Dynamical Conductivities for the Fermionic Lieb Lattice

On the Lieb lattice, each unit cell contains three atoms, and its energy spectrum has a three-band structure, with a flat band touching two dispersive bands at a single point. The spin–orbit coupling term does not affect the flat band. However, it opens the gap between the flat and upper and lower dispersive bands, generating a nontrivial intrinsic Berry phase that leads to topological spin transport features. We calculate the transverse Hall conductivity and the dynamical longitudinal conductivity.