Spectroscopic signatures of two energy scales insuperconducting

underdoped cuprates B. Valenzuela

Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC)

In collaboration with:Elena Bascones(ICMM-CSIC)

Outline

• Conventional superconducting phase in high Tc superconductors?

•Experimental evidence in ARPES and Raman of deviation from d-wave BCS in superconducting underdoped cuprates: two-scales

•Introduction to the phenomenological model proposed to describe the pseudogap (Yang, Rice & Zhang ‘06)

•Results on how two energy scales appear in underdoped superconducting cuprates in ARPES, autocorrelated ARPES and Raman.

Pseudogap State: Fermi arcs and Nodal-Antinodal Dichotomy

Shen et al, Science 307, 901 (2005)

Antinodal region

Nodal region

Superconducting phase

Conventional BCS d-wave

superconductivity?Recently nodal-

antinodal dichotomy has also been observed in underdoped

Scenarios for the High-Tc cuprates

Pseudogap andsuperconductivityhave a common origin

Pseudogap and superconductivity aredifferent instabilities which compete

QCP at xcStandard BCS

xc

d-wave BCS superconductor:

BCS:

d-wave:

)2cos()cos(cos)( SyxSS kk k

2/122 ))()(()( kkk SE

d-wave BCS: A single energy scale s

Nodal velocity v=1/2(ds()/d)|=/4=s

Antinodal gap, max=s(=/2)=s

Gap depends linearly on cos(2): V-shape

coskx-cosky

E

ARPES deviations from d-wave BCS in Underdoped SC

Cuprates

Two scales in Energy spectrum

K. Tanaka et al, Science 314, 1910 (2006)

with underdoping v decreases max increases

U-shape

Pair breaking peak intensity decreases with underdoping in antinodal region (opposite behavior expected from increasing energy scale)

Energy scale of peak in antinodal (nodal) region increases (decreases) with decreasing doping in underdoped cuprates.

Two energy scales in Raman Spectrum in the SC State of Underdoped Cuprates

Le Tacon et al, Nat. Phys. 2, 537 (2006)

Evolution of Nodal and Antinodal energy scales

with x

Le Tacon et al,

Nat. Phys. 2, 537 (2006)

Evolution of Nodal and Antinodal energy scales

with x

Also able to reproduce the decrease in intensity of antinodal Raman peak with underdoping

22

BV and E. Bascones PRl 98, 227002 (2007)

Doping

Energ

y

Coherent + Incoherent part

Yang, Rice,Zhang PRB 73, 174501 (2006)

/2

Phenomenological model for doped spin liquid+QCP to describe the

pseudogap state

),()(),(

kkk

R

tRVB gG

)cos)(cos(2)(0yx kkxt k

)2cos2)(cos(''2coscos)('2)()( 0yxyx kkxtkkxt kk

)cos)(cos()( yxRR kkx k

))(/()(),( 02 kk xRR

)1/(2)( xxxgt

Only diagonal

QCP

“Gapless Fermi arcs”X=0.05 X=0.14 X=0.20

kx kxkx

kykyky

EE E

coskx-cosky coskx-cosky coskx-cosky

Doped spin liquid in the SC State

Four bands with energies ±E±

for x<xc

X=0.10

X=0.14

X=0.18

X=0.20

X=0.25

Pseudogap physics (and scale R)present, if x<xc, in SC state

)),(/()(),(/),(2 kkkk k RSRt

YRZSC gG

Two scales in the Raman spectra

Antinodal (B1g) peak shiftsto higher energy and its intensity decreases with underdoping.

Nodal (B2g) peak shiftsto lower energy with weaker effect on intensitywith underdoping.

X=0.10X=0.14X=0.18X=0.20

X=0.10X=0.14X=0.18X=0.20

BV and E. Bascones PRl 98, 227002 (2007)

Two pair-breaking transitions below xc

X=0.10Pair breaking transitionswith energy 2E+ and 2E- appear for x<xc when enteringthe superconducting state

Only one pair breaking transition can be distinguished for x≥xc

X=0.14

X=0.18

X=0.20

X=0.25

BV and E. Bascones PRl 98, 227002 (2007)

Two pair-breaking transitions below xc

X=0.14, E- X=0.14, E+ X=0.20, E-& E+

BV and E. Bascones PRl 98, 227002 (2007)

Gap at the maximum intensity surface: U-shape in ARPES

X=0.14 (x<xc)

X=0.20 (x ≥ xc)

V-shapeSingle scalev=max

U-shapevdecreasesmax increaseswith underdoping

coskx-cosky

E

coskx-cosky

E

kxkx

kyky

BV and E. Bascones PRl 98, 227002 (2007)

The convergence of the two energy scales and the possible phase-

diagram scenarios

Do not confuse convergence of scales below Tc with convergence of T* and Tc

xc

T=0 QCP scenario BV and E. Bascones PRl 98, 227002 (2007)

Autocorrelation of ARPES data (AC-ARPES)

Dispersive peaks in Superconducting State

Non-Dispersive peaks in Pseudogap from momenta joining the tips of the Fermi arcs

Chatterjee et al, PRL 96, 067005 (2006)

Suggest similar origin for

dispersive and non-dispersive peaks

along bond

AC-ARPES in the absence of Pseudogap Correlations (beyond xc)

Dispersive peaks in SC State

EXPERIMENT

CalculatedAC-ARPESspectra

AC-ARPES in the Pseudogap State (below

xc)

EXPERIMENT

CalculatedAC-ARPESspectra

Chatterjee et al, PRL 96, 067005 (2006)

0 2q3(2

Suggests q*5 as origin of ¾ substructure

along bond

E. Bascones and B. V. cond-mat/0702111

Dispersive and/or non-dispersive peaks can

appear in the SC state below

xc ->

confirmed in Chatterjee

arXiv:0705.41

36

E. Bascones and B. V. cond-mat/0702111

Summary Two energy scales (nodal and antinodal) in the Raman

and ARPES spectra appear naturally in some QCP models below xc

With the YRZ Green’s function scenario v is a good measure of the superconducting order parameter

In this picture the suppression of intensity in B1g channel with underdoping is a consequence of the competition between pseudogap and superconductivity

These results suggest that there is a QCP under the superconducting dome in the high-Tc phase diagram

Other experiments? Autocorrelated ARPES, Prediction: Dispersive and non dispersive peaks in underdoped SC cuprates ->confirmed in experiments

Doping independent slope in B2g at low frequencies

Le Tacon et al, Nat. Phys. 2, 537 (2006)

X=0.14X=0.18X=0.20

BV and E. Bascones PRl 98, 227002 (2007)

Optimally doped (Highest Tc)

X=0 (undoped)Mott insulator

Hole-doped High-Tc Superconductors

Overdoped

(added holes per Cu ion)

O

Cu

Norman et al, Nature 392, 157 (1998)

Yang, Rice,Zhang PRB 73, 174501 (2006)

How to fulfill Luttinger sum rule?

X=0.10X=0.05 X=0.14

X=0.18 X=0.20

Luttinger surface

Topological QCP

Hole pockets

A third “crossing” transition is expected below xc

A transition with energy E-+E+ is expected in bothsuperconducting andpseudogap states

Small effect of this transitionin the subtracted response

Superconducting state

Pseudogap state

X=0.14

X=0.14

BV and E. Bascones PRl 98, 227002 (2007)

Total Raman response in the SC state

The crossing transition is hardly distinguished in the superconducting state

BV and E. Bascones PRl 98, 227002 (2007)

And what else?

B1g: antinodal region participates in superconductivity.

What about QCP models with symmetry-breaking?

Not absolutely ruled out by these experiments but work worse and no clear evidence of phase

transition from other measurements. Pseudogap without long-range, hole pockets,

Luttinger surface, QCP, two gaps in the SC state and vS also in cellular DMFT

BV and E. Bascones PRl 98, 227002 (2007)