Omnidirectional transmission and reflection of pseudospin-1 Dirac fermions in a Lieb superlattice

We study the behavior of pseudospin-1 Dirac fermions in a Lieb lattice subjected to an external periodic potential. It is found that there exists a zero-averaged wave-number passband at the incident energy corresponding to half of the potential step, in contrast to zero-averaged wave-number gap in graphene superlattices. By tuning the sublattice site-energy, the passband can be turned into an omnidirectional gap. Consequently, a transformation from omnidirectional transmission to reflection, accompanied with a switch of conductance from maximum to zero can be realized easily. It is expected that the controllable properties are useful for some applications in optical or electronic devices.