A DCA Study of the High Energy Kink A DCA Study of the High Energy Kink Structure in the Hubbard Model SpectraStructure in the Hubbard Model Spectra

M. Jarrell, A. Macridin, Th. Maier, D.J. Scalapino

Thanks to T. Devereaux, A. Lanzara, W. Meevasana,B. Moritz, G. A. Sawatzky, and F. C. Zhang

Dresden, April 07

OutlineOutline

• HE kink• Model + DCA• Results for Spectra• Possible Method to Analyze Cuprates• Conclusion

Ū Ūχc

sΣ =

Graf

Some High Energy Kink ReferencesSome High Energy Kink References

J. Graf, et al., preprint, cond-mat/0607319.[4] W. Meevasana, et al., preprint, cond-mat/0612541.[5] T. Valla, et al., preprint, cond-mat/0610249.[6] J. Chang, et al., preprint, cond-mat/0610880.[7] B. P. Xie, et al., preprint, cond-mat/0607450.[8] Z.-H. Pan, et al., preprint, cond-mat/0610442.

J. Graf, et al., preprint, cond-mat/0607319.W. Meevasana, et al., preprint, cond-mat/0612541.T. Valla, et al., preprint, cond-mat/0610249.J. Chang, et al., preprint, cond-mat/0610880.B. P. Xie, et al., preprint, cond-mat/0607450.Z.-H. Pan, et al., preprint, cond-mat/0610442.6Q.-H. Wang, et al., preprint, cond-mat/0610491.C. Grober, et al., Phys. Rev. B 62, 4336 (2000).S. Odashima, et al., Phys. Rev. B 72, 205121 (2005).F. Ronning, et al., Phys. Rev. B 71, 094518 (2005).E. Manousakis, preprint, cond-mat/0608467.K. Byczuk, et al., Nature Physics, cond-mat/0609594.A. Macridin, et al. preprint, cond-mat/0701429.cond-mat/0701429

High-Energy Kink (overdoped Bi2201)High-Energy Kink (overdoped Bi2201)

Meevasana et al., cond-mat/0612541

HE kink beginning at about 0.25-0.3 eVHigh energy band

(bottom) falls below LDA

Modelling The CupratesModelling The Cuprates

tU

(Zhang and Rice, PRB 1988, P.W. Anderson)

U=W=8t≈2eV for the cuprates

Small Parameter?Small Parameter?

BCS (conventional) SC:

Small parameter:

Electron-phonon vertex:

Neglect classes of diagrams:

Cuprate (unconventional) SC:

No small energy scale:

But in Cuprates:

Thurston et al. (1989)

Short-ranged AF correlations

Dynamical Cluster ApproximationDynamical Cluster Approximation

Short length scales, within the cluster, treated explicitly.

Long length scales treated within a mean field.

Periodic LatticeDCA (M. Hettler, PRB)

Effective Medium

For a review of quantum cluster approaches: Th. Maier et al., Rev. Mod. Phys. 77, pp. 1027 (2005).

QMC Cluster SolverQMC Cluster Solver

ORNL/CES X1e, Xt3

Effective Medium

QMC in the Infinite Dimensional Limit, M. Jarrell, QMC Methodsin CM Physics, Ed. M. Suzuki, (World Scientific, 1993), p221-34.

The Hubbard Model in Infinite Dimensions: A QMC Study, Mark Jarrell, Phys. Rev. Lett. 69, 168-71 (July 1992).

A QMC Algorithm for Non-local Corrections to the Dynamical Mean-Field Approximation, M. Jarrell, PRB 64, 195130/1-23 (2001).

102—104 procs.

4-site cluster DCA - 2D Hubbard model4-site cluster DCA - 2D Hubbard model

U=8t

MJ, EPL, 2001N

c=4, U=W=2, t'=0

Inverse d-wave pairing susceptibility Inverse d-wave pairing susceptibility ((UU=4=4tt; ; nn=0.90)=0.90)

Cluster Zd4A 0(MF)

8A 1

12A 2

16B 2

16A 320A 424A 426A 4

SuperconductingTransition

Th. Maier, PRL

The Mechanism: Clues from the pairing matrix The Mechanism: Clues from the pairing matrix

P P = + = (1 - Γ )1

Nc=24, U=4t, N=0.9

T/t

χs((p,p),m)

((,0),n)

Th. Maier, PRL

n,

m/t

Nonlocal corrections in spectraNonlocal corrections in spectra

DMF

DCA (Nc=16)

Non-local corrections to DMF distort the Fermi surface.

Act like t' (t'')

Phys. Rev. B 66, 075102 (2002).

A(k,=0) U=8t, t=8

()

(0,0)

High-Energy Kink in the 2D Hubbard High-Energy Kink in the 2D Hubbard ModelModel

n=0.8, U=8t, cluster 16B, Ekink

= - t(0,0) (,) (0,0) (,0)

A. Macridinunpublished

Kink at Ekink

≈-t

(0,0) Dispersion below bare band

High Energy Kink in the Self EnergyHigh Energy Kink in the Self Energy

Features below kink energy E

kink depend

weakly on K

QP Peaks in A(k,) when Re(+- E(k) - (k,))=0

intersection of black and blue lines

-Im(k,) large for Ekink

Abrupt change in slope of Re(k,) for E

kink

signals the start of the waterfall structure in spectra.

Dispersion for large || falls below bare result by causality. Here, Re(k,) ~ a/, where a=∫d (-1/ Im(k,) >0

Bandstructure (t') changes waterfallBandstructure (t') changes waterfall

t'=-0.3t t'=0

(0,0) (,) (0,0) (,)

A. Macridin, PRL036401 (2006)

dive more steep for h-doped (t'<0)less steep for e-doped (t'>0, but AF)

Origin of the HE KinkOrigin of the HE Kink

Spin, charge, and pair terms (different ).

Spin dominates

Ū<U due to QP renormalization.

Spin RSO used for cuprates and Heavy Fermions

Kampf & Schrieffer, RPB 42 (1990).

M. Norman, PRL. 59, 232 (1987).

Berk & Schrieffer, PRL 17 433 (1966).

Valla, ibid.

Ū Ūχc

sΣ =

(0,0) (,0)(0,0) (,)

n=0.8, U=8t, cluster 16B, Ekink

= - t

Origin of the Kink in RSOOrigin of the Kink in RSO

A. Macridinunpublishedcm-0701429

RSO and DCA/QMC self energies agree for <0.

HE kink comes from QP scattering from high energy spin fluctuations.

k

k

magnondispersion

≈2J

(0,0) (,) (,) (0,0)

HE Spin Excitations and dopingHE Spin Excitations and doping

RSO Applied to SuperconductivityRSO Applied to Superconductivity

= ( )Ū Ūχc

sΣ = Ū Ūχc

swherenow

Ū(T)

T

About thesame Ū

obtained from A(k,) Φ

d((π,

0),ω

n)

ωn

pp

Possible method to analyze experimentPossible method to analyze experiment

Extract spin S(q,) from neutron scat.

use to calculate (k,)=

Compare to ARPES to determine Ū

Use interaction in a DCA extension of Migdal Eliashberg (J. Hague) to calculate superconducting properties

Test 1-band model and spin-fluctuation mediated pairingfor the cuprates.

χc

s

χc

s

Ū Ūχc

sΣ = Ū Ūχc

s

ŪŪ

ConclusionConclusion

DCA-QMC simulations of 1-band model captures many cuprate featuresHE kink in 2D HM due to coupling to HE spin fluctuations

Features <0 are well described by coupling quasiparticle to spin fluctuations.Same approximation captures superconducting properties.

Contributes to the method used to analyze experiment

Magnons in 214Magnons in 214