Ubiquitous Generalized ARPES Signatures of Electron Fractionalization in Quasi-Low Dimensional Metals Dr. Jim Allen, Univ of Mi

Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

Ubiquitous generalizd ARPES signatures of electron fractionalization in quasi-low dimensional metals

G.-H. Gweon, J.D. Denlinger1, J.W. Allen University of Michigan, Department of Physics 1 permanent address now Advanced Light Source, LBNL C.G. Olson Ames Laboratory, University of Iowa H. Höchst Synchrotron Radiation Center, University of Wisconsin J. Marcus and C. Schlenker, LEPES, CNRS, Grenoble L.F. Schneemeyer Bell Laboratories, Lucent Technologies

Supported at U-M by U.S. DoE and NSF

University of Michigan FESP02--Groningen

Angle resolved photoemission spectroscopy (ARPES) to measure ρ (k,ω) • Photon In • (Photo-)Electron Out • Electron KE, hν, ⇒ bind. en. ω • Angles θ, φ → k-par, cons. at surf. • k-perp -- not conserved, must model surface potential • Electron Energy Distribution (ω) Surface Normal = ρ (k,ω) x Fermi function x (ARPES cross-section)

ω MDC (fix ω, scan k) EDC (fix k, scan ω) “FS” map ( =EF, scan k region)

∆ Photo-electron lifetime gives k-perp low-dimension better! and extra ∆ω for 3d crystals

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Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 1 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

Luttinger liquid (Tomonaga-Luttinger model) spectral function much different from FL

Meden & Schönhammer ’92, Voit ’93, vc TL lineshape vs · two features- holon and spinon · power law tails E · spinon: F α > ½ edge α < ½ peak (shown)

· gap to EF except for k=kF ρ ω k-summed spectrum LOC( ) approaches EF as power law in EF α-- even though system metallic!! CDW fluctuations can give NFL Σ ≈ pseudogap & mimic kA(k,EF) 0 University of Michigan FESP02--Groningen

Early Experimental Motivations

Cuprate ARPES NFL lineshapes → Signal of LL? ∑ ≈ → Quasi-1-d PES, kA(k,0) 0 LL? CDW pseudogap?

Olson (‘90) Dardel (‘91)

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Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 2 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

Low-D Metals and Fermi Surfaces

30K Li Mo O HTSC cuprates 0.9 6 17 Non-FL SC Non-FL, Non-CDW (24K), Γ Y

SC (1.9K) Χ M 1 11 Borisenko et al (’00)

K0.3MoO3 ” Non-FL Spin gapped ss CDW (180K)

ene Luther-Emery g Model ? AMo6O17 (A=Na,K)

an Hidden Nesting CDW r t

S (~100K) “

G.-H. Gweon thesis

samples from TiTe2 Marcus, Schlenker Fermi Liquid Grenoble Straub et al (’97)

1 Dimensionality of EF Electronic Structure 2 University of Michigan FESP02--Groningen

TiTe2 Fermi liquid lineshape fits near kF

Not FL lineshape at bottom of band Claessen et al PRL, 1992 T = 20K ∆k=0.07Å-1 ∆ω=35 meV

k < kF n k F Z Quadratic tails k > k for k near kF F k kF

Can remove electron for k > kF because of hole/particle pairs in many body ground state University of Michigan FESP02--Groningen

Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 3 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

Li0.9Mo6O17 properties consistent with LL above a mystery phase at 24K

Schlenker (' 85) Also 1.9 K SC diGiorgi (' 88)

specific heat Mystery phase below 24 K • ρ upturn

• weak CV anomaly • no gap > 1 meV • no CDW, SDW reflectivity in x-ray diffraction 300K, 4K same (Pouget, 2001) Schlenker (‘93) Greenblatt (' 84) Above 24 K Linear! consistent with LL ∝ • CV T term exists • χ ∝ const resistivity • ρ ∝ T (in one theory) magnetic susceptibility University of Michigan FESP02--Groningen

Temperature dependence in Li0.9Mo6O17 PES no Fermi edge, no EF gap opening

1 Angle integrated mode

1 hv=33eV, ∆E=30meV 300 K 250 K 113 K

0.8 150 K 100 K 50 K

25 K Intensity (arb. units)

0.2 0.6 12 K 250 K

0 -0.4 -0.2 0 0.2 150 K E - E F (eV) 100 K 0.4 50 K

Intensity (arb. units) ESCALAB HeI 0.1 25 K 12 K

Intensity (arb. units)

0.2

-0.1 0 0.1 E - E F (eV) -1 0 E - E (eV) SRC F 4k T for 250K 4k T for 100K NIM/Scienta B B Gradual change from 250K to 12K. No Fermi edge. No gap. Only edge sharpening at small T University of Michigan FESP02--Groningen

Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 4 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

Li0.9Mo6O17 quasi 1-D Fermi surface

30K Cleavage Plane y x Parallel to surface k Photon energy 24eV (A). y B Scan two angles. Γ Y

Perpendicular to surface Χ M Fix one angle (B). Vary photon energy and 1 11 200K other angle.

SRC, Ames/Montana beamline kkz⊥ ∆Ε = 150meV A Denlinger, Gweon, Allen…,PRL ‘99 kx (24eV) University of Michigan FESP02--Groningen

Li0.9Mo6O17 band structure (Whangbo '88)

M 1D Fermi surface due to bands C and D

D C D B B A C A M

Bands A and B

don't cross EF

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Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 5 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

Γ Li0.9Mo6O17 – ARPES data - Y compared to TL theory for non-zero T (Orgad)

C Unique as quasi-1d B metal with TL lineshape kF

Holon peak

Spinon Using Theory edge of Orgad ’01 α = 0.9 k F vFc = 2 vFs E-E (eV) Finite T ∆Ε=49meV F ∆θ o T = 250 K =0.36 E-EF (eV) University of Michigan FESP02--Groningen

vc/vs Dependence of Finite T TL Line Shape

vc is fixed to track the peak position Li Bronze vc/vs=1 v /v =1.5 ARPES c s Data Edge spacing Edge spacing much too large too large

vc/vs=2 vc/vs=3 vc/vs=4

Best choice Edge spacing Edge spacing too small much too small

E – µ (eV) E – µ (eV) E – µ (eV)

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Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 6 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

α Dependence of Finite T TL Line Shape

Li Bronze ARPES α = 0.6 α = 0.7 Data Too much Too much µ µ weight weight

α = 1.0 α = 0.8 α = 0.9 Still a little OK too much. OK But maybe Best choice OK?

E ± µ (eV) E ± µ (eV) E ± µ (eV)

α limited to 1 in this theory University of Michigan FESP02--Groningen

(K, Na) purple bronzes (quasi 2d, CDW) Fermi surface shows “hidden” one dimensionality

ν ∆ KMo6O17 h =22eV, E=100meV, T=150K (TCDW=80K)

3 weakly interacting QCDW quasi 1d chains 120 degrees apart

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Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 7 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

NaMo6O17 ARPES Lineshapes Strange

Couldn© t interpret data before taking FS map!

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Generalized ARPES signatures of electron fractionalization into density waves

LL a paradigm theory for electron fractionalization. But seldom find materials which map neatly onto any non-FL model

Example: Can© t describe NFLl ineshapes of spin-gapped blue bronze with ANY model

Need to break free from "toy model straightjacket!" Look for generalized signatures of fractionalization

· Vanishing Weight at EF (No QP) e.g. Power Law (Anomalous Dimension α) of LL · Anderson-Ren Power Law Tail Line Shape (Anom. Dim.) · Two (or More) Objects Moving At Different Speeds: e.g. Holon (Peak) and Spinon (Peak or Edge) of LL · Sharp MDC, Broad EDC (Orgad et al '01)

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Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 8 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

Progressive angle integration for FL (TiTe2) and LL (Li purple bronze)

Angle int. TiTe2 Li0.9Mo6O17 T=300 ARPES data ARPES data hν=21.2 eV angle sum to angle sum to ∆E = 33 meV Fermi edge power law

α = 0.9 Fermi edge

[-11o,5o] [-8o,5o] [-3.6o,0.7o] o o [-5o,5o] [-2.9 ,0.7 ] [-2.2o,0.7o] [-3o,3o] [-1.4o,0.7o] o o [-2 ,2 ] [-0.7o,0.7o] [-1o,1o] ≡ o kF ( 0 ) ≡ o kF ( 0 ) -0.5 0 − E EF (eV) E-EF (eV) University of Michigan FESP02--Groningen

Vanishing k-summed EF Weight ?

Quasi 1d α=0 Quasi 1d K0.3MoO3 (FE) Li0.9Mo6O17 TL model α=0.1 α

) =0.7 T=300K α=0.9 T=300K

s T=300K t i ∆E=33meV hν=21.2eV hν=21.2eV

un ∆ α=1.0 ∆E=33meV E=33meV . b r a ( y

t Quasi 2d T=25K i

s ν NaMo6O17 h =21.2eV n ∆ TiTe2 e E=35meV t n I Bi2212 α=0 α=0.3 α=0 T=300K T=115K hν=21.2eV hν=22eV ∆E=33meV ∆E=16meV

E ± µ (eV) important to use (0,0) → (π,π) TL theory for maybe α≠0 non-zero T E range < ∆E

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Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 9 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

Anderson-Ren lineshape visualization

Break follows dispersion ε(k)

Common power law for all spectra α-1 |E-EF| Bi2212 y t i

s Kaminsky '01 n Γ (0,0) − π π e Y ( , ) t n I hν=22 eV T=115K

BUT NOT LL! ε Cutoff LL sing. moves with k

Energy EF VISUALIZATION of Bi2212 ARPES lineshape NO for FL TiTe (Anderson/Ren, 1990) 2

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AR lineshape for quasi 1-d systems

K0.3MoO3 ) s t i T=250K un

. -0.80 b |ω| r a ( y t i ω -0.29

s | | n e t n

I T=250K

Li0.9Mo6O17

E ± µ (eV)

YES for K0.3MoO3 − YES for Li0.9Mo6O17 |ω| 0.8 α = 0.2 −0.29 |ω| α = 0.71 ≠ 0.7, blue bronze trouble not 0.9 but > 0.5 spin gap breaks AR connection to α

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Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 10 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

Narrow MDC and Wide EDC

Orgad et al, EDC PRL 86, 4362 (2001) (kF, EF)

Reported for MDC Bi2212 and static stripe cuprate

T=0, LL Kinematic Constraint of Decomposition of e- into Spinons and Holons Holds for finite T and LE as well. Generalized to other Density Waves? University of Michigan FESP02--Groningen

Sharp MDC and Broad EDC ? For quasi-1d systems

MDC 0 Li0.9Mo6O17 MDC EDC ) V e C ( T=250K D F -0.2 E E -

E Theory (Orgad)

-0.4 Difference Γ Y MDC 0 K0.3MoO3 )

V MDC e

( T=250K F

-0.2 EDC E - E C D -0.4 E Γ ← X k vFs / T (E-EF) / T Both MDC Width and EDC Width Intrinsic University of Michigan FESP02--Groningen

Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 11 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

All Four Fractionalization Signatures in Quasi-2 d (hidden 1-d) NaMo6O17 FS defined by 4 broad EDC unscattered spinon QCDW sharp MDC (peak since α< 0.5)

3 badly scattered holon from Na disorder M-K'

NaMo6O17

k α=0.3 F

T=300K hν=21.2 eV ∆E=33 meV

1 2 Power law at EF A-R lineshape University of Michigan FESP02--Groningen

Bi2212 Line Shape ≈ Na Purple Bronze Line Shape

NaMo6O17 M-K' Na purple bronze % of MK’ spectra as

Rosetta stone k = kF for recognizing

fractionalization in the presence of disorder

in HTSC cuprates

E – µ (eV) Bi2212 Dessau ‘93 PRL

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Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 12 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

Early statements that the cuprate "background" is intrinsic

Can fit Olson et al Bi2212 data with MFL (FL) only if remove "background" 15 (60) times larger than implied by entire VB.

Liu, Anderson, Allen J Phys Chem Sol 1991

Vibronic analogy G.A. Sawatzky, Nature, 1989; Also, further arguments in LANL workshop proceedings, (Addison-Wesley, 1990). University of Michigan FESP02--Groningen

T- linear resistivities in purple bronzes!

⊥c

R. Buder et al J. Phys. Lett. 43, L59 (1982)

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Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 13 Ubiquitous generalized ARPES signatures of electron fractionalization in quasi-low dimensional metals

Summary

Scorecard of generalized fractionalization signatures

• FL example TiTe2 no signatures

• quasi 1-d Li purple bronze (1, 2, 3, 4) LL example

• quasi 1-d K blue bronze (1, 2,--, 4) spin-gapped no lineshape works • quasi 2-d (hidden 1-d) Na purple bronze (1, 2, 3, 4) melted holon α< ½ • quasi 2-d Bi2212 SC cuprate (--, 2, 3, 4) spinon peaky

note: no microscopic derivation of AR lineshape HINTS OF A BIGGER PICTURE !

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Dr. Jim Allen, Univ of Michigan (KITP Correlated Electrons Program 9/17/02) 14