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)

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 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)

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.

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

d-wave BCS superconductor:

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

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

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)

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 2 2 Doping BV and E. Bascones PRl 98, 227002 (2007) Also able to reproduce the decrease in intensity of antinodal Raman peak with underdoping

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, 174501 (2006) QCP

“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

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

Two scales in the Raman spectra BV and E. Bascones PRl 98, 227002 (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.

Two pair-breaking transitions below xc BV and E. Bascones PRl 98, 227002 (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

Two pair-breaking transitions below xc BV and E. Bascones PRl 98, 227002 (2007) X=0.14, E- X=0.14, E+ X=0.20, E-& E+

Gap at the maximum intensity surface: U-shape in ARPES BV and E. Bascones PRl 98, 227002 (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

The convergence of the two energy scales and the possible phase-diagram scenarios BV and E. Bascones PRl 98, 227002 (2007) QCP scenario T=0 Do not confuse convergence of scales below Tc with convergence of T* and Tc xc

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, 067005 (2006) Suggest similar origin for dispersive and non-dispersive peaks

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

AC-ARPES in the Pseudogap State (below xc) along bond EXPERIMENT Chatterjee et al, PRL 96, 067005 (2006) Calculated AC-ARPES spectra E. Bascones and B. V. cond-mat/0702111 q 2 3(2 Suggests q*5 as origin of ¾ substructure

Dispersive and/or non-dispersive peaks can appear in the SC state below xc -> confirmed in Chatterjee arXiv:0705.4136 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 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

Doping independent slope in B2g at low frequencies X=0.14 X=0.18 X=0.20 BV and E. Bascones PRl 98, 227002 (2007) Le Tacon et al, Nat. Phys. 2, 537 (2006)

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

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, 174501 (2006)

A third “crossing” transition is expected below xc Superconducting state BV and E. Bascones PRl 98, 227002 (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

Total Raman response in the SC state BV and E. Bascones PRl 98, 227002 (2007) The crossing transition is hardly distinguished in the superconducting state

And what else? BV and E. Bascones PRl 98, 227002 (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