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We show that if the solutions to the (2+1)-dimensional massless Diracequation for a given 1D potential are known, then they can be used to obtainthe eigenvalues and eigenfunctions for the same potential, orientated at anarbitrary angle, in a tilted anisotropic 2D Dirac material. This simple set oftransformations enables all the exact and quasi-exact solutions associated with1D quantum wells in graphene to be applied to the confinement problem in tiltedDirac materials such as borophene. We also show that smooth electron waveguidesin tilted Dirac materials can be used to manipulate the degree of valleypolarization of quasiparticles travelling along a particular direction of thechannel. We examine the particular case of the hyperbolic secant potential tomodel realistic top-gated structures for valleytronic applications.

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