First-principles calculation of the electronic nematicity in FeSe

We report a density functional theory calculation that produces the nonmagnetic electronic nematic state in FeSe, without explicit breaking of the tetragonal lattice symmetry. We incorporate orbital-resolved interactions by +U and hybrid functional, and precondition the initial wavefunction to find local energy minima with spontaneous symmetry breaking. The lowest-energy nematic state we find features an anti-ferro hexadecapolar charge order, instead of a simple ferro-orbital order, which is important to produce the correct Fermi surface topology in FeSe. We propose that the weak inversion symmetry breaking induced by this multipolar order can be detected by high-precision measurement of the band dispersion as well as second-harmonic generation.