Small Bipolarons in the 2-dimensional Holstein-Hubbard Model. I The Adiabatic Limit

Details Small Bipolarons in the 2-dimensional Holstein-Hubbard Model. I The Adiabatic Limit Small Bipolarons in the 2-dimensional Holstein-Hubbard Model. I The Adiabatic Limit

2000-04-25

arxiv.org/abs/cond-mat/0004416v1

Eur. Phys. J. B. (1999) vol.11, pp.41-58

Physics

Condensed Matter

Superconductivity

Scientific paper

10.1007/s100510050915

The spatially localized bound states of two electrons in the adiabatic two-dimensional Holstein-Hubbard model on a square lattice are investigated both numerically and analytically. The interplay between the electron-phonon coupling g, which tends to form bipolarons and the repulsive Hubbard interaction $\upsilon \geq 0$, which tends to break them, generates many different ground-states. There are four domains in the $g,\upsilon$ phase diagram delimited by first order transition lines. Except for the domain at weak electron-phonon coupling (small g) where the electrons remain free, the electrons form bipolarons which can 1) be mostly located on a single site (small $\upsilon$, large g); 2) be an anisotropic pair of polarons lying on two neighboring sites in the magnetic singlet state (large $\upsilon$, large g); or 3) be a "quadrisinglet state" which is the superposition of 4 electronic singlets with a common central site. This quadrisinglet bipolaron is the most stable in a small central domain in between the three other phases. The pinning modes and the Peierls-Nabarro barrier of each of these bipolarons are calculated and the barrier is found to be strongly depressed in the region of stability of the quadrisinglet bipolaron.

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