Spatial Delocalization and Perfect Tunneling of Matter Waves: Electron Perfect Lens

It is theoretically demonstrated that electron states in semiconductors or graphene can be perfectly transmitted through a complementary material with dual properties, independent of the angle of incidence. It is shown that such complementary material may also provide a strong spatial delocalization of bounded electronic states, changing dramatically the confinement of the wave function, and acting effectively as a lens for the probability wave. The results are the electron analogue of a perfect lens for electromagnetic waves proposed in an earlier work.