Abstract
The Holstein-Hubbard model serves as a useful framework to investigate this interplay between the phonon-induced electron-electron attractive interaction and the direct Coulomb repulsion and can afford interesting phase diagrams due to competition among charge-density wave (CDW), spin-density wave (SDW), and superconductivity. However the detailed nature of the CDW-SDW transition is still not very well known. It is generally believed that the system undergoes a direct insulator to insulator transition from CDW to SDW with the increase of the on-site Coulomb repulsion for a given strength of the electron-phonon coupling and this is the main bottleneck for the polaronic/bipolaronic mechanism of high-temperature superconductivity. We have recently made an investigation to study the nature of the transition from SDW phase to CDW phase within the framework of a one-dimensional Holstein-Hubbard model at half-filling using a variational method. We find that an intervening metallic phase may exist at the crossover region of the CDW-SDW transition. We have also observed that if the anharmonicity of the phonons is taken into account, this metallic phase widens and the polarons become more mobile, which is a more favorable situation from the point of view of superconductivity. We shall finally show that an improved variational calculation widens the metallic phase and makes the polarons more mobile, which reconfirms the existence of the intermediate metallic phase at the SDW-CDW crossover region.
Highlights
The discovery of high-temperature cuprate superconductors is more than twenty years old [1]; the basic mechanism involved for inducing superconductivity in these systems has remained hitherto elusive
Had the change in the energy been sharp at the crossover region, one would have expected a direct transition from the charge-density wave (CDW) to the spin-density wave (SDW) phase
1.5 α already speculated that the physical properties including superconductivity in the alkali-doped fullerenes (A3C60) [68, 69] can be explained in a unified way in terms of a picture that envisages the existence of such a kind of a metallic state in (A3C60) [70, 71]
Summary
The discovery of high-temperature cuprate superconductors is more than twenty years old [1]; the basic mechanism involved for inducing superconductivity in these systems has remained hitherto elusive. According to some of these models, electron-phonon interaction being large enough in the high Tc materials, polarons, or bipolarons should be the natural quasiparticles in the normal phase of these systems. If the electron-phonon coupling is not too strong to overcome the Coulomb correlation, the system would prefer to be in a spin-density wave (SDW) GS which is an antiferromagnetic Mott insulating phase They argue, that the electron-phonon interaction cannot play any role in high-Tc superconductivity. Takada and Chatterjee [44] (hereafter referred to as TC) have shown for the first time within the framework of one-dimensional (1D) HH model at half-filling that there may exist an intervening phase at the CDW-SDW crossover region and, interestingly enough, this phase is metallic This theoretical observation is of great importance because such a metallic state, if exists, would be just ideal for high-Tc superconductivity. In this article we shall present a review of the above scenario
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