Mapping borophene onto graphene: Quasi-exact solutions for guiding potentials in tilted Dirac cones

Abstract

We show that if the solutions to the (2+1)-dimensional massless Dirac equation for a given 1D potential are known, then they can be used to obtain the eigenvalues and eigenfunctions for the same potential, orientated at an arbitrary angle, in a tilted anisotropic 2D Dirac material. This simple set of transformations enables all the exact and quasi-exact solutions associated with 1D quantum wells in graphene to be applied to the confinement problem in tilted Dirac materials such as borophene. We also show that smooth electron waveguides in tilted Dirac materials can be used to manipulate the degree of valley polarization of quasiparticles travelling along a particular direction of the channel. We examine the particular case of the hyperbolic secant potential to model realistic top-gated structures for valleytronic applications.

12 pages, 5 figures and 1 Supplementary Material

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Cited by in corpus (4)

• Signatures of Lifshitz transition in the optical conductivity of two-dimensional tilted Dirac materials
• Optical valley separation in two-dimensional semimetals with tilted Dirac cones
• Lorentzian quantum wells in graphene: the role of shape invariance in zero-energy states trapping
• Designer gapped and tilted Dirac cones in lateral graphene superlattices