Ground state properties of the ionic Hubbard model on a two-leg triangular ladder at 3/4 filling

We study numerically the ionic Hubbard model on a two-leg triangular ladder at 3/4 filling. This model is believed to be the minimal microscopic model describing the physics of Na$_{x}$CoO$_{2}$ at $x=0.5$, and shows a rich phase diagram that depends on a delicate balance between the Coulomb interaction $U$, the hopping amplitude $t$, and the ionic potential $\Delta$. Motivated by experiments analyzing the dopant distribution on Na$_{0.5}$CoO$_{2}$, we focus in the case of a stripe-type ionic potential. In the correlated limit where the Coulomb interaction is large, the ground state of the model is a charge-transfer insulator for large ionic potential and turns metallic for zero ionic potential. Electronic structure calculations point to the regime $\Delta\sim |t|, t<0$ as the one relevant for Na$_{0.5}$CoO$_{2}$, but previous calculations [1] have not fully clarify the nature of ground state of the model in such regime. The aim of this work is to study the metal-insulator transition that occurs in the region $U\gg\Delta\sim |t|$ of the phase diagram as well as the magnetic and charge structures of the associated ground states. \newline [1] J. Merino et al. Phys. Rev. B 80, 045116 (2009).