DMFT approach to many body effects in electronic structure.

Application to the Mott transition across the actinide series [5f’s].

G.Kotliar Phyiscs Department and Center for Materials Theory Rutgers University.

Collaborators: S. Savrasov (NJIT--UCDavis ) K. Haule (Jozef Stefan Institute-Rutgers) Xi Dai (Rutgers-Institute of Theoretical Physics Beigng)

Outline

• Some introductory comments about Dynamical Mean Field Theory.

• The Mott transition across the actinide series, Plutonium and Americium.

• DMFT results for Pu. [Other approaches disorder local moment, mixed level model, LDA+ U …..]

• DMFT results for Am under pressure.• Conclusions.

DMFT Cavity Construction. A. Georges and G. Kotliar PRB 45, 6479 (1992). First happy marriage of atomic and band physics.

Reviews: A. Georges G. Kotliar W. Krauth and M. Rozenberg RMP68 , 13, 1996 Gabriel Kotliar and Dieter Vollhardt Physics Today 57,(2004)

1( , )

( )k

G k ii i

Extremize a functional of the local spectra or the local self energy.

0

1 2

( , ) ( )

( )(cos cos ) ( )(cos .cos ) .......latt k

kx ky kx ky

How good is the local approximation ??? Exact in infinite dimensions as defined by Metzner and Vollhardt (1989).

Cellular DMFT [Kotliar et. al. PRL (2001) ] Test in 1d Hubbard model Capone Civelli Sarma Castellani and Kotliar PRB 69,195105 (2004) ]

Two paths for ab-initio calculation of electronic

structure of strongly correlated materials

Correlation Functions Total Energies etc.

Model Hamiltonian

Crystal structure +Atomic positions

DMFT ideas can be used in both cases.

Towards Ab-Initio DMFT. Incorporate band structure and orbital degeneracy to achieve a

realistic description of materials. LDA+DMFT V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). Similar in spirit LDA ++ Lichtentsein and Katsnelson. PRB 57,6884 (1998). Derive complex Hamiltonians solve them using DMFT.

LDA+DMFT photoemission Allows the computation of realistic photoemission spectra. More recently, Extension to optical conductivity eg[ Haule Savrasov Udovenko and KotliarPhys. Rev. Lett. 94, 036401 (2005). ]

• Functional formulation (Chitra and Kotliar 2000) Phys. Rev. B 62, 12715 (2000). . Full implementation S. Savrasov G. Kotliar (2001-2005) . Phys. Rev. B 69, 245101 (2004). Frequency dependent generalization of the Kohn Sham potential, whose role is to give the exact “local” Greens function. Frequency dependent Kohn-Sham like equations can be derived by extremizing a functional which gives the total energy.

• Theory computes total Energy, linear response phonons. [ Savrasov and Kotliar Phys. Rev. Lett. 90, 056401 (2003). ]

T/W

Phase diagram of a Hubbard model with partial frustration at integer filling. Evolution of the Local Spectra as a function of

U,and T.

Crash Course on the Mott transition in single site DMFT. Georges Kotliar Krauth and Rozenberg RMP (1996))

Mott Transition in the Actinide Series Johansen Phil

Mag. 30, 469(1974) .

J. Lashley et.al.(2004)

Revisit with modern DMFT tools. Savrasov and Kotliar PRL 84,3760 (2000) ……….

Pu phases: A. Lawson Los Alamos Science 26, (2000)

oNon magnetic LDA underestimates the volume of fcc Pu by 30%, Negative shear modulus. Bouchet et.al.12, 1723 (2000) .oLSDA predicts Pu to be magnetic with a large moment ( ~5 Bohr) . Experimentally Pu is not magnetic. [Lashley et. al. cond-matt 0410634]oTreating f electrons as core overestimates the volume by 30 %

Total Energy as a function of volume for Total Energy as a function of volume for Pu Pu W (ev) vs (a.u. 27.2 ev)

(Savrasov, Kotliar, Abrahams, Nature ( 2001)Non magnetic correlated state of fcc Pu.

iw

Zein Savrasov and Kotliar (2005) Following Aryasetiwan et. al. PRB 70

195104. (2004)

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

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

E = Ei - EfQ =ki - kf

DMFT Phonons in fcc DMFT Phonons in fcc -Pu-Pu

  C11 (GPa) C44 (GPa) C12 (GPa) C'(GPa)

Theory 34.56 33.03 26.81 3.88

Experiment 36.28 33.59 26.73 4.78

( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003)

(experiments from Wong et.al, Science, 22 August 2003)

Why is Epsilon Pu (which is smaller than delta Pu) stabilized at higher temperatures ??Compute phonons in bcc structure.

Phonon entropy drives the epsilon delta phase transition

• Epsilon is slightly more delocalized than delta, has SMALLER volume and lies at HIGHER energy than delta at T=0. But it has a much larger phonon entropy than delta.

• At the phase transition the volume shrinks but the phonon entropy increases.

• Estimates of the phase transition following Drumont and G. Ackland et. al. PRB.65, 184104 (2002); (and neglecting electronic entropy). TC ~ 600 K.

Double well structure and 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)]

Natural consequence of the conclusions on the model Hamiltonian level. We had two solutions at the same U, one metallic and one insulating. Relaxing the

volume expands the insulator and contract the metal.

F(T,V)=Fphonons+Finvar

“Invar model “ for Pu-Ga. Data fits only if the excited state has zero stiffness.

J. Tobin et. al. PHYSICAL REVIEW B 68, 155109 ,2003

K. Haule , Pu- photoemission with DMFT using vertex corrected NCA.

Approach the Mott point from the right Am under Approach the Mott point from the right Am under pressurepressure

Density functional based electronic structure calculations: Non magnetic LDA/GGA predicts volume 50% off. Magnetic GGA corrects most of error in volume but gives m~6B

(Soderlind et.al., PRB 2000). Experimentally, Am has non magnetic f6 ground state with J=0 (7F0)

Experimental Equation of State (after Heathman et.al, PRL 2000)

Mott Transition?“Soft”

“Hard”

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

Mott transition in open (right) and closed (left) shell systems. Superconductivity ?

S S

U U

TLog[2J+1]

Uc

~1/(Uc-U)

J=0

???

Tc

Photoemission spectra using Hubbard I solver [Lichtenstein and Katsnelson, PRB 57, 6884,(1998 ), Svane cond-mat 0508311] and Sunca . [Savrasov Haule and Kotliar cond-mat 0507552] Hubbard bands width is

determined by multiplet splittings.

Photomission Spectra of Am under pressure. Sunca. Onset of mixed valence. Savrasov Haule

Kotliar (2005)

Resistivity of Am under pressure. J. C. Griveau Rebizant Lander and Kotliar PRL 94, 097002 (2005).

Conclusions

• Mott transition in Americium and Plutonium. In both cases theory (DMFT) and experiment suggest gradual more subtle evolution than in earlier treatments.

• DMFT: Physical connection between spectra and structure. Studied the Mott transition open and closed shell cases. .

• DMFT: method under construction, but it already gives quantitative results and qualitative insights. Interactions between theory and experiments.

• Pu: simple picture of the phases. alpha delta and epsilon. Interplay of lattice and electronic structure near the Mott transition.

• Am: Rich physics, mixed valence under pressure . Superconductivity near the Mott transition.

•