Spin-Fluctuation-Driven Nematic Charge-Density-Wave in Cuprate Superconductors: Charge-Orbital-Spin Multimode Fluctuations Caused by Vertex Corrections

We explain the recently discovered nematic charge-density-wave (CDW) state in cuprate superconductors on the basis of the three-orbital $d$-$p$ Hubbard model, by including the vertex correction (VC) [1]. Due to the strong charge-spin interference given by the VC, the CDW instability at $q=(\Delta_{\rm FS},0)$, $(0,\Delta_{\rm FS})$ is strongly promoted near the magnetic critical point. Here, $\Delta_{\rm FS}$ is the wavenumber connected by the neighboring hot spots. The obtained spin-fluctuation-driven CDW is described as the ``intra-unit-cell orbital order'' accompanied by the charge transfer between the neighboring atomic orbitals. The obtained nematic-type charge pattern is similar to the STM results. The CDW in cuprates has a close relation to the nematic orbital order in Fe-based superconductors. [1] Y. Yamakawa and H. Kontani, arXiv:1406.7520.