  We investigate the electronic structures of FeSe in the presence of different
possible orders. We find that only ferro-orbital order (FO) and collinear
antiferro-magnetism (C-AFM) can simultaneously induce splittings at $\Gamma$
and M. Bicollinear antiferro-magnetism (B-AFM) and spin-orbit coupling (SOC)
have very similar band structure on $\Gamma$-M near the Fermi level. The
temperature insensitive splitting at $\Gamma$ and the temperature dependent
splitting at M observed in recent experiments can be explained by the d-wave
bond nematic (dBN) order together with SOC. The recent observed Dirac cones and
their temperature ($T$) dependence in FeSe thin films can also be well
explained by the dBN order with band renormalization. Their thickness- and
cobalt-doping- dependent behaviors are the consequences of electron doping and
reduction of Se height. All these suggest that the nematic order in FeSe system
is the dBN order.
