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

Abstract

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 ) [X. Long et al., npj Quantum Mater. 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 of the Fermi surfaces before the emergence of a nematic ground state. The resulting nematic ground state is a multipolar state having both antiferro-hexadecapoles in the E-representation and ferro-multipoles in the B2-representation on each Fe site. Cooperative coupling between the E and B2 multipoles in local coordinate with the D 2d point group will play an important role in the formation of the dxz, dyz orbital-splitting nematic state not only in FeSe but also in other iron pnictides.

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

“…1 Under such the Lifshitz transitioned normal states for U > U LT , we have found that further increase of U stabilizes the symmetry broken nematic states above U =3.4 eV, as already shown in our previous study [11], where a multipolar nematic state becomes ground state with the hexadecapoles (Q 4α,x , Q 4α,y , Q 4β,x , Q 4β,y ) and multipoles (O xy , Q 4β,z ) corresponding to the E and B 2 irreducible representation of the D 2d point group at each Fe site (see table in Ref. [11]).…”

“…When U =0 eV, we have obtained ε kn > 0 at Γ and Z points as shown in Figs. 1 (a) and (b), yielding the three h-FSs consisting of the 28th, 29th, and 30th bands as shown in our previous study [11] and the DFT calculation of FeSe [7].…”

“…The degenerated pDOS ρ xz/yz (ε) for U =3 eV [see Fig. 1 (g)] is clearly separated, with the peak of ρ yz (ε) (ρ xz (ε)) splitting to lower (higher) energy due to the B 2 -multipole order [11]. In addition to this d xz -d yz splitting, we have obtained a remarkable suppression of ρ m (ε) near ε F involving ρ xy (ε) and ρ x 2 −y 2 (ε), which is responsible for the energy gain of the nematic state by forming a partial gap-like structure around 0.2 eV∼0.4 eV due to the E-type multipole mixing.…”

“…In this study, we aim to clarify the normal and nematic states of nonmagnetic FeSe by performing DFT+U calculations based on the all-electron full-potential code, WIEN2k [10]. In addition to the detailed analysis of the changes in the normal state up to the nematic state, we have evaluated the order parameters in the nematic state without any assumptions from the multipole moment calculations to elucidate the mechanism of the nematic state [11].…”