1. B. Valenzuela Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC)
Spectroscopic signatures of two energy scales in superconducting underdoped cuprates
B. Valenzuela
Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC)
In collaboration with:
Elena Bascones
(ICMM-CSIC)

2. 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.

3. Pseudogap State: Fermi arcs and Nodal-Antinodal Dichotomy
Antinodal region
Nodal region
El pseudogap se ve en todos los cupratos y experimentalmente lo que se ve es una reduccion de la densidad de estados o una reduccion
En los procesos de scattering. ARPES NODAL ANTINODAL
Shen et al, Science 307, 901 (2005)

4. Superconducting phase
Conventional BCS
d-wave superconductivity?
Recently nodal-antinodal dichotomy has also been observed in underdoped
It is a condensate of Cooper pairs. Experimentos de fotoemisión revelan picos en el espectro de excitaciones indicando la presencia de
Cuasipartículas que predice la teoría BCS. Simetría d-wave no trivial. Sin embargo experimentos de Raman y ARPES muy recientes
Nos dicen que parece que hay dos escalas una nodal y otra antinodal en la zona superconductora infradopada.

5. Scenarios for the High-Tc cuprates
QCP at xc
Standard BCS
La superconductividad es una inestabilidad del estado normal y por lo tanto para entender el origen de la superconductividad necesitamos
Entender el estado normal del que surge. RVB: el pseudogap (J-tx) se forma cuando los spines forman singletes y este spin gap reduce el
Escattering entre los huecos que da lugar a un pico de Drude mas estrecho en la fase del pseudogap. Pares de Cooper se forman
En T* y coherencia a Tc. xc
Pseudogap and
superconductivity
have a common origin
Pseudogap and superconductivity are
different instabilities which compete

6. d-wave BCS superconductor:

7. d-wave BCS: A single energy scale Ds
Gap depends linearly
on cos(2f): V-shape
coskx-cosky
Nodal velocity vD=1/2(dDs(f)/df)|f=p/4=Ds Antinodal gap, Dmax=Ds(f=p/2)=Ds

8. ARPES deviations from d-wave BCS in Underdoped SC Cuprates
U-shape
K. Tanaka et al, Science 314, 1910 (2006)
Two scales in Energy spectrum
with underdoping vD decreases
Dmax increases

9. Two energy scales in Raman Spectrum in the SC State of Underdoped Cuprates
Energy scale of peak in antinodal (nodal) region increases (decreases) with decreasing doping in underdoped cuprates.
Pair breaking peak intensity decreases with underdoping in antinodal region (opposite behavior expected from increasing energy scale)
Le Tacon et al, Nat. Phys. 2, 537 (2006)

10. Evolution of Nodal and Antinodal energy scales with x
Le Tacon et al,
Nat. Phys. 2, 537 (2006)

11. Evolution of Nodal and Antinodal energy scales with x2 2
Doping
BV and E. Bascones PRl 98, (2007)
Also able to reproduce the decrease in intensity of antinodal Raman peak with underdoping

12. Phenomenological model for doped spin liquid+QCP to describe the pseudogap state
Coherent + Incoherent part
Only diagonal /2
En cupratos el mayor reto es combinar teoría (no perturbativas) con experimento porque al no saber que teoría se debe usar es dificil interpretar el experimento. Es necesario una teoría fenomenológica consistente con todos los experimentos, como el gap en BCS.
Yang, Rice,Zhang PRB 73, (2006)
QCP

13. “Gapless Fermi arcs” X=0.05 X=0.14 X=0.20 E E E ky ky ky kx kx kx
coskx-cosky
coskx-cosky
coskx-cosky

14. Doped spin liquid in the SC State
X=0.10
Pseudogap physics
(and scale DR)
present, if x<xc, in
SC state
X=0.14
X=0.18
X=0.20
Four bands
with energies ±E±
for x<xc
X=0.25

15. Two scales in the Raman spectra
BV and E. Bascones PRl 98, (2007)
X=0.10
X=0.14
X=0.18
X=0.20
X=0.10
X=0.14
X=0.18
X=0.20
Antinodal (B1g) peak shifts
to higher energy and
its intensity decreases
with underdoping.
Nodal (B2g) peak shifts
to lower energy with weaker effect on intensity
with underdoping.

16. Two pair-breaking transitions below xc
BV and E. Bascones PRl 98, (2007)
X=0.10
Pair breaking transitions
with energy 2E+ and 2E-
appear for x<xc when entering
the superconducting state
X=0.14
X=0.18
X=0.20
Only one pair breaking
transition can be
distinguished for x≥xc
X=0.25

17. Two pair-breaking transitions below xc
BV and E. Bascones PRl 98, (2007)
X=0.14, E-
X=0.14, E+
X=0.20, E-& E+

18. Gap at the maximum intensity surface: U-shape in ARPES
BV and E. Bascones PRl 98, (2007)
X=0.14 (x<xc)
X=0.20 (x ≥ xc) E E
coskx-cosky
coskx-cosky ky ky
U-shape
vD decreases
Dmax increases
with underdoping
V-shape
Single scale
vD=Dmax kx kx

19. The convergence of the two energy scales and the possible phase-diagram scenarios
BV and E. Bascones PRl 98, (2007)
QCP scenario
T=0
Do not confuse convergence
of scales below Tc with
convergence of T* and Tc xc

20. 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
along bond
Chatterjee et al,
PRL 96, (2006)
Suggest similar origin for
dispersive and non-dispersive peaks

21. AC-ARPES in the absence of Pseudogap Correlations (beyond xc)
Dispersive peaks in SC State
Calculated
AC-ARPES
spectra
EXPERIMENT

22. AC-ARPES in the Pseudogap State (below xc)
along bond
EXPERIMENT
Chatterjee et al,
PRL 96, (2006)
Calculated
AC-ARPES
spectra
E. Bascones and B. V.
cond-mat/ q 2
3(2
Suggests q*5 as origin of ¾ substructure

23. Dispersive and/or non-dispersive peaks can appear in the SC state below xc -> confirmed in Chatterjee arXiv:
E. Bascones and B. V. cond-mat/

24. 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 vD 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

25. Doping independent slope in B2g at low frequencies
X=0.14
X=0.18
X=0.20
BV and E. Bascones PRl 98, (2007)
Le Tacon et al, Nat. Phys. 2, 537 (2006)

26. Hole-doped High-Tc SuperconductorsCu O
(added holes per Cu ion)
Norman et al, Nature 392, 157 (1998)
Overdoped
X=0 (undoped)
Mott insulator
Optimally doped
(Highest Tc)

27. How to fulfill Luttinger sum rule?
Luttinger surface
X=0.05
X=0.10
X=0.14
Hole pockets
X=0.18
X=0.20
Topological QCP
Yang, Rice,Zhang PRB 73, (2006)

28. A third “crossing” transition is expected below xc
Superconducting state
BV and E. Bascones PRl 98, (2007)
A transition with
energy E-+E+
is expected in both
superconducting and
pseudogap states
X=0.14
Pseudogap state
X=0.14
Small effect of this transition
in the subtracted response

29. Total Raman response in the SC state
BV and E. Bascones PRl 98, (2007)
The crossing transition is hardly distinguished in the superconducting state

30. And what else?
BV and E. Bascones PRl 98, (2007)
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 vD ~DS also in cellular DMFT