Doping effects on electronic states in electron-doped FeSe: Impact of self-energy and vertex corrections

TL;DR

This study investigates how doping affects electronic states in electron-doped FeSe, emphasizing the roles of self-energy and vertex corrections, and finds that orbital fluctuations mediate superconductivity over a broad doping range.

Contribution

It introduces a multiorbital model including vertex corrections and self-energy effects, revealing their crucial roles in orbital fluctuations and superconductivity in doped FeSe.

Findings

Orbital order disappears at doping level x~0.03.

Orbital fluctuations increase with doping due to vertex corrections.

Orbital-fluctuation-mediated s++-wave state is stable across wide doping range.

Abstract

The pairing glue of high-$T_{\rm c}$ superconductivity in heavily electron-doped (e-doped) FeSe, in which hole-pockets are absent, has been an important unsolved problem. Here, we focus on a heavily e-doped bulk superconductor Li$_{1-x}$Fe$_x$OHFeSe ($T_{\rm c} \sim 40$K). We construct a multiorbital model beyond the rigid band approximation and analyze the spin and orbital fluctuations by taking both vertex corrections (VCs) and self-energy into consideration. Without e-doping ($x=0$), the ferro-orbital order without magnetism in FeSe is reproduced by the VCs.The orbital order quickly disappears when the hole-pocket vanishes at $x \sim 0.03$. With increasing $x$ further, the spin fluctuations remain small, whereas orbital fluctuations gradually increase with $x$ due to the VCs. The negative feedback due to the self-energy is crucial to explain experimental phase diagram. Thanks to both vertex and self-energy corrections, the orbital-fluctuation-mediated $s_{++}$-wave state appears for a wide doping range, consistent with experiments.