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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)
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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.
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Pseudogap State: Fermi arcs and Nodal-Antinodal Dichotomy
Shen et al, Science 307, 901 (2005)
Antinodal region
Nodal region
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Superconducting phase
Conventional BCS d-wave
superconductivity?Recently nodal-
antinodal dichotomy has also been observed in underdoped
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Scenarios for the High-Tc cuprates
Pseudogap andsuperconductivityhave a common origin
Pseudogap and superconductivity aredifferent instabilities which compete
QCP at xcStandard BCS
xc
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d-wave BCS superconductor:
BCS:
d-wave:
)2cos()cos(cos)( SyxSS kk k
2/122 ))()(()( kkk SE
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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
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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
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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)
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Evolution of Nodal and Antinodal energy scales
with x
Le Tacon et al,
Nat. Phys. 2, 537 (2006)
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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
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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
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“Gapless Fermi arcs”X=0.05 X=0.14 X=0.20
kx kxkx
kykyky
EE E
coskx-cosky coskx-cosky coskx-cosky
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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
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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)
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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)
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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)
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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)
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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)
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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
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AC-ARPES in the absence of Pseudogap Correlations (beyond xc)
Dispersive peaks in SC State
EXPERIMENT
CalculatedAC-ARPESspectra
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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
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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
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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
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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)
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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)
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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
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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)
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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)
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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)