Particle Hole Asymmetry in the Pseudogap Particle-Hole Asymmetry in - PowerPoint PPT Presentation

Particle Hole Asymmetry in the Pseudogap Particle-Hole Asymmetry in the Pseudogap Phase of the High Tc Superconductors Peter Johnson Condensed Matter Physics and Materials Science Department BNL BNL Hvar 2008 Hvar 2008

A Cuprate Bi 2 Sr 2 Ca 1 Cu 2 O 8+ δ O Mott Insulator/AFM at ½ Filling Doped Mott Insulator/AFM a.k.a. Bi2212, BSCCO δ BSCCO Phase Diagram NFL T * T N T Ong T c max = 91 K in Bi2212 T PG AFM Fluc. SC T T c d ‐ SC FL fig. by E. W. Hudson δ

Fermi Surface of Bi2212 “Normal” Tight Binding d ‐ wave SC Fermi Surface In Pseudogap State only have “Normal” Tight Binding FS Type Fermi Surface Consists of 4 points called Nodes Fermi “Arcs” M M Y Y M M M M Y Y Y Y . . Γ Γ Γ Γ Γ M M M M M . . Length of arc varies as T/T*

Consider the Pseudogap Regime Th F The Fermi surface in the pseudogap regime is generally thought to consist of i f i th d i i ll th ht t i t f Fermi arcs with the spectral function peaking at the Fermi level and gapped regions where the spectral function shows a minimum at the Fermi level.

A Brief Word About Real Space – STM/STS r ∆ ( r ) for OD 89K, UD 79K, 75K, 65K K. McElroy et al , PRL 94 , 197005 K.M. Lang et al , Nature, 415 , 412 STM is spatially resolved and can measure the ~ integrated occupied and STM is spatially resolved and can measure the ~ integrated occupied and unoccupied DOS for each atom Near T=0 the Cuprates are electronically disordered in real space though they appear to be very well ordered in k space h b ll d d k

Can we bridge the gap between STS and Photoemission? Can we bridge the gap between STS and Photoemission?

Photoelectron Spectrometer /multi-channel detection in emission angle and kinetic energy/ Wide-band Energy Analyzer 2-Dimensional (Energy and Angle) high-resolution electron detector Magnifying Magnifying high-transmission Excitation imaging Electron Lens radiation h ν Photoelectrons Resolution:- ∆ E: ~1 meV ∆ 1 Sample ∆ k: 0.01 Å -1

∫ ∫ ω ≈ ω ω ω − ω ω ARPES RPE ( ( , ) ) ( ( ( ( , ' ). ) ( ( ' ). ) ( ( ' ) ) ' I k k A k k f f R d d Intensity Use thermal excitation of electrons !! ω ∝ ω ω ⊗ ω ( , ) ( ( , ) ( )) ( ) I k A k f R Photoemission measures the occupied states

The photoemission intensity ∫ ω ≈ ω ω ω − ω ω ( , ) ( ( , ' ). ( ' ). ( ' ) ' I k A k f R d How does the PES community look at the other side of the gap, at the hole states?? Either Either Symmetrize the data Raw Data T = 140 K T C ~ 65 K T C 65 K or divide ω ω ( ( , ) ) I I k k ≈ ω ( , ) A k ω ω ( ). ( ) f R

This is the spectrum that is measured experimentally

The Image The Image

ARPES ∫ ∫ ω ≈ ω ω ω − ω ω ( , ) ( ( , ' ). ( ' ). ( ' ) ' I k A k f R d Intensity y ⎛ ⎞ +∞ π ω − ω ' ( ( ) ) ( ( ) ) ( ) ( ) ∫ ∫ ⎜ ω = ω ω = ω ω , , ' , , ' ( ( , , ) ) S k d K I k A k f f ⎜ ⎜ ω 1 1 / / 4 4 2 ⎝ ⎠ − ∞ 0 ( ( ) ) ( ) ( ) ( ( ) ) ( ) 5 4 − π = 2 sin 8 5 4 π π − π π cos cos 2 2 cos cos 8 8 8 8 x K K x x e e x x To be published Nature p

Summary of different analyses Summary of different analyses Di idi Dividing by simple Fermi function b i l F i f ti after removal of the resolution broadening

The spectral function for a conventional BCS superconductor takes the form: 2 Γ 2 Γ 1 u 1 v ω ω = k + + k ( ( , ) ) A A k k π ω − + Γ π ω + + Γ 2 2 2 2 ( ) ( ) E E k k ⎛ ⎛ ± ⎞ ⎞ + 2 = 2 ε ε − for , p probabilit y y of removing g an electron ( (adding g a hole) ) 1 1 c u E E ⎜ ⎜ = 2 2 k k k k 1 1 k k F F c ⎜ ⎟ k 2 − 2 = 2 ⎝ ⎠ for , probabilit y of adding an electron above E E c v k F k k 2 + 2 = 1 u v k k = = ε ε − 2 + + ∆ ∆ 2 ( ( ) ) E E E E k k F k

T = 80 K (T C = 91 K) After analysis analysis PES spectra before f analysis

T < T C OP ( T C = 91 K) UD (T C = 65 K) (a) (a) (c) T = 80 K T = 80 K T = 50 K T = 50 K (b) (d) (d)

1 1 2 2 3 3 OP 91K T = 140 K UD 60K (d) α = 0 deg α = 9 deg α = 18 deg

Divided by Fermi function T = 140 K T 140 K T C ~ 60 K Raw Data Symmetrized

Calculations relating to Fermi Pockets Xiao-Gang Wen and Patrick A. Lee g PRL 80, 2193 (1998) K. Yang, TM Rice, FC Zhang PRB 73 , 174501 (2006) Zh Zhang and Rice d Ri Private Communication

What can we say about the Fermi pockets?

ARPES spectra in the cuprates from d-density wave theory Chakravarty et al, Phys Rev B, 68 100504 (2003) Q( π,π ) ⎛ ⎛ ⎞ ⎞ ε − 1 E ⎜ ⎟ 2 = ± 1 Coherence Factors k F v ⎜ ⎟ k 2 ⎝ ⎝ ⎠ ⎠ E k

“Phenomenological theory of the pseudogap state” g y p g p Yang, Rice and Zhang, Phys Rev. B 73, 174501 (2006) “Doped Spin Liquid: Luttinger Sum Rule and Low Temperature Order” Konik, Rice and Tsvelik, Phys Rev. Lett. 96, 086407 (2006)

Magnetic Zone Boundary E F Binding En Energy (eV) ( V) K(A -1 ) ( ) Linear Log 5% or less

Fermi pocket K Yang TM Rice FC Zhang K. Yang, TM Rice, FC Zhang PRB 73 , 174501 (2006) Submitted Fermi arc length t = T/T* to Nature A Kanigel et al A. Kanigel et al. , Nature Phys. 2 , 447 (2006).

120K 50K 40K 110K 2 2 1 Preformed Cooper pairs?? Particle-hole asymmetry

The observation of pairing along the anti-nodal direction is consistent with 1 Dimensional models of the Pseudogap consistent with “1-Dimensional models” of the Pseudogap regime. e g e.g. -- “Spin-gap proximity effect mechanism of high-temperature superconductivity” f hi h t t d ti it ” V. J. Emery, S. A. Kivelson and O. Zachar Phys Rev B 56 , 6120 (1997) “Phenomenological Theory of the Underdoped g y p Phase of a High- Tc Superconductor” A. M. Tsvelik and A.V. Chubukov Phys Rev Lett 98 237001 (2007) Phys Rev Lett 98 , 237001 (2007)

Conclusions 1. The particle-hole asymmetry observed in the ARPES spectra in the pseudogap regime is consistent with the presence of Fermi hole pockets m p 2. The observations are not consistent with pockets generated by scattering vectors of the type Q( π π ) by scattering vectors of the type Q( π,π ) 3. In the pseudogap phase preformed pairs are formed in the anti nodal direction along the copper oxygen bonds and not anti-nodal direction along the copper-oxygen bonds and not in the nodal region.

Hongbo Yang Hongbo Yang Jon Rameau T n V ll Tony Valla BNL BNL Alexei Tsvelik Genda Gu

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