Symmetry breaking and (pseudo)spin polarization in Veselago lenses for massless Dirac fermions
arXiv:1703.05708 · doi:10.1103/PhysRevB.95.115310
Abstract
We study Veselago lensing of massless Dirac fermions by n-p junctions for electron sources with a certain polarization. This polarization corresponds to pseudospin for graphene and to real spin for topological insulators. Both for a point source and for injection into a sample through a narrow lead, we find that polarization leads to spatial symmetry breaking. For the Green's function, this results in a vertical displacement, or even complete vanishing of the main focus, depending on the exact polarization. For injection through a lead, it leads to a difference between the amounts of current emitted with positive and negative transversal momenta. We study both systems in detail using the semiclassical approximation. By comparing the results to the exact solutions, we establish that semiclassical methods provide a very effective way to study these systems. For the Green's function, we derive an easy-to-use analytical formula for the vertical displacement of the main focus. For current injection through a lead, we use semiclassical methods to identify two different scattering regimes.
Accepted for publication in Phys. Rev. B
References in corpus (18)
- The electronic properties of graphene
- Chiral tunneling and the Klein paradox in graphene
- Valley filter and valley valve in graphene
- Electronic States of Graphene Nanoribbons
- Quantum interference and Klein tunneling in graphene heterojunctions
- Veselago Lens for Electrons: Focusing and Caustics in Graphene p-n Junctions
- Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene
- Evidence of Klein tunneling in graphene p-n junctions
- Detecting Topological Currents in Graphene Superlattices
- Klein Backscattering and Fabry-Perot Interference in Graphene Heterojunctions
- Moir{é} patterns as a probe of interplanar interactions: graphene on h-BN
- Caustics due to Negative Refractive Index in Circular Graphene p-n Junctions
- Tuning the valley and chiral quantum state of Dirac electrons in van der Waals heterostructures
- Modeling Klein tunneling and caustics of electron waves in graphene
- Scattering of two-dimensional massless Dirac electrons by a circular potential barrier
- Semiclassical theory of potential scattering for massless Dirac fermions
- Probing of valley polarization in graphene via optical second-harmonic generation
- Alkali doping of graphene: the crucial role of high temperature annealing