Lieb lattices and pseudospin-1 dynamics under barrier- and well-like electrostatic interactions

This work considers the confining and scattering phenomena of electrons in a Lieb lattice subjected to influence rectangular electrostatic barrier. In this setup, hopping amplitudes between nearest neighbors orthogonal directions are considered different, next-nearest neighbor interaction describes spin-orbit coupling. makes it possible confine generate bound states, exact number which is exactly determined for null parallel momentum such case, proved that one even odd state always generated, states increases non-null increasing values momentum. That is, carry current. regime, energy where resonant tunneling occurs. The existence perfect form super-Klein exist regardless bang gap opening. Finally, shown reflection appears when solutions coupled intermediate flat-band solution.