Orbital Nematic Instability in Two-Orbital Hubbard Model: Renormalization-Group + Constrained RPA Analysis

TL;DR

This paper combines renormalization-group and RPA methods to analyze orbital susceptibilities in a two-orbital Hubbard model, revealing a ferro-orbital instability linked to nematic order near quantum critical points, relevant for Sr_{3}Ru_{2}O_{7} and similar materials.

Contribution

It introduces a novel combined analytical scheme to accurately study orbital susceptibilities and identifies a mechanism for orbital nematic order driven by vertex corrections.

Findings

Ferro-orbital instability occurs near magnetic or superconducting quantum criticality.

Vertex corrections induce nematic order in the model.

The mechanism explains nematic order in Sr_{3}Ru_{2}O_{7} and may apply to other multiorbital systems.

Abstract

Motivated by the nematic electronic fluid phase in Sr_{3}Ru_{2}O_{7}, we develop a combined scheme of the renormalization-group method and the random-phase-approximation-type method, and analyze orbital susceptibilities of the (d_{xz},d_{yz})-orbital Hubbard model with high accuracy. It is confirmed that the present model exhibits a ferro-orbital instability near the magnetic or superconducting quantum criticality, due to the Aslamazov-Larkin-type vertex corrections. This mechanism of orbital nematic order presents a natural explanation for the nematic order in Sr_{3}Ru_{2}O_{7}, and is expected to be realized in various multiorbital systems, such as Fe-based superconductors.