Orbital order in FeSe: The case for vertex renormalization
We study the structure of the orbital order Γ = † xz d xz - d † yz d yz > in FeSe in light of recent scanning tunneling microscopy and angle-resolved photoemission spectroscopy (ARPES) data, which detect the shapes of the hole and electron pockets in the nematic phase. The geometry of the pockets indicates that the sign of Γ is different between the hole and electron pockets (Γ h and Γ e ). We argue that this sign change cannot be reproduced if one solves for the orbital order within the mean-field approximation, as the mean-field analysis yields either no orbital order, or order with the same sign of Γ e and Γh. We argue that another solution with the opposite signs of Γ e and Γ h emerges if we include the renormalizations of the vertices in the d -wave orbital channel. We show that the ratio |Γ e /Γ h | is of order one, independent of the strength of the interaction. We also compute the temperature variation of the energy of d xz and d yz orbitals at the center of electron pockets and compare the results with ARPES data.