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| Main Author: | |
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| Format: | Preprint |
| Published: |
2016
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1611.00247 |
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| _version_ | 1866915031611867136 |
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| author | Doost, Mark Behzad |
| author_facet | Doost, Mark Behzad |
| contents | 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 Schrödinger'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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1611_00247 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Foldy-Wouthuysen Green's function and WKB transfer matrix method for Dirac tunneling through monolayer graphene with a mass gap Doost, Mark Behzad Mesoscale and Nanoscale Physics Quantum Physics 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 Schrödinger'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. |
| title | Foldy-Wouthuysen Green's function and WKB transfer matrix method for Dirac tunneling through monolayer graphene with a mass gap |
| topic | Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/1611.00247 |