Orbital order in FeSe: The case for vertex renormalization

Abstract

We study the structure of the d-wave orbital order in FeSe in light of recent STM and ARPES data, which detect the shapes of hole and electron pockets in the nematic phase. The geometry of the pockets indicates that the sign of the orbital order $\Gamma = \langle d^{\dagger}_{xz} d_{xz}- d^{\dagger}_{yz} d_{yz}\rangle$ is different between hole and electron pockets $(\Gamma_h$ and $\Gamma_e$). We argue that this sign change cannot be reproduced if one solves for the orbital order within mean-field approximation, as the mean-field analysis yields either no orbital order, or order with the same sign of $\Gamma_e$ and $\Gamma_h$. We argue that another solution with the opposite signs of $\Gamma_e$ and $\Gamma_h$ emerges if we include the renormalizations of the vertices in $d-$wave orbital channel. We show that the ratio $|\Gamma_e/\Gamma_h|$ is of order one, independent on 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.