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arXiv:0902.1980

Incoherent Tunneling Amplitude in High Tc Cuprates

Philip Warren Anderson, Philip A. Casey

Published Feb 11, 2009• 0 citations
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Abstract

A 2004 paper of Anderson and Ong calculated the asymmetric coherent spectrum of point-contact tunneling into a Gutzwiller-projected superconductor. We here correct some details of that paper and present recipes for the manyquasiparticle, incoherent spectrum, the major portion of which results from the spin-flip decay of the injected quasiparticle. An illustrative example is shown.

DOI
10.48550/arxiv.0902.1980

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A 2004 paper of Anderson and Ong calculated the asymmetric coherent spectrum of point-contact tunneling into a Gutzwiller-projected superconductor. We here correct some details of that paper and present recipes for the manyquasiparticle, incoherent spectrum, the major portion of which results from the spin-flip decay of the injected quasiparticle. An illustrative example is shown.
Using a new method for the solution of the fluctuation exchange approximation equations, which allows the determination of the self-energy ${\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$ of the 2D one-band Hubbard model on the real frequency axis, we calculate the doping dependence of the quasiparticle excitations of high-Tc{T}_{c}Tc​ superconductors. We obtain new results for the shadows of the Fermi surface, their dependence on the deformation of the quasiparticle dispersion, an anomalous $\ensuremath{\omega}$ dependence of $\mathrm{Im}{\ensuremath{\Sigma}}_{\mathrm{k}}(\ensuremath{\omega})$, and a related violation of the Luttinger theorem. This sheds new light on the influence of short range magnetic order on the low energy excitations and its significance for photoemission experiments.
I present a formalism for dealing directly with the effects of the Gutzwiller projection implicit in the $t\text{\ensuremath{-}}J$ model which is widely believed to underlie the phenomenology of the high-Tc{T}_{c}Tc​ cuprates. I suggest that a true BCS condensation from a Fermi-liquid state takes place but in the unphysical space prior to projection. The theory which results upon projection does not follow conventional rules of diagram theory and in fact in the normal state is a Z=0Z=0Z=0 non-Fermi liquid. Anomalous properties of the ``strange metal'' normal state are predicted and compared to experiments.
Low-lying one-particle anomalous excitations are studied for Gutzwiller-projected strongly correlated BCS states. It is found that the one-particle anomalous excitations are highly coherent, and the numerically calculated spectrum can be reproduced quantitatively by a renormalized BCS theory, thus strongly indicating that the nature of low-lying excitations described by the projected BCS states is essentially understood within a renormalized Bogoliubov quasiparticle picture. This finding resembles the well-known fact that a Gutzwiller-projected Fermi gas is a Fermi liquid. The present results are consistent with numerically exact calculations of the two-dimensional $t\text{\ensuremath{-}}J$ model as well as recent photoemission experiments on high-TC{T}_{\mathrm{C}}TC​ cuprate superconductors.
Rigorous relations for Gutzwiller projected BCS states are derived. The obtained results do not depend on the details of model systems, but solely on the wave functions. Based on the derived relations, physical consequences are discussed for strongly correlated superconducting states such as high-TC{T}_{\mathrm{C}}TC​ cuprate superconductors.