What is the Fermi wavelength of a graphene lattice in the tight binding model?

[Boccard]

TL;DR Summary

Fermi wavelength of a tight binding system

I am trying to figure out what the Fermi wavelength of my system is. Specifically I am looking at simulation a graphene lattice in the tight binding model. For this, I know that the Fermi energy (undoped) of my system is 3t (for simplicity I set t = 1). But how do I figure out what the Fermi wavelength is for the purpose of what my system can accuratly simulate in length (in units of lattice spacing)?
Also, if I dope my system, how does that interact with the Fermi energy?

 

[BigJDubs]

The Fermi wavelength is related to the Fermi energy by the equation $\lambda_F = \frac{h}{\sqrt{2mE_F}}$. In your case, since you have set $t = 1$, the Fermi energy is $E_F = 3$ and so the Fermi wavelength is $\lambda_F = \frac{h}{\sqrt{2m3}}$. If you dope your system, the Fermi energy will adjust accordingly, and so the Fermi wavelength will also change.