Orbital order in FeSe - the case for vertex renormalization

TL;DR

This paper investigates the orbital order in FeSe, demonstrating that vertex renormalization is essential to reproduce the experimentally observed sign change of orbital order between hole and electron pockets, which mean-field approaches cannot capture.

Contribution

The study shows that including vertex renormalizations in the d-wave orbital channel explains the sign change of orbital order in FeSe, a feature not captured by mean-field analysis.

Findings

Vertex renormalization reproduces sign change of orbital order.

Ratio |Γ_e/Γ_h| is approximately one, independent of interaction strength.

Temperature dependence of orbital energies matches ARPES data.

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.