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

TL;DR

This paper investigates how anisotropic next-nearest-neighbor hopping influences the orientation and stability of diagonal charge-striped phases in a strongly-correlated electron system modeled by an extended Falicov-Kimball Hamiltonian.

Contribution

It provides a rigorous analysis of the impact of anisotropic next-nearest-neighbor hopping on the degeneracy and orientation of diagonal-striped phases, extending previous understanding of hopping anisotropy effects.

Findings

Anisotropic next-nearest-neighbor hopping reduces the $rac{ ext{pi}}{2}$-rotation degeneracy.

Stripes tend to align along the direction of weaker next-nearest-neighbor hopping.

The effect is similar to anisotropy in nearest-neighbor hopping.

Abstract

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