Nematicity, magnetism and superconductivity in FeSe under pressure: Unified explanation based on the self-consistent vertex correction theory

Rich electronic phase diagram in FeSe under pressure vividly demonstrates the strong interplay between the nematicity, magnetism and superconductivity in Fe-based superconductors. Here, we construct the multiorbital Hubbard model for FeSe under pressure by referring to the first-principles calculations, and analyze the electronic states by including the higher-order many-body effects called the vertex correction (VC). When the pressure-induced $\dxy$-orbital Fermi pocket appears, the spin fluctuations on the $\dxy$ orbital are enhanced, whereas those on $\dxz,\dyz$ orbitals are reduced. For this reason, nonmagnetic orbital order $O=n_{xz}-n_{yz}$, which is caused by the spin fluctuations on $\dxz,\dyz$ orbitals via the VC, is suppressed and replaced with the magnetism of $\dxy$-orbital $d$-electrons. The nodal $s$-wave state at ambient pressure ($O\ne0$) and the enhancement of $T_{\rm c}$ under pressure are driven by the cooperation between spin and orbital fluctuations.