The observed sharp ‘kink’ in the ARPES has been related to the phonon or magnetic mode as a possible signature of the force that create the superconducting state in HTSCs. A group of scientists from Canada and the USA have studied this situation by Fourier-transform infrared (FTIR) spectroscopy of optimally doped (Tc=96 K) and highly overdoped (Tc=82, 65, and 60 K) Bi2212 crystals. The optical self energy derived from FTIR (4πσ(ω)=-iω[ε(ω)-εH]=-iωp2/[2Σop(ω)-ω]; Σop(ω)= Σ1op(ω)+iΣ2op(ω)) is in close related with the quasiparticle self energy (Σqp(ω)) from ARPES.
Most important results of this study:
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At high frequencies the scattering rate (1/τ(ω)=-2Σ2op(ω)) has a linear frequency dependence originate from marginal Fermi-liquid behavior. The overall scattering rate decreases as the doping increases, and drop suddenly below 700 cm-1 at low temperatures (Fig. 1a-d).
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There is a sharp peak in Σ1op(ω), optical resonance mode, around 700 cm-1 which clearly separated from the broad continuum. This peak tracks the depressions in 1/τ(ω) in both frequency and amplitude, and weakens by increasing the doping and temperature (Fig. 1e-h).
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Σ1op(ω) has been derived from FTIR and ARPES include qualitative similar features (sharp peak and broad continuum in Fig. 2), although part of the difference in the amplitude and frequency of the peaks could be related to the deriving method.
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The amplitude of the resonance peak weakens with doping and disappears completely at critical hole concentration p=0.225±0.010, where the superconductivity is still large enough to show with Tc=55 K.
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The center frequency of the mode is proportional to Tc (Ωresop≈8 kBTc from FTIR and 5.6 kBTc from ARPES) and reaches the maximum at the optimally doped phase for both FTIR and ARPES.
Discussion:
The authors have discussed that neither the continuum nor the peak resonance features could originate from the phonons: the continuum’s spectral weight extends beyond the cut-off frequency of phonons; and the sharp peak appear at Tc of overdoped and slightly above Tc in the underdoped samples which is the characteristics of magnetic resonance mode. The amplitude of the coupling of optical resonance mode to charge carriers (Fig. 3c and 1a-d) extrapolates to zero at a critical doping of p=0.23, where the superconductivity is still exist. This study rules out both the magnetic resonance mode and phonons as the principal cause of high-Tc superconductivity, suggest the universal broad background as a good candidate signature of the ‘glue’ that make pairs.
Ref.: J. Hwang, T. Timusk, and G.D. Gu, Nature 427 (2004) 714.
