Graphene Superlattices & Kronig-Penney model

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Numerically, Kronig-Penney model in graphene superlattices (SL) is drastically different from those in semiconductor SL. In semiconductors, transverse momentum k// can be isolated from the longitudinal momentum q, even if the superlattices potential is complex. In graphene, however, [tex]k_y[/tex] cannot be isolated from [tex]k_x[/tex]. So Kronig-Penney model is numerically a 1D problem in the calculation of the density of states, while KP model in graphene is a 2D problems which is very difficult due to the failure in interpolation. Let me give a more detailed explaination:

in semiconductor: [tex]\cos(q \ell)=f(q,E-\frac{\hbar^2 k^2_{//}}{2m^*})[/tex]
in graphene: [tex] \cos(k_x \ell)=f(k_y,E(k_x,k_y))[/tex]
[tex] f [/tex] is a function from the trace of the transfer matrix, (actually is a complex expression which can not be written in analytical form.)

I search the keywords "graphene, kronig-penney" using google, but can not find a numerical methods in the calculation of density of states in graphene superlattices. Who can help?
 
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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