DFT+U study on the multipolar nematic state of nonmagnetic FeSe

Iron-based superconductor FeSe has been known to exhibit the so-called nematic state, in which the rotational symmetry is broken while keeping the translational symmetry, below the structural phase transition temperature $T_S$=90 K [1]. The splitting of the $d_{xz}$/$d_{yz}$ degenerate orbitals in the electronic bands measured in the angle-resolved photoemission spectroscopy (ARPES) experiment is much larger than that expected from the lattice distortion, suggesting that the nematic state is of electronic origin. In addition, unlike other iron-based materials, there is no magnetic order but there appears the enhancement of orbital fluctuations toward $T_S$, suggesting orbital-dependent correlation effects [2] and the possibility of BCS-BEC crossover [3], which have attracted much attention.
Recent ARPES experiments have revealed the detailed band structure of the normal and nematic states [1]. The Fermi surfaces of the normal state, which consist of two hole surfaces around the Γ point and two electron surfaces around the M point, are much smaller than the Fermi surface of the density functional theory (DFT) calculation. On the other hand, for the nematic state, a new type of nematic states with orbital hybridization between $d_{xy}$ and $d_{xz}$/$d_{yz}$ orbitals has recently been obtained as the ground state in the DFT+$U$ calculation [4] by adjusting the initial charge distribution. In particular, this band structure around the M point is interesting since it matches the features of the ARPES experiment [5].
In this study, we investigate the electronic structure of FeSe in the normal and nematic states based on the DFT+$U$ method in combination with the multipole analyses, and discuss their microscopic properties and origin [6]. In the normal state, the topological change of the Fermi surface occurs before the appearance of the nematic ground state due to the increase of the on-site Coulomb interaction $U$. The resulting nematic ground state is a multipolar state having both antiferro-hexadecapoles in the E-representation and ferro-multipoles in the $B_2$-representation on each Fe site, where the appearance of the $E$-type multipoles induces the hybridization of $d_{xy}$ and $d_{xz}$/$d_{yz}$ orbitals. Such a cooperative coupling of the $E$ and $B_2$ representations in multipoles is inherent in correlated multi-orbital systems, and is expected to play an important role in the formation of $d_{xz}$/$d_{yz}$ orbital splitting nematic states in other iron-based superconductors.