Entropy and electronic orders of the three-orbital Hubbard model with antiferromagnetic Hund coupling

TL;DR

This study explores the phase diagram of a doped three-orbital Hubbard model with antiferromagnetic Hund coupling, revealing orbital freezing, composite orders, and high-temperature superconductivity near quarter filling.

Contribution

It provides new insights into the doped system's phase diagram, especially the stabilization of composite orders and high-$T_c$ superconductivity, extending previous half-filled studies.

Findings

Orbital freezing increases entropy in the half-filled model.

Composite order is suppressed in the doped Mott regime.

High-$T_c$ superconductivity occurs around quarter filling ($n=1.5$).

Abstract

An antiferromagnetic Hund coupling in multiorbital Hubbard systems induces orbital freezing and an associated superconducting instability, as well as unique composite orders in the case of an odd number of orbitals. While the rich phase diagram of the half-filled three-orbital model has recently been explored in detail, the properties of the doped system remain to be clarified. Here, we complement the previous studies by computing the entropy of the half-filled model, which exhibits an increase in the orbital-frozen region, and a suppression in the composite ordered phase. The doping dependent phase diagram shows that the composite ordered state can be stabilized in the doped Mott regime, if conventional electronic orders are suppressed by frustration. While antiferro orbital order dominates the filling range $2\lesssim n \le 3$, and ferro orbital order the strongly interacting region for $1\lesssim n < 2$, we find superconductivity with a remarkably high $T_c$ around $n=1.5$ (quarter filling). Also in the doped system, there is a close connection between the orbital freezing crossover and superconductivity.