= Quantum capacitance of a graphene cone
{title2=$c_q=2e^2|E_F|/[\pi(\hbar v_F)^2]$}
The <quantum capacitance> per unit <area> is $c_q=e^2D(E_F)$. Differentiating the gate equation gives
$$
\frac{1}{c_{\rm diff}}=\frac{1}{c_g}+\frac{1}{c_q},\qquad
c_{\rm diff}=e\frac{dn}{dV_g}.
$$
Thus the available electronic states act as a second contribution in series with geometric <capacitance>. At exact neutrality the ideal zero-<temperature> model has $c_q=c_{\rm diff}=0$; actual finite-<temperature> or spatially nonuniform samples need a broader description. A capacitance measurement can therefore probe the <density of states>, rather than geometry alone.
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