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We study characteristic band structures of the fermions on a square kagomelattice, one of the two-dimensional lattices hosting a corner-sharing networkof triangles. We show that the band structures of the nearest-neighbortight-binding model exhibit many characteristic features, including a flat bandwhich is ubiquitous among frustrated lattices. On the flat band, we elucidateits origin by using the molecular-orbital representation and also findlocalized exact eigenstates called compact localized states. In addition to theflat band, we also find two spin-1 Dirac cones with different energies. Thesespin-1 Dirac cones are not described by the simplest effective DiracHamiltonian because the middle band is bended and the energy spectrum isparticle-hole asymmetric. We also investigated the Hofstadter problem on asquare kagome lattice in the presence of an external field and find that theprofile of the Chern numbers around the modified spin-1 Dirac cones coincideswith the conventional one.

Flat band, spin-1 Dirac cone, and Hofstadter diagram in the fermionic square kagome model