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Analysis of the Quasiparticle Spectral Function in the Underdoped Cuprates

We applied the approach of K.-Y. Yang, T. M. Rice and F.-Ch. Zhang (YRZ) to analyze the high resolution angular resolved photo-emission spectroscopy (ARPES) data in BiSCO obtained recently at Brookhaven. In the YRZ ansatz a constant RVB gap is assumed which leads to Luttinger zeros along the antiferromagnetic Brillouin zone (AFBZ) and four Fermi pockets centered on the nodal directions. We relax the assumption of a constant RVB gap function, treating it as a Ising order parameter accompanied by thermal fluctuations. If these thermal fluctuations are very strong leading to strictly short range correlations in the spatial dependence of the RVB gap, then the reconstruction of the Fermi surface into pockets will not survive. We examined the intermediate case of critical fluctuations leading to a power law falloff of the RVB gap correlations. To this end we followed the analysis recently developed by two of us to treat the effect of the power law correlations in the antiferromagnetic 2-dimensional xy model on the single electron Green's function. The partial truncation of the Fermi surface to form pockets survives in the presence of power law correlations. The linewidth of the quasiparticle peaks increases with the exponent of the power law correlations. If this exponent is set at the value of critical fluctuations in the 2-dimensional Ising model a relatively small linewidth is obtained. If this exponent is doubled, a linewidth comparable to the values found in recent ARPES experiments on underdoped BiSCO (Tc = 65 K) at T = 140K was obtained. The anisotropic suppression of the quasiparticle peak around the Fermi pockets hides the back side of the pockets closest to the AFBZ to give essentially Fermi arcs seen experimentally.