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

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,...

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Bibliographic Details
Published in:Scientific reports 2022-05, Vol.12 (1), p.7688-7688, Article 7688
Main Authors: Ng, R. A., Wild, A., Portnoi, M. E., Hartmann, R. R.
Format: Article
Language:English
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639/301/357/918
639/301/357/918/1052
639/705/1041
639/766/119
639/766/119/995
639/766/483
639/766/483/1139
639/766/483/640
Eigenvalues
Graphene
Humanities and Social Sciences
multidisciplinary
Science
Science (multidisciplinary)
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Summary: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.
ISSN:2045-2322
2045-2322
DOI:10.1038/s41598-022-11742-3