Multipolar nematic state of nonmagnetic FeSe based on the DFT+$U$

Clarifying the origin of nematic state in FeSe is one of urgent problems in the field of iron-based superconductivity. Motivated by the discovery of a nematic solution in the density-functional theory implemented by on-site Coulomb interaction (DFT+$U$) [npj Quantum Mater. \textbf{5}, 50 (2020)], we reexamine the $U$ dependence of electronic states in the nonmagnetic normal state of FeSe and perform full multipolar analyses for the nematic state. We find that with increasing $U$ the normal state experiences a topological change in the Fermi surfaces before the emergence of a nematic ground state. The resulting nematic ground state is a multipolar state having both antiferrohexadecapoles in the $E$ representation and ferromultipoles in the $B_2$ representation on each Fe site. Cooperative coupling between the $E$ and the $B_2$ multipoles in the local coordinate with the $D_{2d}$ point group will play an important role in the formation of the $d_{xz},~d_{yz}$ orbital-splitting nematic state not only in FeSe, but also in other iron pnictides.