Theory for Superconducting Properties of the Cuprates: Doping Dependence of the Electronic Excitations and Shadow States

The superconducting phase of the 2D one-band Hubbard model is studied within the FLEX approximation and by using an Eliashberg theory. We investigate the doping dependence of $T_c$, of the gap function $\Delta ({\bf k},\omega)$ and of the effective pairing interaction. Thus we find that $T_c$ becomes maximal for $13 \; \%$ doping. In {\it overdoped} systems $T_c$ decreases due to the weakening of the antiferromagnetic correlations, while in the {\it underdoped} systems due to the decreasing quasi particle lifetimes. Furthermore, we find {\it shadow states} below $T_c$ which affect the electronic excitation spectrum and lead to fine structure in photoemission experiments.Comment: 10 pages (REVTeX) with 5 figures (Postscript

Comment on "A Tale of Two Theories: Quantum Griffiths Effects in Metallic Systems" by A. H. Castro-Neto and B. A. Jones

In a recent paper Castro-Neto and Jones argue that because the observability of quantum Griffiths-McCoy effects in metals is controlled by non-universal quantities, the quantum Griffiths-McCoy scenario may be a viable explanation for the non-fermi-liquid behavior observed in heavy fermion compounds. In this Comment we point out that the important non-universal quantity is the damping of the spin dynamics by the metallic electrons; quantum Griffiths-McCoy effects occur only if this is parametrically weak relative to other scales in the problem, i.e. if the spins are decoupled from the carriers. This suggests that in heavy fermion materials, where the Kondo effect leads to a strong carrier-spin coupling, quantum Griffiths-McCoy effects are unlikely to occur.Comment: 2 page

Unbinding of giant vortices in states of competing order

Funding: EPSRC (UK) via Grants No. EP/I031014/1 and No. EP/H049584/1.We consider a two-dimensional system with two order parameters, one with O(2) symmetry and one with O(M), near a point in parameter space where they couple to become a single O(2+M) order. While the O(2) sector supports vortex excitations, these vortices must somehow disappear as the high symmetry point is approached. We develop a variational argument which shows that the size of the vortex cores diverges as 1/root Delta and the Berezinskii-Kosterlitz-Thouless transition temperature of the O(2) order vanishes as 1/1n(1/Delta), where Delta denotes the distance from the high-symmetry point. Our physical picture is confirmed by a renormalization group analysis which gives further logarithmic corrections, and demonstrates full symmetry restoration within the cores.Publisher PDFPeer reviewe