Bishop’s Lodge, Santa Fe 2007

Modelling the Localized to Itinerant Electronic Transition in the Heavy Fermion System CeIrIn5

K HauleRutgers University

Collaborators : J.H. Shim & Gabriel Kotliar

Santa Fe 2007

Outline

LDA+DMFT results for CeIrIn5 Local Ce 4f - spectra of CeIrIn5 and comparison to AIPES) Momentum resolved spectra and comparison to ARPES Optical conductivity Two hybridization gaps and its connection to optics Fermi surface in DMFT

J. H. Shim, KH, and G. Kotliar Science, November 1 2007; Science Express1149064

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Standard theory of solidsStandard theory of solids

Band Theory: electrons as waves: Rigid band picture: En(k) versus k

Landau Fermi Liquid Theory applicable

Very powerful quantitative tools: LDA,LSDA,GWVery powerful quantitative tools: LDA,LSDA,GW

Predictions:

•total energies,

•stability of crystal phases

•optical transitions

M. Van SchilfgardeM. Van Schilfgarde

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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 – Strong correlation –

Standard theory failsStandard theory fails

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V2O3Ni2-xSex organics

Universality of the Mott transitionUniversality of the Mott transition

First order MITCritical point

Crossover: bad insulator to bad metal

1B HB model 1B HB model (DMFT):(DMFT):

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Basic questions to addressBasic questions to address

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 challenge

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DMFT + electronic structure methodDMFT + electronic structure method

(G. Kotliar S. Savrasov K.H., V. Oudovenko O. Parcollet and C. Marianetti, RMP 2006).

obtained by DFT

Ce(4f) obtained by “impurity solution”Includes the collective excitations of the system

Self-energy is local in localized basis,in eigenbasis it is momentum dependent!

all bands are affected: have lifetimefractional weight

Ce-f orbital

other “light” orbitals

hybridization

Dyson equation

Basic 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

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“Bands” are not a good concept in DMFT!

Frequency dependent complex object instead of “bands”

lifetime effectsquasiparticle “band” does not carry weight 1

DMFTDMFT

Spectral function is a good concept

In FL regime:Hybridization:

at low energy q.p. hybridization becomes at high energy

In DMFT:

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DMFT is not a single impurity calculation

Auxiliary impurity problem:

High-temperature given mostly by LDA

low T: Impurity hybridization affected by the emerging coherence of the lattice

(collective phenomena)

Weiss field temperature dependent:

Feedback effect on makes the crossover from incoherent to coherent state very slow!

high T

low T

DMFT SCC:

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Ce

In

Ir

CeIn

In

Crystal structure of 115’s

CeIn3 layer

IrIn2 layer

IrIn2 layer

Tetragonal crystal structure

4 in plane In neighbors

8 out of plane in neighbors

3.27au

3.3 au

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Crossover scale ~50K

in-plane

out of plane

•Low temperature – Itinerant heavy bands

•High temperature Ce-4f local moments

ALM in DMFTSchweitzer&Czycholl,1991

Coherence crossover in experiment

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•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?

?

k

A()

•Where in momentum space q.p. appear?

•What is the momentum dispersion of q.p.?

Issues for the system specific study

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(e

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 frequency

SO

•At 300K, only Hubbard bands

J. H. Shim, KH, and G. Kotliar Science, November 1 2007; 1149064

Santa Fe 2007

Very slow crossover!

T*

Slow crossover pointed out by NPF 2004

Buildup of coherence in single impurity case

TK

cohere

nt

spect

ral

weig

ht

T scattering rate

coherence peak

Buildup of coherence

Crossover around 50K

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Consistency with the phenomenological approach of

NPF

Remarkable agreement with Y. Yang & D. Pines cond-mat/0711.0789!

+C

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ARPESFujimori, 2006

Angle integrated photoemission vs DMFT

Experimental resolution ~30meV, theory predicts 3meV broad band

Surface sensitive at 122eV

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Angle integrated photoemission vs DMFT

ARPESFujimori, 2006

Nice agreement for the• Hubbard band position•SO split qp peak

Hard to see narrow resonance

in ARPES since very little weight

of q.p. is below Ef

Lower Hubbard band

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T=10K T=300Kscattering rate~100meV

Fingerprint of spd’s due to hybridization

Not much weight

q.p. bandSO

Momentum resolved Ce-4f spectraAf(,k)

Hybridization gap

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DMFT qp bands

LDA bands LDA bands DMFT qp bands

Quasiparticle bands

three bands, Zj=5/2~1/200

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Momentum resolved total spectra A(,k)

Fujimori, 2003

LDA+DMFT at 10K ARPES, HE I, 15K

LDA f-bands [-0.5eV, 0.8eV] almostdisappear, only In-p bands remain

Most of weight transferred intothe UHB

Very heavy qp at Ef,hard to see in total spectra

Below -0.5eV: almost rigid downshift

Unlike in LDA+U, no new band at -2.5eV

Large lifetime of HBs -> similar to LDA(f-core)rather than LDA or LDA+U

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Optical conductivity

Typical heavy fermion at low T:

Narrow Drude peak (narrow q.p. band)

Hybridization gap

k

Interband transitions across hybridization gap -> mid IR peak

CeCoIn5

no visible Drude peak

no sharp hybridization gap

F.P. Mena & D.Van der Marel, 2005

E.J. Singley & D.N Basov, 2002

second mid IR peakat 600 cm-1

first mid-IR peakat 250 cm-1

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•At 300K very broad Drude peak (e-e scattering, spd lifetime~0.1eV) •At 10K:

•very narrow Drude peak•First MI peak at 0.03eV~250cm-1

•Second MI peak at 0.07eV~600cm-1

Optical conductivity in LDA+DMFT

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CeIn

In

Multiple hybridization gaps

300K

e V

10K

•Larger gap due to hybridization with out of plane In•Smaller gap due to hybridization with in-plane In

non-f spectra

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Fermi surfaces of CeM In5 within LDA

Localized 4f:LaRhIn5, CeRhIn5

Shishido et al. (2002)

Itinerant 4f :CeCoIn5, CeIrIn5

Haga et al. (2001)

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de Haas-van Alphen experiments

LDA (with f’s in valence) is reasonable for CeIrIn5

Haga et al. (2001)

Experiment LDA

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Fermi surface changes under pressure in CeRhIn5

Fermi surface reconstruction at 2.34GPa Sudden jump of dHva frequencies Fermi surface is very similar on both sides, sl

ight increase of electron FS frequencies Reconstruction happens at the point of maxim

al Tc

Shishido, (2005)localized itinerant

We 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

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Electron fermi surfaces at (z=0)

LDA+DMFT (10 K)LDA LDA+DMFT (400 K)

X M

X

XX

M

MM

2 2

Slight decrease of the electron

FS with T

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R A

R

RR

A

AA

3

a

3

LDA+DMFT (10 K)LDA LDA+DMFT (400 K)

Electron fermi surfaces at (z=)No a in DMFT!No a in Experiment!

Slight decrease of the electron

FS with T

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LDA+DMFT (10 K)LDA LDA+DMFT (400 K)

X M

X

XX

M

MM

c

2 2

11

Electron fermi surfaces at (z=0)Slight decrease of the electron

FS with T

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R A

R

RR

A

AA

c

2 2

LDA+DMFT (10 K)LDA LDA+DMFT (400 K)

Electron fermi surfaces at (z=)No c in DMFT!No c in Experiment!

Slight decrease of the electron

FS with T

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LDA+DMFT (10 K)LDA LDA+DMFT (400 K)

X M

X

XX

M

MM

g h

Hole fermi surfaces at z=0

g h

Big change-> from small hole like to large electron like

1

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Hole fermi surface at z=

R A

R

RR

A

AANo Fermi surfaces

LDA+DMFT (400 K)LDA+DMFT (10 K)LDA

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dHva freq. and effective mass

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Gradual decrease of electron FS

Most of FS parts show similar trend

Big change might be expected in the plane – small hole like FS pockets (g,h) merge into electron FS 1 (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 surfacesFermi surfaces

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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 type’s 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 1 electron FS.

ConclusionsConclusions

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ARPES of CeIrIn5

Fujimori et al. (2006)

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•Ir atom is less correlated than Co or Rh (5d / 3d or 4d)

•CeIrIn5 is more itinerant(coherent) than Co (further away from QCP)

CeCoIn5 CeRhIn5 CeIrIn5

Tc[K] 2.3K 2.1K@p>1.5GPa

0.4K

Cv/T[mJ/molK^2] 300 50 750

Why CeIrIn5?

Phase diagram of 115’s

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General impurity problem

Diagrammatic expansion in terms of hybridization +Metropolis sampling over the diagrams

•Exact method: samples all diagrams!•Allows correct treatment of multiplets

k

K.H. Phys. Rev. B 75, 155113 (2007)

Continuous time “QMC” impurity solver, expansion in terms of hybridization

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Ce 4f partial spectral functions

LDA+DMFT (10K) LDA+DMFT (400K)

Blue lines : LDA bands