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arXiv:cond-mat/0511557 · Journal of Physics A Mathematical and General

Influence of anisotropic next-nearest-neighbour hopping on diagonal charge-striped phases

Volodymyr Derzhko

Published Aug 18, 2006• 3 citations
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Abstract

We consider the model of a strongly correlated system of electrons on a two-dimensional square lattice described by an extended Falicov–Kimball Hamiltonian where the stability of some axial and diagonal striped phases was proved. Introducing a next-nearest-neighbour hopping, small enough not to destroy the striped structure, we examine rigorously how the presence of the next-nearest-neighbour hopping anisotropy reduces the π/2-rotation degeneracy of the diagonal-striped phase. The effect appears to be similar to that in the case of anisotropy of the nearest-neighbour hopping: diagonal stripes are oriented in the direction of the weaker next-nearest-neighbour hopping.

DOI
10.1088/0305-4470/39/36/002

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We consider the model of a strongly correlated system of electrons on a two-dimensional square lattice described by an extended Falicov–Kimball Hamiltonian where the stability of some axial and diagonal striped phases was proved. Introducing a next-nearest-neighbour hopping, small enough not to destroy the striped structure, we examine rigorously how the presence of the next-nearest-neighbour hopping anisotropy reduces the π/2-rotation degeneracy of the diagonal-striped phase. The effect appears to be similar to that in the case of anisotropy of the nearest-neighbour hopping: diagonal stripes are oriented in the direction of the weaker next-nearest-neighbour hopping.
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We have examined the effects of extended hopping parameters in the $t\text{\ensuremath{-}}{t}^{\ensuremath{'}}\text{\ensuremath{-}}{t}^{\ensuremath{''}}\text{\ensuremath{-}}J$ model on the binding and spatial distribution of charge carriers. Previous studies have shown that a negative next-nearest-neighbor hopping in the physical parameter range serves to weaken striped behavior in the model. We show using exact diagonalization that a physically relevant set of parameters for the hole doped cuprates that includes next-next-nearest-neighbor hopping strengthens the binding of the holes and enhances stripe behavior in the underdoped regime.