Orbital Order in Two-orbital Hubbard Model

TL;DR

This paper investigates the emergence of orbital order in a simplified two-orbital Hubbard model, revealing that vertex corrections induce nematic order without the need for the $d_{xy}$ orbital, and identifies conditions for different orbital orders.

Contribution

It demonstrates that orbital order can arise from vertex corrections in a minimal two-orbital model, challenging the belief that the $d_{xy}$ orbital is necessary for nematic order.

Findings

Orbital order appears due to vertex corrections in the two-orbital model.

The $d_{xy}$ orbital is not essential for nematic orbital order.

A rotated $45^ ext{o}$ orbital order emerges in heavily hole-doped cases.

Abstract

In strongly correlated multi-orbital systems, various ordered phases appear. In particular, the orbital order in iron-based superconductors attracts much attention since it is considered to be the origin of the nematic state. In order to clarify the essential condition for realizing orbital orders, we study simple two-orbital ($d_{xz}$, $d_{yz}$) Hubbard model. We find that the orbital order, which corresponds to the nematic order, appears due to the vertex corrections even in the two-orbital model. Thus, $d_{xy}$ orbital is not essential to realize the nematic orbital order. The obtained orbital order depends on the orbital dependence and the topology of fermi surfaces. We also find that another type of orbital order, which is rotated $45^\circ$, appears in the heavily hole-doped case.