Modelling the Localized to Itinerant Electronic Transition in the Heavy Fermion System CeIrIn5K HauleRutgers University

Collaborators : J.H. Shim & Gabriel Kotliar

OutlineLDA+DMFT results for CeIrIn5Local Ce 4f - spectra of CeIrIn5 and comparison to AIPES)Momentum resolved spectra and comparison to ARPESOptical conductivityTwo hybridization gaps and its connection to opticsFermi surface in DMFTJ. H. Shim, KH, and G. Kotliar Science, November 1 2007; Science Express1149064

Standard theory of solidsBand Theory: electrons as waves: Rigid band picture: En(k) versus k Landau Fermi Liquid Theory applicableVery powerful quantitative tools: LDA,LSDA,GWPredictions:total energies,stability of crystal phases optical transitions

Fermi Liquid Theory does NOT work . Need new concepts to replace rigid bands picture!

Breakdown of the wave picture. Need to incorporate a real space perspective (Mott).

Non perturbative problem.Strong correlation Standard theory fails

V2O3Ni2-xSexk organicsUniversality of the Mott transitionFirst order MITCritical pointCrossover: bad insulator to bad metal1B HB model (DMFT):

How to computed spectroscopic quantities (single particle spectra, optical conductivity phonon dispersion) from first principles?

How to relate various experiments into a unifying picture.

New concepts, new techniques.. DMFT maybe simplest approach to meet this challengeBasic questions to address

DMFT + electronic structure method(G. Kotliar S. Savrasov K.H., V. Oudovenko O. Parcollet and C. Marianetti, RMP 2006).obtained by DFTCe(4f) obtained by impurity solutionIncludes the collective excitations of the systemSelf-energy is local in localized basis,in eigenbasis it is momentum dependent!all bands are affected: have lifetimefractional weightCe-f orbitalother light orbitalshybridizationDyson equationBasic idea of DMFT+electronic structure method (LDA or GW): For less correlated bands (s,p): use LDA or GWFor correlated bands (f or d): add all local diagrams by solving QIM

Bands are not a good concept in DMFT!Frequency dependent complex objectinstead of bandslifetime effectsquasiparticle band does not carry weight 1DMFTSpectral function is a good conceptIn FL regime:Hybridization:at low energy q.p. hybridization becomesat high energyIn DMFT:

DMFT is not a single impurity calculationAuxiliary impurity problem:High-temperature D given mostly by LDAlow T: Impurity hybridization affected by the emerging coherence of the lattice (collective phenomena)Weiss fieldtemperature dependent:Feedback effect on D makes the crossover from incoherent to coherent state very slow!DMFT SCC:

Crystal structure of 115s CeIn3 layerIrIn2 layerIrIn2 layerTetragonal crystal structure4 in plane In neighbors8 out of plane in neighbors3.27au3.3 au

in-planeout of planeCoherence crossover in experiment

How does the crossover from localized moments to itinerant q.p. happen?How does the spectral weight redistribute?

How does the hybridization gap look like in momentum space?Where in momentum space q.p. appear?

What is the momentum dispersion of q.p.?Issues for the system specific study

Temperature dependence of the local Ce-4f spectra At low T, very narrow q.p. peak (width ~3meV)SO coupling splits q.p.: +-0.28eV Redistribution of weight up to very high frequencySOAt 300K, only Hubbard bandsJ. H. Shim, KH, and G. Kotliar Science, November 1 2007; 1149064

Slow crossover pointed out by NPF 2004 scattering ratecoherence peakBuildup of coherenceCrossover around 50K

Consistency with the phenomenological approach of NPFRemarkable agreement with Y. Yang & D. Pines cond-mat/0711.0789!+C

ARPESFujimori, 2006Angle integrated photoemission vs DMFTExperimental resolution ~30meV, theory predicts 3meV broad bandSurface sensitive at 122eV

Angle integrated photoemission vs DMFTARPESFujimori, 2006Nice agreement for the Hubbard band positionSO split qp peak

Hard to see narrow resonance in ARPES since very little weight of q.p. is below EfLower Hubbard band

T=10KT=300K

Quasiparticle bandsthree bands, Zj=5/2~1/200

Fujimori, 2003LDA+DMFT at 10KARPES, HE I, 15KLarge lifetime of HBs -> similar to LDA(f-core)rather than LDA or LDA+U

Optical conductivityTypical heavy fermion at low T:Narrow Drude peak (narrow q.p. band)Hybridization gapInterband transitions across hybridization gap -> mid IR peakno visible Drude peakno sharp hybridization gapF.P. Mena & D.Van der Marel, 2005E.J. Singley & D.N Basov, 2002second mid IR peakat 600 cm-1

At 300K very broad Drude peak (e-e scattering, spd lifetime~0.1eV) At 10K: very narrow Drude peakFirst MI peak at 0.03eV~250cm-1Second MI peak at 0.07eV~600cm-1Optical conductivity in LDA+DMFT

Multiple hybridization gaps300KLarger gap due to hybridization with out of plane InSmaller gap due to hybridization with in-plane Innon-f spectra

Fermi surfaces of CeM In5 within LDALocalized 4f:LaRhIn5, CeRhIn5

Shishido et al. (2002)Itinerant 4f :CeCoIn5, CeIrIn5

Haga et al. (2001)

de Haas-van Alphen experimentsLDA (with fs in valence) is reasonable for CeIrIn5Haga et al. (2001)ExperimentLDA

Fermi surface changes under pressure in CeRhIn5Fermi surface reconstruction at 2.34GPaSudden jump of dHva frequenciesFermi surface is very similar on both sides, slight increase of electron FS frequenciesReconstruction happens at the point of maximal TcShishido, (2005)localizeditinerantWe can not yet address FS change with pressure We can study FS change with Temperature -At high T, Ce-4f electrons are excluded from the FSAt low T, they are included in the FS

Electron fermi surfaces at (z=0)LDA+DMFT (10 K)LDALDA+DMFT (400 K)a2a2

Electron fermi surfaces at (z=p)a3aa3LDA+DMFT (10 K)LDALDA+DMFT (400 K)

LDA+DMFT (10 K)LDALDA+DMFT (400 K)cb2b2b1b1Electron fermi surfaces at (z=0)

cb2b2LDA+DMFT (10 K)LDALDA+DMFT (400 K)Electron fermi surfaces at (z=p)

LDA+DMFT (10 K)LDALDA+DMFT (400 K)ghHole fermi surfaces at z=0ghBig change-> from small hole like to large electron likee1

Hole fermi surface at z=pNo Fermi surfacesLDA+DMFT (400 K)LDA+DMFT (10 K)LDA

dHva freq. and effective mass

Gradual decrease of electron FS

Most of FS parts show similar trend

Big change might be expected in the G plane small hole like FS pockets (g,h) merge into electron FS e1 (present in LDA-f-core but not in LDA)

Fermi surface a and c do not appear in DMFT results Increasing temperature from 10K to 300K: Fermi surfaces

Crossover from local moment regime to heavy fermion state is very slow.

Width of heavy quasiparticle bands is predicted to be only ~3meV. We predict a set of three heavy bands with their dispersion.

Mid-IR peak of the optical conductivity is split due to presence of two types of hybridization

Ce moment is more coupled to out-of-plane In then in-plane In

Fermi surface changes gradually with temperature and most of electron FS parts are only slightly decreases with increasing temperature. Hole pockets merge into e1 electron FS.

Conclusions

ARPES of CeIrIn5Fujimori et al. (2006)

Ir atom is less correlated than Co or Rh (5d / 3d or 4d)CeIrIn5 is more itinerant(coherent) than Co (further away from QCP)Why CeIrIn5?Phase diagram of 115s

General impurity problemDiagrammatic expansion in terms of hybridization D+Metropolis sampling over the diagramsExact method: samples all diagrams!Allows correct treatment of multipletsK.H. Phys. Rev. B 75, 155113 (2007) Continuous time QMC impurity solver, expansion in terms of hybridization

Ce 4f partial spectral functionsLDA+DMFT (10K)LDA+DMFT (400K)Blue lines : LDA bands