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

To understand the rich electronic phase diagram in FeSe under pressure that vividly demonstrates the strong interplay between the nematicity, magnetism and superconductivity, we analyze the electronic states by including the higher-order many-body effects called the vertex correction (VC). We predict the pressure-induced emergence of xy-orbital hole-pocket based on the first-principles analysis. Due to this pressure-induced Lifshitz transition, the spin fluctuations on the xy orbital are enhanced, whereas those on xz,yz orbitals are gradually reduced. For this reason, nonmagnetic orbital order $O = n_{xz} - n_{yz}$, which is driven by the spin fluctuations on xz,yz orbitals through the intra-orbital VCs, is suppressed, and it is replaced with the magnetism of xy-orbital d-electrons. The nodal s-wave state at ambient pressure ($O > 0$) and the enhancement of Tc under pressure are driven by the cooperation between the spin and orbital fluctuations.