Orbital Nematic Instability in Two-Orbital Hubbard Model: A Renormalization-Group Study

Motivated by the nematic electronic fluid phase in Sr$_3$Ru$_2$O$_7$, we analyze the ($d_{xz}$, $d_{yz}$)-orbital Hubbard model by the one-loop renormalization-group method [1]. We find that, in the weak-interaction case, the $q=0$ component of the orbital susceptibility $\chi^{\mathrm{q}}(q)$ is critically enhanced by the Aslamazov-Larkin (AL) type vertex correction due to the superconducting fluctuations. In the strong-interaction case, we also find the development of $\chi^{\mathrm{q}}(q)$ driven by the AL-type vertex correction due to spin fluctuations, consistently with the perturbation analysis [2]. Thus the strong orbital nematic fluctuation, i.e., orbital Pomeranchuk instability, emerges near the magnetic or superconducting quantum criticality. 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 [3]. \\ \noindent [1] M. Tsuchiizu, S. Onari, and H. Kontani, arXiv:1209.3664. \\ \noindent [2] Y. Ohno, M. Tsuchiizu, S. Onari, and H. Kontani, arXiv:1209.3629. \\ \noindent [3] S. Onari and H. Kontani, Phys. Rev. Lett. \textbf{109}, 137001 (2012).