Developing semiclassical Wentzel-Kramers-Brillouin theory for 
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 model

Blaise, Kathy; Ejiogu, Chinedu; Iurov, Andrii; Zhemchuzhna, Liubov; Gumbs, Godfrey; Huang, Danhong

doi:10.1103/physrevb.107.045128

Cited by 3 publications

(2 citation statements)

References 84 publications

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“…For this case, the properties of such electrons are not very much different from their classical counterparts and could be effectively described by classical dynamics. However, in contrast to a perturbation theory, the interaction between a particle and an external potential can be very strong, implying that in a number of cases the WKB description can still be valid even as other types of approximation fail [41][42][43][44][45][46]. Therefore, from this point of view, it is essential and crucial to develop a semi-classical WKB theory for each newly discovered Dirac lattice, such as α-T 3 or Kekulé-patterned graphene.…”

Section: Of 15mentioning

confidence: 99%

Application of WKB Theory to Investigating Electron Tunneling in Kek-Y Graphene

Iurov¹,

Zhemchuzhna²,

Gumbs³

et al. 2023

Preprint

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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.

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Section: Of 15mentioning

confidence: 99%

Application of WKB Theory to Investigating Electron Tunneling in Kek-Y Graphene

Iurov¹,

Zhemchuzhna²,

Gumbs³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…In this case, the properties of such electrons are not much different from their classical counterparts and could be effectively described by classical dynamics. However, in contrast to a perturbation theory, the interaction between a particle and an external potential can be very strong, implying that in a number of cases, the WKB description can still be valid even as other types of approximation fail [41][42][43][44][45][46]. Therefore, from this point of view, it is essential and crucial to develop a semi-classical WKB theory for each newly discovered Dirac lattice, such as α-T 3 or Kekulé-patterned graphene.…”

Section: Introductionmentioning

confidence: 99%

Application of the WKB Theory to Investigate Electron Tunneling in Kek-Y Graphene

et al. 2023

Self Cite

View full text Add to dashboard Cite

In this paper, we have constructed a WKB approximation for graphene having a Y-shaped Kekulé lattice distortion and a special folding of the K and K′ 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 Kekulé-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 Δ0≪1 (a good fit to its actual value Δ0∽ 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 Kekulé-patterned graphene has been explored and analyzed in detail.

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Tunneling valley Hall effect induced by coherent geometric phase

Zeng

2024

Phys. Rev. B

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Developing semiclassical Wentzel-Kramers-Brillouin theory for α−T3 model

Cited by 3 publications

References 84 publications

Application of WKB Theory to Investigating Electron Tunneling in Kek-Y Graphene

Application of WKB Theory to Investigating Electron Tunneling in Kek-Y Graphene

Application of the WKB Theory to Investigate Electron Tunneling in Kek-Y Graphene

Tunneling valley Hall effect induced by coherent geometric phase

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