to follow a “state” as you vary parameters.
MFT Compares different “states” of the system for the same value of parameters.  Understand “Mechanism”
MFT Separates what can be understood in models from what requires more realistic treatment. .
DMFT strategy and Correlated Superconductivity 3 3

4. D Dynamical Mean Field Theory 4
Maps solid to an effective quantum impurity model
DMFT sumps up all local diagrams
(to all orders in perturbation theory) D
LDA+DMFT
Cluster DMFT

5. Momentum Space Picture
Link +Plaquette as reference frame
Emergent low energy particle hole symmetry ! 5
Real Space Picture
T=| ↑, ↑ >
1+= 1/√2(|0, ↑> + | ↑, 0>)
E=|0, 0>
S=1/√2( | ↑, ↓> -| ↑↓ >)
Holes in a sea of singlets
Stanescu, T. D., and P. Phillips,PRL 91, (2003)
QCP K. Haule and GK
PRB 76, (2007).
Fermi Liquid
OSMT Ferrero et. al.
Phys. Rev. B 80, (2009)
Momentum Space Picture
Overdoped
Underdoped

6. As the apical oxygen is pulled out of the plane Tcmax goes UP!7
Phys. Rev. Lett. 87, (2001)
As the apical oxygen is pulled out of the plane Tcmax goes UP! 11

7. Theoretical issues with Andersen’s proposal.
Within Slave Boson MFT, t-J model. Tcmax decreases as t’ /t increases.
Within Hubbard model cluster DMFT studies of superconductivity Tcmax decreases as t’/t increases. In many studies, for example in CDMFT
Earlier DMRG for ladders, White and Scalapino reached identical conclusion. 7

8. Larger t’/t than cuprates but no Tc8

9. M. Greenblatt’s group (Rutgers)
Magnetic Transition is observed in trilayer compoudn
Alternative view, Viktor Paardo and Warren Pickett. 9

10. New Proposal: C. Weber C. Yee K. Haule GK cond-mat arXiv:1108.3028
The main effect of the distance of the apical oxygen to the plane is to control the charge transfer gap: ed-ep
Moving the apical oxygen away from te plane ALSO increases tpp’ as Andersen pointed out. But the increase of tpp’ is detrimental to Tc.
Moving the apical oxygen away from the plane reduces the charge transfer gap and increases Tc.
Backed up by LDA+DMFT calculations using LDA+DMFT in the LAPW and using a downfolding method with the same value of Edc for all materials 10

11. Correlations: deriving the starting Hamiltonian to do LDA+DMFT gives parameters.11

12. Increasing tpp’ hurts Tc
Causation: Reducing ed-ep helps Tc (pushing apical away from the plane)
Increasing tpp’ hurts Tc
Moving the apical oxygen away form the plane reduces ed-ep but also increases tpp’ . We believe the reduction of ep-ed is dominant. 12

13. Damascelli et. al. RMP(2010) Armitage Fournier and Greene RMP(2003)13

14. Building phase diagram magnetization at T=0 vs d.
Single site
Two site 14

15. Origin of magnetism :Comparing the AF and the “underlying PM state “
<KE>sdw -<KE>pm
Weber Haule and GK Nature Physics 10, 1038 (2010).
NCCO magnetizes to lower its double occupancy ! Slater.
LSCO gains kinetic energy when it magnetizes. [Mott ] NCCO pays kinetic energy [Slater ]
Can be traced to the structure: absence of apical oxygens reduces the charge transfer energy 15

16. N. Bontemps, R. P. S. M. Lobo and A. F
N. Bontemps, R.P.S.M. Lobo and A.F. Santander-Syro,Annals of Physics, 326, 1547 (2006)
Overdoped
Underdoped
PCCO
BSCO 16

17. And back to the d9 nickelates
Chuck Ye e et. al. 17

18. Thanks for your attention!
References.
C.Weber, K.Haule, G.Kotliar Nature Phys. 6, 574 (2010).
arXiv: Cédric Weber, Chuck-Hou Yee, Kristjan Haule, Gabriel Kotliar
Chuck Yee et al in preparation 18

20. Effective Hoppings

23. Hubbard model : plaquette in a medium.
Lichtenstein and Kastnelson PRB (2000) 16

24. Momentum Space Picture: High T
Link DMFT. Normal state Real Space Picture. Ferrero et. al. (2010) (similar to plaquette Haule and GK) (2006)
Singlet formation. S (singlet),T (triplet) N=2 singlet, triplet
E (empty) N=0
1+ states with 1 electron in + orb
Momentum Space Picture: High T
Underdoped region: arcs shrink as T is reduced. Overdoped region FS sharpens as T is reduced. 17

25. Optimal doping: Coherence scale seems to vanish
underdoped
scattering
at Tc
optimally
overdoped Tc
Particle hole symmetry is restored at critical point. Orbital selective Mott Transition.

26. Ex= Jij(< Si. Sj >s- < Si . Sj>n)/t
Superexchange Mechanism? . K. Haule and GK Phys. Rev. B 76, (2007).
Reminiscent of PW Anderson RVB Science 235, 1196 (1987) and slave boson picture G. Kotliar and J. Liu P.RB 38,5412 (1988)
Ex= Jij(< Si. Sj >s- < Si . Sj>n)/t
How is the energy distributed in q and w ?
D.J. Scalapino and S.R. White, Phys. Rev. B 58, 8222 (1998).
Expts; Dai et.al. 18

27. Weber Yee Haule GK cond-mat

28. Phys. Rev. Lett. 87, (2001)

29. Reducing ed=ep helps Tc
Increasing tpp’ hurts Tc
Moving the apical oxygen reduces ed-ep but also incrases tpp’

30. Realistic DMFT as a conceptual tool and a computational tool
DMFT (simple yet accurate ? ) reference frame to think about electrons in solids and compute their properties.
Compare different “states” of the system for the same value of parameters.  Understand Mechanism for ordering , magnetic, superconducting, exotic, ……….
Bridge between atomic information and physical and spectroscopical properties. [Structure-Property relation Learning --> Design ? ]
Qualitative and quantitative system specific results gives us confidence in the method. Many examples (sp, 3d,4d, 5d, 4f, 5f…)
NEEDED: improvments in obtaning and understanding the solutions of the DMFT euqations. Fluctuations around DMFT> 23

31. Optical Spectral Weights in LSCO and NCCO (up to 1.5 ev)
Cedric Weber, Kristjan Haule, Gabriel Kotliar Nature Physics 10, 1038 (2010). Comanac et. al. Nature PhysicsNature Phys. 4, 287290 (2008). 20

32. Cuprates Superconductors
Plaquette DMFT reasonable reference frame to think about the qualitative physics of cuprates, starting from high temperatures.
High Tc materials. are near the single site DMFT Mott boundary. LSCO more correlated than NCCO, role of apical oxygens.
High temperature superconductivity occurs in the region where neither wave/itinerant nor localized/ particle picture fully applies. 22

33. Cuprates : fundamental questions Mechanism of Superconductivity
Quasiparticles glued by spin fluctuations.
Predicted d-wave symmetry of order parameter . D. Scalapino , D. Pines
K >
-K>
SC emerges from doping RVB paired spins in Mott insulator.
[ P. W. Anderson, Science 235, 1196 (1987)
Predicted d-wave symmetry of order paramteter
and the pseudogap at low doping. G. Kotliar and J. Liu Phys.Rev. B 38,5412 (1988) 15

39. Optical Conductivity Schlesinger t.al (1993)
Shining light on correlated electrons. Optical conductivity Failure of the Standard Model: Anomalous Spectral Weight Transfer
= Neff (T, )depends on T
Optical Conductivity Schlesinger t.al (1993)
Very Non local transfer of spectral weight in FeSi D. Van der Marel et.al (2005) [ 1 ev 800 cm-1] Weight does not recover up to 5 ev. s
Other probes for correlated electrons X-rays, neutrons, electrons, the kitchen sink, theory ………. 6

40. Slave boson MFT. D wave symmetry of the SC OP
G. Kotliar and J. Liu
PRB 38,5412 (1988) 18
D wave symmetry of the SC OP
SC order and Tc decrease as x decreases.
Low doping . pseudogap with D wave symmetry .
VF is weakly dependent on doping, .
Coherence incoherence crossover on the overdoped side.
Related T=0 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, (2001)

41. "The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe..The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. At each level of complexity entirely new properties appear. Psychology is not applied biology, nor is biology applied chemistry. We can now see that the whole becomes not merely more, but very different from the sum of its parts."(Anderson 1972)

42. PWAnderson:Nature Physics 2, 138 (2006)
“It has been my (published) opinion for years that the cause of high-temperature superconductivity is no mystery. We now have a workable theory — not just for calculating the broad outlines (the transition temperature Tc, energy-gap shape, effect of doping, pseudogap temperature) but details of the anomalous phenomenology.”
don’t
“A crude version of this theory was published in 1988 by Zhang and co-authors (Supercond. Sci. Technol. 1, 36–38; 1988), based partly on my earlier ideas, and in a similar paper, Kotliar and Liu came to the same conclusions independently (Phys. Rev. B 38, 5142–5145; 1988). But the successes weren't then recognized because experiments were too primitive.”
theory was
Cluster (link/plaquette)DMFT, promising new avenue 19

43. Mean-Field : Classical vs Quantum
Classical case
Quantum case
Hard!!!
Easy!!!
QMC: J. Hirsch R. Fye (1986)
NCA : T. Pruschke and N. Grewe (1989)
PT : Yoshida and Yamada (1970)
NRG: Wilson (1980)
Pruschke et. al Adv. Phys. (1995)
Georges et. al RMP (1996)
IPT: Georges Kotliar (1992). .
QMC: M. Jarrell, (1992),
T. Pruschke D. Cox and M. Jarrell (1993),
ED:Caffarel Krauth and Rozenberg (1994)
Projective method: G Moeller (1995).
NRG: R. Bulla et. al. PRL 83, 136 (1999)
,……………………………………...
Animate, and expand.
A. Georges, G. Kotliar (1992)

44. Structure Property Relation in Correlated Systems: c axis optics in YBCO.
Compare with experiments
Long sought goal: link structure to property. Dream becoming reality with the development of LDA+ cluster DMFT. Here we start with the structure of YBCO in the underdoped regime, we start from the structure, we derived electronic structure via LDA+ 2-site cluster DMFT which reduces the problem to 2-sites in a medium. The electronic spectral function near the fermi surface (spectra) shows characteristic arcs . The cycle continues the evaluatino of the optical conductivity which compares favorably with experiments.(by the UCSD group).
Reference : M. Ferrero O. Parcollet G. Kotliar .A.Georges and D. Basov Phys. Rev. B 82, (2010)
C axis optical conductvity
Spectra

45. With decreasing doping gap increases, coherence peaks
Ratio AS/AN
Ratio more universal,
more symmetric
With decreasing doping gap
increases, coherence peaks
less sharp->Non BCS
McElroy,.. JC Davis,
PRL 94, (2005)
Exp:Bi2212 with STM
Alternative explanation Fang, et.al. PRL vol 96, (2006).
Sanibel 2008

46. Early studies Hubbard model : plaquette in a medium.
Lichtenstein and Kastnelson PRB (2000) Stanescu, T. D., and P. Phillips, 2003, Phys. Rev. Lett. 91, DCA in 2x2 Jarrell, M., T. Maier, et. al. 2001, Europhys. Lett. 56, 563. 20

48. Z. P. Yin, KH, G. Kotliar Nature Physics in press .
QUALITATIVE INSIGHTS: a) Strongly Frequency Dependent Spin and Orbital Exchange Splitting b) Spin splitting large at high frequency. Orbital splitting large at low frequency. c) Qualitative difference between BaFe2As2 and Oxides.
Z. P. Yin, KH, G. Kotliar Nature Physics in press .

50. A. Georges and G. Kotliar PRB 45, 6479 (1992).
Hubbard Model
DMFT
Collective field describing the localization delocalization phenomena
Can be sublattice dependent, spin dependent, superconducting.. … 8
Require that the effective medium produces the best possible local spectral function.
DMFT self consistency condition
A. Georges and G. Kotliar PRB 45, 6479 (1992).

51. Mean-Field : Classical vs Quantum
Classical case
Quantum case
Hard!!!
Easy!!!
QMC: J. Hirsch R. Fye (1986)
NCA : T. Pruschke and N. Grewe (1989)
PT : Yoshida and Yamada (1970)
NRG: Wilson (1980)
Pruschke et. al Adv. Phys. (1995)
Georges et. al RMP (1996)
IPT: Georges Kotliar (1992). .
QMC: M. Jarrell, (1992),
T. Pruschke D. Cox and M. Jarrell (1993),
ED:Caffarel Krauth and Rozenberg (1994)
Projective method: G Moeller (1995).
NRG: R. Bulla et. al. PRL 83, 136 (1999)
,……………………………………...
Animate, and expand.
A. Georges, G. Kotliar (1992)

53. Why do we need a MFT of correlated materials ?
Few exact solutions available.
Need for simplification, understanding, design.
Separate essential ingredients [e.g. phonons, orbitals, structure etc. ] responsible for an effects.
Separate long wavelength non linearities (fluctuations, collective modes, defects) from local physics.
Bridge between atomic information and physical and spectroscopical properties. [Structure-Property relation  Design]
Compare different “states” of the system for the same value of parameters.  Understand the Mechanism .

54. DMFT Strategy and Ideas
Breaks problems in two parts a) study of mean field states from b ) evaluation of their energies.
Second step, and detailed comparison experiments s within realistic implementions of electronic structure, e.g. LDA+DMFT.
Qualitative lessons can be drawn from a) applied to simple models.
Tools to think about correlated materials, e.g. Weiss fields, valence histograms, impurity model reference frames. etc.
Locality assumption exact at high T.

55. Difficulties Technical Issues
2x2 cluster DMFT equations are considerably harder to solve and to interpret than single site DMFT.
Uniqueness: no unique formulation of cluster DMFT
Landscape of DMFT Solutions Problem
Even within the same scheme at low T. In some region of parameters of the Hamiltonian, there are at low temperature many many solutions to the DMFT equations with different broken symmetries and ever increasing unite cells.

56. RVB phase diagram of the Cuprate Superconductors. Superexchange.
Tc controlled by J.
Trvb, onset of spin pairing.
< b>, TBE , coherence temperature, formation of QP..
Superconducting dome. Pseudogap evolves into SC
Problems: a) poor description of the incoherent part b) MFT too uniform c) other states i.e. AF.
Restricted form of the electron self energy.
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, (2001)

58. Theory : arXiv:1007.2867 Magnetism and Charge Dynamics in Iron Pnictides
Z. P. Yin, K. Haule, G. Kotliar
arXiv:

59. Zhiping Yin, Rutgers University
X’ Z Y’
X’ Z Y’
The in-plane optical conductivity is way much better than in c-axis.
4/25/2017
arXiv:
Zhiping Yin, Rutgers University

60. Evolution of the correlations in Hunds metals
LDA+DMFT
LDA
Static Magnetic Moment is Determined by strength of correlatoins AND by the shape of the Fermi Surface

62. On First Principles Approaches to Materials Science
Auguste Compte (1830). “ Every attempt to emply mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry “
Paul Dirac (1929) “The underlying laws necessary for the mathematical theory of the whole chemistry are thus completely known and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble “
“Approximate practical methods of applying quantum mechanics should be developed which can lead to an explanation of the main features of complex atomic systems without too much computation”

63. In the Rise of Complexity 1953-2002, PW Anderson writes:
“ …John Slater, already in 1953 , was obsessed with what I have rudely called the Great Solid State Dream machine. He envisioned that the new electronic computer could be applied to the task of automatically providing the electronic structure of any desired solid; and he literally believed that he would have the answers to any conceivable question . The latter idea was wrongheaded; but the former has gradually become a reality with the rise of what is now known as LDA. It is not enough appreciated that Slater himself provided the key element in that method. “

64. Phil Anderson on the rise of complexity 1953-2002
But there are many cases where it fails spectacularly: essentially all of the interesting class of substances with magnetic inner shell atoms, most of which exhibit what has been called the Mott Phenomenon- a dominance of the local repulsion among inner shell electrons. “…A new version of the Dream Machine has recently been invented which is quite successful in most of these cases-DMFT, dynamical mean field theory cooked up by Georges and Kotliar where the assumption of locality of the self energy in time is abandoned… “
Phil Anderson on the rise of complexity

65. Correlated electrons are not well described by either the itinerant (wave) picture, or the localized (particle) picture. Difficult non perturbative problem. Theoretical Approaches
Phenomenology
Study of exactly soluble (by numerical and analytical means) 1-d Hamiltonians
Approximate methods for models in 2d-3d
Guessing effective low energy theories.
Dynamical Mean Field Theory . [ Exact in the Metzner Vollhard limit of infinite dimensions – now can bridge between structure and property of materials ]

68. LDA+DMFT. V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G
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++
Spectra=- Im G(k,w) 12

69. Conceptual Underpinning Diagrams: PT in W and G.
Introduce projector Gloc Wloc
: Chitra and Kotliar Phys. Rev. B 62, (2000) and Phys. Rev.B (2001).  

70. Test notion of locality in LMTO basis set in various materials.
Proof of Principle Implementation
Full implementation in the context of a a one orbital lattice model.
P Sun and G. Kotliar Phys. Rev. B 66, (2002). Propose GW+DMFT .
P.Sun and GK PRL (2004). Test various levels of self consistencyin Gnonloc Pinonloc
Test notion of locality in LMTO basis set in various materials.
N. Zeyn S. Savrasov and G. Kotliar PRL 96, , 2006
N Zeyn S. Savrasov and G. K PRL 96, (2006)
GW self energy for Si
Beyond GW
Still, summing all diagramas with dynamical U and obtaining the GW starting point is extremely expensive. So this is still
a point of principle rather than a practical tool.
Coordination Sphere
Coordination Sphere

71. LDA+DMFT as an approximation to the general scheme
U is parametrized in terms of Slater integrals F0 F2 F4 ….
Recent calculations using B3LYP hybrid + DMFT for Ce2O3. D. Jacob K. Haule and GK EPL 84, (2008)
Total energy is derived from a functional of the density and Gloc
CHARGE SELF CONSISTENT LDA+DMFT S. Savrasov GK (2002)
Savrasov, Kotliar, Abrahams, Nature ( 2001) 12

72. LDA+DMFT Self-Consistency loop [Savrasov Kotliar 2002] Derived from the functional.
Edc U
DMFT
REVIEW : G. Kotliar S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, C.A. Marianetti, RMP 78, 865 (2006).

73. Total Energy as a function of volume for Pu W (ev) vs (a.u. 27.2 ev)
Bistability of a material near the Mott transition. Model realization of the Johanssen ideas.
Central for understanding the physics of Pu.. New paradigm for thinking, about materials.
N, Zein Following Aryasetiwan Imada Georges Kotliar Bierman and Lichtenstein. PRB (2004)
Savrasov, Kotliar, Abrahams, Nature ( 2001)
Non magnetic correlated state of fcc Pu.

74. Superexchange Mechanism . K. Haule and GK Phys. Rev. B 76, (2007). Compare “normal “ and SC state at the same tempearture!
Reminiscent of PW Anderson RVB Science 235, 1196 (1987) and slave boson picture G. Kotliar and J. Liu P.RB 38,5412 (1988) 31

76. Neutron spectroscopy with LDA+DMFT
Theory: H. Park , K. Haule and GK
Experiments: L Harriger H. Luo M. Liu T. Perring C Frost H. Ju M. Norman and Pengcheng Dai : arXiv:

77. CUPRATES

78. Return to models, Hubbard, t-J
Kinetic Energy
Exchange Energy
Plaquette DMFT:
Lichtenstein and Kastnelson PRB (2000)
T. Maier, et. al. 2001, Europhys. Lett. 56, 563.
Sordi et.al. . arXiv:
Civelli et. al. Phys. Rev. Lett. 100, (2008)
Haule and Kotliar Phys. Rev. B 76, (2007)
Bath 1 2
Real Space
Link DMFT Ferrero et. al. Europhys. Lett. 85, (2009) Stanescu and Phillips P RB,69, (2004).
Momentum Space 26

79. Early studies of plaquette and link DMFT of Hubbard
Lichtenstein and Kastnelson PRB (2000) Stanescu, T. D., and P. Phillips, 2003, Phys. Rev. Lett. 91, DCA in 2x2 Jarrell, M., T. Maier, et. al. 2001, Europhys. Lett. 56, 563.

81. Electron and Hole Doped Cuprates : Similar but Yet Different, why. C
Electron and Hole Doped Cuprates : Similar but Yet Different, why? C. Weber et.al. Nature Physics 2010
Apical oxygen
NCCO : Robust AF Phase
Comensurate Magnetism
Lower Tc
T^2 resistivity.
Non monotonic angle dependence of SC order parameter ………
Review: Armitage Fournier Green (2009) 18

82. DMFT studies of copper oxides
Good agreement with many experiments follow from a simple [ plaquette/link /site ] reference frame.
In general, better modeling with DMFT (more sites, more orbitals etc ) better results.
Power of mean field theory : comparing “normal “ and magnetic states, comparing “normal” and superconducting states
Strength of correlations (as quantified by single site DMFT) the most fundamental difference between NCCO and LSCO compounds. NCCO ( D < Dc2 )and LSCO (D > Dc2)straddle the Zaanen Sawatsky Allen localization delocalization boundary. Traced to the absence of apical oxygen in NCCO (structure property relation). 25

84. Iron Pnictides

85. Iron Pnictides- Chalcogenides
(Fe++)(Se__)
Ba++(Fe++)2(As---)2
FeSe1-0.08, 1.48GPa),
Mizuguchi et.al., arXiv:

86. Similarity/differences with cuprates
Iron pnictides
(electron, hole, isovalent doping)
AFM: Antiferromagnetic metal
SC: Superconductor
T: Tetragonal
O: Orthorombic PG
hole
electron
isovalent
In high Tc’s carrier doping seems essential. In pnictides, isovalent (chemical pressure) works as well. It is just important to kill magnetism.

87. Basic Questions Relevant degreens of freedom, effective hamiltonians
Strength of the correlations . Localized vs itinerant Fe d electrons
Mechanism of the superconductivity and magnetism…….
New arena to test the LDA+DMFT methodology [ with and without experimental informantion!]

88. High temperature universality and V2O3
M. Rozenberg G. Kotliar H. Kajueter G Thomas D. Rapkine J Honig and P Metcalf Phys. Rev. Lett. 75, 105 (1995)
Mo, Denlinger, Kim, Park, Allen, Sekiyama, Yamasaki, Kadono, Suga, Saitoh, Muro, Metcalf, Keller, Held, Eyert, Anisimov, Vollhardt PRL . (2003)
T=170
T=300
Spinodal Uc2
Critical endpoint
P. Limelette et.al. Science 302,
89 (2003) 20

89. Coherence Incoherence Crossover
LaO1-0.1F0.1FeAs
Hubbard U is not the “relevant” parameter.
The Hund’s coupling brings correlations!
Specific heat within LDA+DMFT
for LaO1-0.1F0.1FeAs at U=4eV n
LDA value
For J=0 there is negligible mass enhancement at U~W!
K. Haule and G. Kotliar cond-mat arXiv: ,

90. wc=3000cm-1 ~ ev
M. M. Qazilbash,1,, J. J. Hamlin,1 R. E. Baumbach,1 Lijun Zhang,2 D. J. Singh,2 M. B. Maple,1 and D. N. Basov1
Nature Physics 5, 647 (2009)

91. Photoemission reveals now Z ~ .3

92. Freq. dep. U matrix well parametrized by F0 F2 F4
F0 = 4:9 eV, F2 = 6:4 eV and F4 = 4:3 eV., nc=6.2
Z =1/2 for x2- y2 and z2 , Z =1/3 f xz; yz zx orbitals.

93. F0 = 4:9 eV, F2 = 6:4 eV F4 = 4:3 eV., nc=6.2
LDA+DMFT calculations Kutepov Haule Savrasov and Kotliar PRB (2010). Mass renormalization = 3 without satellites
Exp: W.Z. Hu et.al., PRL 101, (2008)

94. LDA+DMFT Magnetic moment .95 muB Expt 1 muB
EXPT: Hu, W. Z. et al. Phys. Rev. Lett. 101, (2008).
EXPT: Nakajima, M. et al. Phys. Rev. B 81, (2010)
Theory Yin et. al. (2010) L

95. Origin of the anisotropy is electronic
Optical features sharpen in the polarized spectra. Experimental predictions. Measurements underway ( not easy !)

96. Orbital polarization of the frequency dependent hybridization Weiss field. Lives only at very low energies.

97. Magnetic Stripe Phase of the FeAs materials: new insights from LDA+DMFT Z. Yin K. Haule and GK [ in preparation]
Focus on changes of Neff(L, T) at various energy scales L, in going to the magnetic state.
a) At low energies conductivity goes up. Rapid coherence crossover from an incoherent normal state compensates for a loss of carriers. Gain kinetic energy at very low energies!
For intermediate L, loss in carriers (kinetic energy )

98. Mass enhancement, plasma frequency Optical conductivity
U=5eV, J=0.7eV
Interband peak ~ 0.6eV
PRB 82, (2010)
Plasma frequency:
LDA ~ 2.6eV
DMFT ~ 1.6eV
Exp ~ 1.6eV
Drude weight
Mass enhancement of Fe-5d bands
m*/mLDA~3
Exp: W.Z. Hu et.al., PRL 101, (2008) .
Theory : Fourth generation of LDA+DMFT methods and codes. Kutepov Haule Savrasov and Kotliar (2010). Mass renormalization without satellites !

99. Go back to basics: U’s for DMFT. ( Kutepov et. al
Go back to basics: U’s for DMFT. ( Kutepov et. al. building on the PT in G and W by R. Chitra and G. K)
Rigorous Definition of the Hubbard U and the Weiss Field Delta in a Solid. Kutepov et.al (2010) .
Define a projector. Use the same projector in calculating the U’s that you will use in your DMFT calculation
Approximate Wloc and Piloc using Self Consistent GW. Kutepov et. al. 2010
Eliminate the hybridization to the semicore states included in GW but not in LDA +DMFT by rescaling

100. DMFT Concepts and Tools in electronic structure
Local Self Energies and Correlated Bands
Local Spectral Function
Weiss Weiss field, collective hybridizationfunction, quantifies the degree of localization
Valence Histograms. Describes the history of the “atom” in the solid, multiplets!
Functionals of density and spectra give total energies

101. A. Georges and G. Kotliar PRB 45, 6479 (1992).
Hubbard Model
DMFT
Collective field describing the localization delocalization phenomena
Can be sublattice dependent, spin dependent, etc.. … 8
DMFT self consistency condition
A. Georges and G. Kotliar PRB 45, 6479 (1992).

102. Trvb, onset of spin pairing.
RVB phase diagram of the Cuprate Superconductors. Correct prediction d wave symmetry of SC order parameter (and generic cuprate phase diagram) many years before the experiment.
Tc controlled by J.
Trvb, onset of spin pairing.
< b>, TBE , coherence temperature, formation of QP..
Superconducting dome. Pseudogap evolves into SC
Problems: a) poor description of the incoherent part b) MFT too uniform c) other states i.e. AF. d) Restricted form of the electron self energy.
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, (2001)

103. Reducing ed=ep helps Tc
Increasing tpp’ hurts Tc
Moving the apical oxygen reduces ed-ep but also incrases tpp’