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arXiv:cond-mat/9403061

Correlation Induced Vanishing of the Gap Function on the Fermi Surface in High $T_c$ Superconductors

G. Baskaran, D. G. Kanhere, Mihir Arjunwadkar, Rahul D. Basu

Published Mar 16, 1994• 0 citations
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Abstract

We present physical arguments as well as numerical evidence to show that the Cooper pair (gap) function vanishes on the Fermi surface in strongly correlated electron systems such as \tJ and \lU Hubbard models in one and two dimensions. Using exact diagonalization, we study a correlation function which is a measure of the gap function even in a finite system, and present numerical results for this correlation function on small clusters of 8 (Hubbard) and 16 ($t-J$) sites.

DOI
10.48550/arxiv.cond-mat/9403061

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We present physical arguments as well as numerical evidence to show that the Cooper pair (gap) function vanishes on the Fermi surface in strongly correlated electron systems such as \tJ and \lU Hubbard models in one and two dimensions. Using exact diagonalization, we study a correlation function which is a measure of the gap function even in a finite system, and present numerical results for this correlation function on small clusters of 8 (Hubbard) and 16 (t−Jt-Jt−J) sites.
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The one-dimensional Hubbard model with repulsive interaction is studied. We calculate the asymptotic correlation functions in the less-than-half-filled band case. In particular, our approach centers on the large-U wave function and emphasizes the finite phase shifts on the Fermi surface. This is important since the concept of finite phase shifts can be easily applied to higher dimensions. We then discuss the non-Fermi-liquid behavior of this model and the relevance to the understanding of the two-dimensional Hubbard model, which is believed to give a good description of the high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors.
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The evolution of the Fermi surface upon hole doping is studied in the t-J model of correlated electrons by exact diagonalization of chains and planes. In one dimension at low hole doping, the momentum distribution function n(k) indicates the presence of pocketlike features at the (noninteracting) Fermi momentum, while increasing the density of holes a large Fermi surface is observed. Although the results in two dimensions are consistent with this picture, conclusive evidence for the existence of hole pockets (at intermediate doping levels) cannot be provided in the present study of 4\ifmmode\times\else\texttimes\fi{}4 and \ensuremath{\surd}18 \ifmmode\times\else\texttimes\fi{} \ensuremath{\surd}18 square lattices. In order to improve the resolution in momentum space, twisted boundary conditions are used for the two-dimensional clusters.