As I know, the only allowed interband transitions for graphene according to dirac cone is simply given by h(bar) . omega>E_f(Fermi level energy); however, N. M. R. Peres, et.al. in their recent paper of "Optical bistability of graphene in the terahertz range" have shown intrinsic optical bistability for transitions beyond such transition rule; i.e. for E_f >> h(bar) . omega. Which transition rule verifies such transition? Maybe the answer can be explored through the surface plasmon resonance attainable at each E_f. Could anyone help me to ensure about? Otherwise, I have already convinced about the ordinary nonlinear behavior of graphene which is dominant for interband transitions according to Vl A Margulis, et.al. or according to J. B. Khurgin.
http://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.125425
http://iopscience.iop.org/2040-8986/16/12/125203/
http://scitation.aip.org/content/aip/journal/apl/104/16/10.1063/1.4873704
Hi Morteza,
I'm not too familiar to these recent publications you cite, but I can try to answer your question simply, so you can try to understand them better.
If you take the simple tight binding model of graphite, you will find that the solution of the Shroedinger equation (close to the Fermi Level) can be approximated with a double (top-down) inversed cone (Dirac Cone) where the tips (so called K Points) are located at the Fermi level (see link).
This is true for a system of indefinite size and perfectly flat, without external perturbations. If you have a finite system, or a system with a special geometry (i.e. Graphene strip, etc...), doped or under external fields, you have to add now bundary conditions. This implies that now the Shroedinger equation should respect them, and from the continuous Dirac cone (general solution), only few quantized states are allowed. This creates Bands inside your cone.
Due to these bands, your system is not linear anymore and you can now have interband and intraband transitions.
http://pubs.rsc.org/services/images/RSCpubs.ePlatform.Service.FreeContent.ImageService.svc/ImageService/Articleimage/2014/CS/c4cs00102h/c4cs00102h-f1_hi-res.gif
Thanks to Prof.Lolli; I think the reason can be described as follows: For high frequency range, the graphene conductivity will be very small and graphene will no more exhibit intrinsic OB. As N. M. R. Peres, et.al. have mentioned in their paper, in order to observe OB, we need to utilize large input power which may be considered as a drawback for applications in optical processing. (Refer to Xiaoyu Dai, et.al.)
https://www.osapublishing.org/oe/abstract.cfm?URI=oe-23-5-6497
it has nothing to do with width of graphene sheet,like when we are converting into GNR,it will give rise to band gap,which was not earlier there?
regards
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