The electronic structure of FeSe thin films grown on SrTiO3 substrate is studied by angle-resolved photoemission spectroscopy (ARPES). We reveal the existence of Dirac cone band dispersions in FeSe thin films thicker than 1 Unit Cell below the nematic transition temperature, whose apex are located -10 meV below Fermi energy. The evolution of Dirac cone electronic structure for FeSe thin films as function of temperature, thickness and cobalt doping is systematically studied. The Dirac cones are found to be coexisted with the nematicity in FeSe, disappear when nematicity is suppressed. Our results provide some indication that the spin degrees of freedom may play some kind of role in the nematicity of FeSe.
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