Engineering polar discontinuities in honeycomb lattices

Engineering polar discontinuities in honeycomb lattices.

Unprecedented and fascinating phenomena have been recently observed at oxide interfaces between centrosymmetric cubic materials, where polar discontinuities can give rise to polarization charges and electric fields that drive a metal-insulator transition and the appearance of a two-dimensional electron gas. Lower-dimensional analogues are possible, and honeycomb lattices offer a fertile playgro...

Nonlinear wave dynamics in honeycomb lattices

We study the nonlinear dynamics of wave packets in honeycomb lattices and show that, in quasi-onedimensional configurations, the waves propagating in the lattice can be separated into left-moving and right-moving waves, and any wave packet composed of only left (or only right) movers does not change its intensity structure in spite of the nonlinear evolution of its phase. We show that the propa...

Klein tunneling in deformed honeycomb lattices.

We study the scattering of waves off a potential step in deformed honeycomb lattices. For deformations below a critical value, perfect Klein tunneling is obtained; i.e., a potential step transmits waves at normal incidence with nonresonant unit-transmission probability. Beyond the critical deformation a gap forms in the spectrum, and a potential step perpendicular to the deformation direction r...

Nonlinear Wave Packets in Deformed Honeycomb Lattices

The spectrum of a Schrödinger operator with a perfect honeycomb lattice potential has special points, called Dirac points where the lowest two branches of the spectrum touch. Deformations can result in the merging and disappearance of the Dirac points and the originally intersecting dispersion relation branches separate. Corresponding to these deformations, nonlinear envelope equations are deri...

Phonons in conventional and auxetic honeycomb lattices