Interatomic Coulomb interaction and electron nematic bond order in FeSe

Despite having the simplest atomic structure, bulk FeSe has an observed electronic structure with the largest deviation from the band theory predictions among all Fe-based superconductors and exhibits a low temperature nematic electronic state without intervening magnetic order. We show that the Fe-Fe interatomic Coulomb repulsion $V$ offers a natural explanation for the puzzling electron correlation effects in FeSe superconductors. It produces a strongly renormalized low-energy band structure where the van Hove singularity sits remarkably close to Fermi level in the high-temperature electron liquid phase as observed experimentally. This proximity enables the quantum fluctuations in $V$ to induce a rotational symmetry breaking electronic bond order in the $d$-wave channel. We argue that this emergent low-temperature $d$-wave bond nematic state, different from the commonly discussed ferro-orbital order and spin-nematicity, has been observed recently by several angle resolved photoemission experiments detecting the lifting of the band degeneracies at high symmetry points in the Brillouin zone. We present a symmetry analysis of the space group and identify the hidden antiunitary $T$-symmetry that protects the band degeneracy and the electronic order/interaction that can break the symmetry and lift the degeneracy. We show that the $d$-wave nematic bond order, together with the spin-orbit coupling, provide a unique explanation of the temperature dependence, momentum space anisotropy, and domain effects observed experimentally. We discuss the implications of our findings on the structural transition, the absence of magnetic order, and the intricate competition between nematicity and superconductivity in FeSe superconductors.