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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

O Bi2Sr2Ca1Cu2O8+δ

a.k.a. Bi2212, BSCCO

Mott Insulator/AFM at ½ Filling Doped Mott Insulator/AFM

δ

BSCCO Phase Diagram

T

T* TN TOng NFL Tc

max = 91 K in Bi2212

AFM PG

• Fluc. SC

T

• fig. by E. W. Hudson

δ

d‐SC Tc FL

Fermi Surface of Bi2212

M Y

“Normal” Tight Binding Type Fermi Surface d‐wave SC Fermi Surface Consists of 4 points called Nodes

M Y

In Pseudogap State only have Fermi “Arcs”

M Y

“Normal” Tight Binding FS

M Y

. .

M M Γ Y M M Γ Y M Γ

. .

M Γ M Γ

Length of arc varies as T/T*

Consider the Pseudogap Regime

Th F i f i th d i i ll th ht t i t f The Fermi surface in the pseudogap regime is generally thought to consist of 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

65K 75K, 79K, UD 89K, OD for ) (r r ∆

STM is spatially resolved and can measure the ~ integrated occupied and

• 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 unoccupied DOS for each atom Near T=0 the Cuprates are electronically disordered in real space though h b ll d d k they appear to be very well ordered in k space

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 Excitation radiation Magnifying high-transmission imaging Electron Lens hν Photoelectrons

∆ 1

Sample Resolution:- ∆E: ~1 meV

∆k: 0.01 Å-1

RPE

) ( ) ( ) ( ( ) ( d f k k

∫

ARPES Intensity

' ) ' ( ). ' ( ). ' , ( ( ) , ( ω ω ω ω ω ω d R f k A k I

∫

− ≈

Use thermal excitation

) ( )) ( ) , ( ( ) , ( ω ω ω ω R f k A k I ⊗ ∝

• f electrons !!

Photoemission measures the occupied states

The photoemission intensity

' ) ' ( ). ' ( ). ' , ( ( ) , ( ω ω ω ω ω ω d R f k A k I

∫

− ≈

How does the PES community look at the other side of the gap, at the hole states?? Either

Raw Data Symmetrize the data

Either

T = 140 K TC ~ 65 K TC 65 K

• r divide

) ( ω k I ) , ( ) ( ). ( ) , ( ω ω ω ω k A R f k I ≈

This is the spectrum that is measured experimentally

The Image The Image

ARPES Intensity

' ) ' ( ). ' ( ). ' , ( ( ) , ( ω ω ω ω ω ω d R f k A k I

∫

− ≈

y

( ) ( ) ( )

ω ω ω ω ω ω π ω f k A k I K d k S ) , ( ' , ' ' ,

4 / 1

= ⎞ ⎜ ⎜ ⎛ − =

∫

+∞

∫

( ) ( ) ( )

ω f ) , ( , 2 ,

4 / 1

⎠ ⎜ ⎝

∫

∞ −

( )

( )

( )

( )

8 8 cos 2 cos

4 5 8 sin 2

4 5

π π

π

− =

−

x e x K

x

( ) ( )

( )

8 8 cos 2 cos π π x e x K

To be published Nature p

Summary of different analyses Summary of different analyses

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

The spectral function for a conventional BCS superconductor takes the form:

2 2

1 1 ) ( Γ + Γ

k k

v u k A ω

2 2 2 2

) ( ) ( ) , ( Γ + + + Γ + − =

k k

E E k A ω π ω π ω

⎞ ⎜ ⎛ −

F k

E ε 1 1

2

2 2

hole) a (adding electron an removing

• f

y probabilit , for

k k

u c = +

⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ± =

k F k k

E E c ε 1 2 1

2

F 2 2

E above electron an adding

• f

y probabilit , for ) ( g g y p

k k k k

v c = −

1

2 2

= +

k k

v u

2 2

) ( E E ∆ + = ε ) (

k F k k

E E ∆ + − = ε

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

(a) OP ( TC = 91 K) UD (TC = 65 K)

T < TC

(a) (c)

T = 50 K T = 80 K T = 50 K T = 80 K

(b) (d) (d)

1 2 3 1 2 3 OP 91K

T = 140 K

UD 60K

(d)

α = 9 deg α = 0 deg α = 18 deg

Divided by Fermi function T = 140 K T 140 K TC ~ 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 d Ri Zhang and Rice 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)

⎞ ⎛ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − ± =

k F k k

E E v ε 1 2 1

2

Coherence Factors

⎠ ⎝

“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 Binding En ( V) EF Energy (eV) 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) Fermi arc length t = T/T* A Kanigel et al

Submitted to Nature

• A. Kanigel et al.,

Nature Phys. 2, 447 (2006).

40K 110K 50K 120K 2 1 2

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 f hi h t t d ti it ”

• f high-temperature superconductivity”
• 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 BNL Tony Valla BNL Alexei Tsvelik Genda Gu

The End