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arXiv · 1611.00247

Foldy-Wouthuysen Green's function and WKB transfer matrix method for Dirac tunneling through monolayer graphene with a mass gap

Mark Behzad Doost
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Abstract

I provide a transfer matrix method for the Foldy-Wouthuysen representation of the Dirac equation. I derive the relationship between the reflection and transmission coefficients of the Dirac spinors and the wavefunction in the transformed representation. I develop a WKB approximation for Dirac fermions that has the same elegant form as the WKB solution to Schr\"{o}dinger's equation. My WKB approximation is to all orders and includes the semi-classical turning point. I provide an extension to fully 2-dimensional periodic structures by Fourier methods for band-gap engineering. I verify my methods for all energies by comparison with analytic solutions developed in the Dirac spinor representation. Rich appendices detail my research into the Green's functions of Dirac fermions, where I rigorously derive the free space Green's functions for the Foldy-Wouthuysen representation of the Dirac equation.

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Mark Behzad Doost. 2016-10-30. Foldy-Wouthuysen Green's function and WKB transfer matrix method for Dirac tunneling through monolayer graphene with a mass gap. https://arxiv.org/abs/1611.00247

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