Instead of an orbiting 3D lattice, this version draws the physics that generates the number: a Dirac-cone band cross-section, its density of states g(E), and a capacitor-network schematic, all computed live from the same equations.
1/C_total = 1/C_Q + 1/C_H
C_total = C_Q · C_H / (C_Q + C_H)
C_Q(V,T) = (2e²k_BT)/(π(ħv_F)²) · ln[2(1+cosh(eV/k_BT))]
g(E) = 2|E| / (π(ħv_F)²) (states per unit area per unit energy)
The left plot is graphene's linear dispersion E(k) = ±ħv_F|k| shown as a cross-section through the Dirac cone; the shaded wedge is the Fermi sea filled up to the induced Fermi level EF. The right plot is the density of states g(E) that dispersion produces — it vanishes at the Dirac point and grows linearly with |E|, which is exactly why adding charge near neutrality is expensive and CQ is small there. Integrating g(E) from 0 to EF gives the induced carrier density, and at T→0 that integral reduces exactly to the CQ(V,T) formula above — the two panels are two views of one calculation, not separate illustrations.
Below, the capacitor-network schematic draws CQ and CH as two real plate pairs wired in series; each gap width is drawn proportional to 1/C, so the schematic makes visible why the smaller capacitance dominates a series stack. The bar chart alongside compares CQ, CH and Ctotal directly.
- Gate voltage — shifts EF away from the Dirac point; watch the filled wedge grow in the band plot and the shaded area grow under g(E).
- CH — electrolyte double-layer stiffness; changes the CH plate gap and bar directly.
- Ion concentration — sets the density of the 2D ion swarm drawn at the CH plates (illustrative packing, not a Debye-length solve).
- Temperature — thermally rounds the V-shaped minimum of CQ(V) in the sparkline, exactly per the formula.