Towards an ab -initio theory of correlated materials . The challenge of the iron pnictides . Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University. Work with K. Haule Z. Ying A. Kutepov (Rutgers) S. Savrasov (U.C. Davis). Outline.
Towards an ab-initio theory of correlated materials . The challenge of the iron pnictides.Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University
Work with K. Haule Z. Ying A. Kutepov (Rutgers) S. Savrasov (U.C. Davis)
First Principles DMFT –framework.
Collaborators (cuprates) Kristjan Haule AndreyKutepovS. Savrasov (UC Davis) K. Haule (Rutgers)
$upport : NSF -DMR , DOE-Basic Energy Sciences, MURI, NSF materials world network.
S. V. Faleev, M. van Schilfgaarde, and T. Kotani,
Phys. Rev. Lett. 93, 126406 (2004).
atomic levels LDAImpurity Solver
Machine for summing all local diagrams in PT in U to all orders.
Quantifying the degree of
The power of the method increased tremendously fueled by advances in impurity solvers.
Extensions to cluster of sites, CDMFT capture short range correlations, k dependent self
Over the past few years evidence for the accuracy of the method for Hubbard models accumulated very rapidly from: a) comparison of different cluster sizes,
b) comparison of dmft predictions with experiments
c) experiments in cold atom traps realizing the Hubbard model and compared with DMFT
d) It’s now possible to compare with exact numerical solutions of Hubbard model at high temperatures. (agreement within a few percent) [Gull et. al.]
Just as with LDA, we know how to interpret the results and where and how ( in which direction ) it is biased. Local approximation is very accurate in many regions of parameter space.
Non locality in time is essential. [ Warning for other methods!!!]
LDA+DMFT. V. advances in impurity solvers. 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)
Introduce projector GlocWloc
: Chitra and Kotliar Phys. Rev. B 62, 12715 (2000) and Phys. Rev.B (2001).
Proof of Principle Implementation advances in impurity solvers.
Full implementation in the context of a a one orbital lattice model.
P Sun and G. KotliarPhys. Rev. B 66, 85120 (2002). Propose GW+DMFT .
P.Sun and GK PRL (2004). Test various levels of self consistencyinGnonlocPinonloc
Test notion of locality in LMTO basis set in various materials.
N. Zeyn S. Savrasov and G. Kotliar PRL 96, 226403, 2006
N Zeyn S. Savrasov and G. K PRL 96, 226403 (2006)
GW self energy for Si
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.
LDA+DMFT as an approximation to the general scheme advances in impurity solvers.
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, 57009 (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)
Total Energy as a function of volume for advances in impurity solvers. Pu W(ev) vs (a.u. 27.2 ev)
N, ZeinFollowing AryasetiwanImada Georges KotliarBierman and Lichtenstein. PRB 70 195104. (2004)
Savrasov, Kotliar, Abrahams, Nature ( 2001)
Non magnetic correlated state of fccPu.
C advances in impurity solvers. 11 (GPa)
DMFT Phonons in fcc d-Pu
( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003)
(experiments from Wong et.al, Science, 22 August 2003)
Physical Picture of Plutonium as a Non Magnetic Strongly Correlated Mixed Valent Metal.
Different Phases differ in the Redistribution of Spectral Weight.
Havela advances in impurity solvers. et. al. Phys. Rev. B 68, 085101 (2003)
Pu is non magnetic – Cm is magnetic TN ~ 150 K.
K.Haule J. Shim and GK Nature 446, 513 (2007)
together with optimal projector, given finite computational resources [ Wanniers, projective LMTO’s etc ]
STILL NEEDED practical solvers with retarded interactions.
FeSe1-0.08, (Tc=27K @ 1.48GPa),
Mizuguchi et.al., arXiv: 0807.4315
LDA+ DMFT for advances in impurity solvers. LaFxO1-xFeAs
Correlations are important: LaOFeAs is on the itinerant side but not too far away from the metal-insulator transition . Non trivial renormalizations Z~ .2 -.3
Typical parameters U=4eV, J=0.7eV. Bad semimetal at high temperatures. Large scattering rate.
ALL 5 d bands important (for J>0.3) relatively small crystal fields
For J=0.7eV, Uc2 =4.5 Correlated insulator.
“Since the Coulomb correlation is below the critical U for this system to undergo a Mott transition, an itinerant approach might be adequate. This will involve a generalization of the spin-fluctuation exchange mechanism to a multiorbital situation. In adition the pairing interaction might involve not just spin but also orbital fluctuations within the d subshell. “
The electron phonon coupling is too small to account for superconductivity. ( similar results obtained by D. Singh and
Boeri et. al.)
K. Haule J. Shim and GK . PRL
100, 226402 (2008)
LDA value advances in impurity solvers.
J~0.35 gives correct order ofMagnituder.FeAs and Mott Hunds materials
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
For J=0 there is negligible mass enhancement at U~W!
K. Haule, G. Kotliar,
Z= 1- b(U/W)2
M*/M < 2
When U/W < 1 PT theory works
Z-1 -1 < 1
Spectral weight distributed within W
When U/W > 1 PT theory fails
Weight transferred outside W
Z < .5
M*/M > 2
YOU CANNOT HAVE THE CAKE [ substantial mass renormalization ] AND EAT IT TOO
[not have satellites ]
Z advances in impurity solvers. -1 -1 =.6
Z=.5 advances in impurity solvers.
OPTICAL CONDUCTIVITY TO THE RESCUE ? advances in impurity solvers.
wc=3000cm-1 ~ .3 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)
Photoemission reveals now Z ~ .3 advances in impurity solvers.
Go back to basics: U’s for DMFT. ( advances in impurity solvers. Kutepov et. al. building on the PT in G and W by R. Chitra and G. K)Eliminate the hybridization to the semicore states included in GW but not in LDA +DMFT by rescaling
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
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; yzzxorbitals.
DMFT F0 = 4:9 eV, F2 = 6:4 eV and F4 = 4:3 eV., nc=6.2
There is transfer of spectral weight to high energies, spectral weight is conserved. But the DOS is featuresless no satellites, and resembles the LDA!
Big difference between oxides and pnictides. Pnictides can have substantial mass renormalizations and no sharp satellites!!!
structure [ (0, pi) state [ stripe ]
Predicted a strong anisotropy of the magnetic excitation spectra. J. Dong et al PRL 83, 27006 (2008). Z. P, Yin, et al, PRL 101, 047001 (2008).
transition in underdoped iron pnictide superconductors.
Chuang, T.-M., et al. Nematic electronic structure in the "parent" state of the iron-based superconductor
Ca(Fe1xCox)2As2. Science 327, 181 (2010).
PROBLEMS WITH LOCALIZED PICTURE
EXPT: Hu, W. Z. et al. Phys. Rev. Lett. 101, 257005. (2008).
EXPT: Nakajima, M. et al. Phys. Rev. B 81, 104528 (2010)
Theory Yin et. al. (2010)
Optical features sharpen in the polarized spectra. Experimental predictions. Measurements underway ( not easy !)
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!
Focus on changes of Neff(L, T) at various energy scales L, in going to the magnetic state.
END OF THE EDUCATIONAL PART
Nanostructures-interfaces-impurities advances in impurity solvers.
Local self energy approximation
F Sum of local 2PI graphs with local U matrix and local G
Notice Explicit Dependence on : U , DC, and Projectors
[ Orbitals ], and Independence of basis set.
R. Chitraand Gkotliar Phys.Rev.B62:12715 (2000). S. Savrasovand G. Kotliar PRB Phys. Rev. B 69, 245101 (2004).
GW+DMFT Why it should work ? advances in impurity solvers.
GW+DMFT proposed and fully implmented in the context of a a one orbital lattice model.
P Sun and G. KotliarPhys. Rev. B 66, 85120 (2002).
Test various levels of self consistency in GnonlocPinonlocP.Sun and GK PRL (2004). See also GW+dc+UBiermann, F.Aryasetiawan. and A. Georges, PRL 90, 86402 (2003)
Test notion of locality in LMTO basis set in various materials. N. Zeyn S. Savrasov and G. Kotliar PRL 96, 226403, (2006). Include higher order graphs, first implementation of GW+DMFT (with a perturbative impurity solver).
GW self energy for Si
N advances in impurity solvers. Zeyn S. Savrasov and G. K PRL 96, 226403 (2006)
Cutoff Radius R
Impurity advances in impurity solvers.
10K advances in impurity solvers.
Cerium 115Multiple hybridization gaps
C. Yee G. advances in impurity solvers. Kotliar K. Haule Phys. Rev. B 81, 035105 (2010)
C-.O.Almbladh, U.von Barth and R.vanLeeuwenInt.J.Mod.Phys. B13, 535 (1999)
Introduce Notion of Local Greens functions, Wloc, Gloc G=Gloc+Gnonloc .
Ex. Ir>=|R, r> Gloc=G(Rr, R r’) dR,R’
Sum of 2PI graphs
One can also view as an approximation to an exact Spectral Density Functional of Gloc and Wloc. One can do further PT in GlocGnonloc by keeping perturbative corrections in
An exact impurity solver, advances in impurity solvers.
continuous time QMC - expansion in terms of hybridization
P. Werner et. al. PRL (2006) K.H.aule Phys. Rev. B 75, 155113 (2007)
General impurity problem
Diagrammatic expansion in terms of hybridization D
+Metropolis sampling over the diagrams
alpa->delta volume collapse transition
Curium has large magnetic moment and orders antiferromagneticallyPu does is non magnetic.
Keep all bands, no advances in impurity solvers. downfolding, apply correlations to Fe orbitals. Use realistic parameters CAN HAVE MASS RENORMALIZATIONS AND NOT SATELLITES!!!
fraction of the original width (Z 0.2 – 0.3) . At high temperatures, bad (semi-)metal with large scattering rate. Coherence incoherence crossover.
Local Self Energies and Correlated Bands
Orbitally Resolved Spectral Functions
Transfer of spectral weight.
Weiss Weiss field, collective
hybridization function, quantifies the degree of localization
Valence Histograms. Describes the
Probability of finding the correlated
state site in the solid in a given configuration
J. H. Shim, K. Haule, and G. Kotliar, Nature London 446, 513 (2007).
Functionals of density and
spectra, total energies: spectral
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).
Second problem: soft underbelly of the interface between electronic structure and DMFT .