Spin-Fluctuation-Driven Nematic Charge-Density-Wave in Cuprate Superconductors: Impact of Aslamazov-Larkin-Type Vertex Correction

We present a microscopic derivation of the nematic charge-density-wave (CDW) formation in cuprate superconductors based on the three-orbital d-p Hubbard model, by introducing the vertex correction (VC) into the charge susceptibility. The CDW instability at $q=({\mathrm{\Delta }}_{FS},0)$, $(0,{\mathrm{\Delta }}_{FS})$ appears when the spin fluctuations are strong, due to the strong charge-spin interference represented by the VC. Here, ${\mathrm{\Delta }}_{FS}$ is the wavenumber between the neighboring hot spots. The obtained spin-fluctuation-driven CDW is expressed as the “intra-unit-cell orbital order” accompanied by the charge transfer between the neighboring atomic orbitals, which is actually observed by the STM measurements. We predict that the cuprate CDW and the nematic orbital order in Fe-based superconductors are closely related spin-fluctuation-driven phenomena.