The Talbot Effect for two-dimensional massless Dirac fermions.

A monochromatic beam of wavelength λ transmitted through a periodic one-dimensional diffraction grating with lattice constant d will be spatially refocused at distances from the grating that are integer multiples of . This self-refocusing phenomena, commonly referred to as the Talbot effect, has been experimentally demonstrated in a variety of systems ranging from optical to matter waves. Theoretical predictions suggest that the Talbot effect should exist in the case of relativistic Dirac fermions with nonzero mass. However, the Talbot effect for massless Dirac fermions (mDfs), such as those found in monolayer graphene or in topological insulator surfaces, has not been previously investigated. In this work, the theory of the Talbot effect for two-dimensional mDfs is presented. It is shown that the Talbot effect for mDfs exists and that the probability density of the transmitted mDfs waves through a periodic one-dimensional array of localized scatterers is also refocused at integer multiples of zT. However, due to the spinor nature of the mDfs, there are additional phase-shifts and amplitude modulations in the probability density that are most pronounced for waves at non-normal incidence to the scattering array.

Suppressing Klein tunneling in graphene using a one-dimensional array of localized scatterers.

Graphene's unique physical and chemical properties make it an attractive platform for use in micro- and nanoelectronic devices. However, electrostatically controlling the flow of electrons in graphene can be challenging as a result of Klein tunneling, where electrons normally incident to a one-dimensional potential barrier of height V are perfectly transmitted even as V → ∞. In this study, theoretical and numerical calculations predict that the transmission probability for an electron wave normally incident to a one-dimensional array of localized scatterers can be significantly less than unity when the electron wavelength is smaller than the spacing between scatterers. In effect, placing periodic openings throughout a potential barrier can, somewhat counterintuitively, decrease transmission in graphene. Our results suggest that electrostatic potentials with spatial variations on the order of the electron wavelength can suppress Klein tunneling and could find applications in developing graphene electronic devices.