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PRB147
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my questions stemmed from reading the article in Physica E. Vol. 86, 10-16.
(https://www.sciencedirect.com/science/article/pii/S1386947716311365)
Why does the graphene Fermi velocity ##v_F## appear in Eq.(11) in this article,?
Eq.(11) is as follows:
$$
\frac{\partial \Omega_p(z,t)}{\partial z}+\frac{1}{v_F}\frac{\partial \Omega_p(z,t)}{\partial t}=i\alpha\gamma_3\rho_{21}(z,t)
$$
where ##\alpha=\frac{N\omega_1|\mu_{21}\cdot e_p|^2}{2\epsilon_r \hbar v_F \gamma_3}##,
and ##\Omega_p(z,t)=\Omega^0_p\eta (z,t)##; ##\eta(0,\tau)=\Omega^0_p e^{-[(\tau-\sigma)/\tau_0]^2}##.
As is well known, the graphene Fermi velocity ##v_F## comes from the nearest
neighboring carbon atom hopping #t# and their distance #a#, and even if slowly varying envelope
approximation(SVEA) has been considered, the group velocity of the pulse cannot be the Fermi velocity.
Could any professionals provide help, either guide me the derivation of the equation or provide
some effective references which can be used to derive the equation.
(https://www.sciencedirect.com/science/article/pii/S1386947716311365)
Why does the graphene Fermi velocity ##v_F## appear in Eq.(11) in this article,?
Eq.(11) is as follows:
$$
\frac{\partial \Omega_p(z,t)}{\partial z}+\frac{1}{v_F}\frac{\partial \Omega_p(z,t)}{\partial t}=i\alpha\gamma_3\rho_{21}(z,t)
$$
where ##\alpha=\frac{N\omega_1|\mu_{21}\cdot e_p|^2}{2\epsilon_r \hbar v_F \gamma_3}##,
and ##\Omega_p(z,t)=\Omega^0_p\eta (z,t)##; ##\eta(0,\tau)=\Omega^0_p e^{-[(\tau-\sigma)/\tau_0]^2}##.
As is well known, the graphene Fermi velocity ##v_F## comes from the nearest
neighboring carbon atom hopping #t# and their distance #a#, and even if slowly varying envelope
approximation(SVEA) has been considered, the group velocity of the pulse cannot be the Fermi velocity.
Could any professionals provide help, either guide me the derivation of the equation or provide
some effective references which can be used to derive the equation.
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