Quasi-exact solutions for guided modes in two-dimensional materials with tilted Dirac cones

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Abstract

We show that if the solutions to the (2+1)-dimensional massless Dirac equation for a given one-dimensional (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 2D Dirac material possessing tilted, anisotropic Dirac cones. 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 8-Pmmn 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.

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Ng, R. A., Wild, A., Portnoi, M. E., & Hartmann, R. R. (2022). Quasi-exact solutions for guided modes in two-dimensional materials with tilted Dirac cones. Scientific Reports, 12(1). https://doi.org/10.1038/s41598-022-11742-3

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