# Orbital transmutation and the electronic spectrum of FeSe in the nematic phase

## TL;DR

This paper investigates the temperature-dependent electronic spectrum of FeSe in its nematic phase, proposing two scenarios involving orbital transmutation due to hybridization and spin-orbit coupling, to explain experimental observations from ARPES and STM.

## Contribution

It introduces two theoretical scenarios explaining orbital transmutation in FeSe's nematic phase, reconciling experimental data with orbital hybridization and surface effects.

## Key findings

- Orbital transmutation occurs across the nematic transition.
- Spin-orbit coupling induces orbital character changes.
- Surface hybridization affects observed orbital modes.

## Abstract

We consider the electronic spectrum near $M=(\pi,\pi)$ in the nematic phase of FeSe ($T<T_{{\rm nem}}$) and make a detailed comparison with recent ARPES and STM experiments. Our main focus is the unexpected temperature dependence of the excitations at the $M$ point. These have been identified as having $xz$ and $yz$ orbital character well below $T_{{\rm nem}}$, but remain split at $T>T_{{\rm nem}}$, in apparent contradiction to the fact that in the tetragonal phase the $xz$ and $yz$ orbitals are degenerate. Here we present two scenarios which can describe the data. In both scenarios, hybridization terms present in the tetragonal phase leads to an orbital transmutation, a change in the dominant orbital character of some of the bands, between $T > T_{\rm nem}$ and $T \ll T_{\rm nem}$. The first scenario relies on the spin-orbit coupling at the $M$ point. We show that a finite spin-orbit coupling gives rise to orbital transmutation, in which one of the modes, identified as $xz$ ($yz)$ at $T \ll T_{{\rm nem}}$, becomes predominantly $xy$ at $T > T_{{\rm nem}}$ and hence does not merge with the predominantly $yz$ ($xz$) mode. The second scenario, complementary to the first, takes into consideration the fact that both ARPES and STM are surface probes. In the bulk, a direct hybridization between the $xz$ and $yz$ orbitals is not allowed at the $M$ point, however, it is permitted on the surface. In the presence of a direct $xz/yz$ hybridization, the orbital character of the $xz/yz$ modes changes from pure $xz$ and pure $yz$ at $T \ll T_{{\rm nem}}$ to $xz \pm yz$ at $T > T_{{\rm nem}}$, i.e., the two modes again have mono-orbital character at low $T$, but do not merge at $T_{{\rm nem}}$. We discuss how these scenarios can be distinguished in polarized ARPES experiments.