Conductivity in a symmetry broken phase: Spinless fermions with $1/d$ corrections

Details Conductivity in a symmetry broken phase: Spinless fermions with $1/d$ corrections Conductivity in a symmetry broken phase: Spinless fermions with $1/d$ corrections

1996-09-30

arxiv.org/abs/cond-mat/9609286v1

Phys. Rev. B 54, 10436 (1996)

Physics

Condensed Matter

23 pages, 19 figures included with psfig, Revtex; Physical Review B15, in press (October/November 1996) depending on the print

Scientific paper

10.1103/PhysRevB.54.10436

The dynamic conductivity $\sigma(\omega)$ of strongly correlated electrons in a symmetry broken phase is investigated in the present work. The model considered consists of spinless fermions with repulsive interaction on a simple cubic lattice. The investigated symmetry broken phase is the charge density wave (CDW) with wave vector $Q=(\pi,\pi,\pi)^\dagger$ which occurs at half-filling. The calculations are based on the high dimensional approach, i.e. an expansion in the inverse dimension $1/d$ is used. The finite dimensionality is accounted for by the inclusion of linear terms in $1/d$ and the true finite dimensional DOS. Special care is paid to the setup of a conserving approximation in the sense of Baym/Kadanoff without inconsistencies. The resulting Bethe-Salpeter equation is solved for the dynamic conductivity in the non symmetry broken and in the symmetry broken phase (AB-CDW). The dc-conductivity is reduced drastically in the CDW. Yet it does not vanish in the limit $T \to 0$ due to a subtle cancellation of diverging mobility and vanishing DOS. In the dynamic conductivity $\sigma(\omega)$ the energy gap induced by the symmetry breaking is clearly discernible. In addition, the vertex corrections of order $1/d$ lead to an excitonic resonance lying within the gap.

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