e^2}{\kappa q} \Pi(q),
\label{eq4}$$ where the static 2D electronic polarizability function $\Pi(q)$ is given by $$\Pi(q) = N_F \left [ 1- \theta(q-2k_F) \sqrt{1-(2k_F/q)^2} \right ],
\label{eq5}$$ where $N_F = m/\pi \hbar^2$ and $\theta(x) = 0$ (1) for $x <0$ ($x>0$) is the Heaviside step (or theta) function and the 2D Fermi wave vector $k_F$ is determined by the 2D carrier density through the formula $k_F
= (2\pi n)^{1/2}$. We note that the 2D Fermi energy ($E_F$) is given by $E_F = \hbar^2k_F^2/2m = \pi \hbar^2 n/m$. The RPA screening function $\varepsilon(q)$ can be expressed in the convenient form $$\varepsilon(q) = 1 + q_s/q,$$ which is exactly equivalent to Eqs. (\[eq4\]) and (\[eq5\]) if we define the 2D screening wave vector $q_s$ to be $$q_s = q_{TF} \left [ 1- \theta(q-2k_F) \sqrt{1-(2k_F/q)^2} \right ],
\label{eq8}$$ where the 2D Thomas-Fermi wave vector $q_{TF}$ is defined to be $$q_{TF} = 2 m e^2/(\kappa \hbar^2).$$ We note that (1) the Thomas-Fermi wave vector $q_{TF}$ is proportional to the 2D density of states at the Fermi energy $N_F = m/\pi \hbar^2$ (and is inversely proportional to the effective background lattice dielectric constant $\kappa$), and (2) screening is constant in 2D for $0 \leq q \leq 