Iurov, A.; Zhemchuzhna, L.; Gumbs, G.; Huang, D. Application of the WKB Theory to Investigate Electron Tunneling in Kek-Y Graphene. Appl. Sci.2023, 13, 6095.
Iurov, A.; Zhemchuzhna, L.; Gumbs, G.; Huang, D. Application of the WKB Theory to Investigate Electron Tunneling in Kek-Y Graphene. Appl. Sci. 2023, 13, 6095.
Iurov, A.; Zhemchuzhna, L.; Gumbs, G.; Huang, D. Application of the WKB Theory to Investigate Electron Tunneling in Kek-Y Graphene. Appl. Sci.2023, 13, 6095.
Iurov, A.; Zhemchuzhna, L.; Gumbs, G.; Huang, D. Application of the WKB Theory to Investigate Electron Tunneling in Kek-Y Graphene. Appl. Sci. 2023, 13, 6095.
Abstract
In this paper, we have constructed a WKB approximation for graphene having a Y-shaped Kekul\'e lattice distortion and a special folding of the $\mbox{\boldmath$K$}$ and $\mbox{\boldmath$K$}^\prime$ valleys, which leads to very specific linear energy dispersions with two non-equivalent pairs of subbands. These obtained semi-classical results, which include the action, electron momentum and wave functions, are utilized to analyze the dynamics of electron tunneling through non-square potential barriers. In particular, we explore resonant scattering of an electron by a potential barrier built on Kekul\'e-distorted graphene. Mathematically, a group of consecutive equations for a semi-classical action have been solved by following a perturbation approach under the condition of small strain-induced coupling parameter $\Delta_0 \ll 1$ (a good fit to its actual value $\Delta_0 \backsim 0.1$). Specifically, we consider a generalized model for Kek-Y graphene with two arbitrary Fermi velocities. The dependence of the electron transmission amplitude on the potential profile $V(x)$ and band parameters of Kekul\'e-patterned graphene has been explored and analyzed in details.
Keywords
WKB approximation; semi-classical action; electron tunneling; transmission amplitude
Subject
Physical Sciences, Condensed Matter Physics
Copyright:
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