Quantum Capacitance: 2DEG & Graphene

Density of states, gate voltage sweep, and the quantum capacitance C_Q
Temperature (K)10
Gate voltage (V)0.00
Disorder broadening (meV)10
2DEG (parabolic band)
Graphene (linear Dirac)
Quantum capacitance C_Q = e²·D(E_F) reflects the density of states at the Fermi level.
2DEG: parabolic dispersion → constant DOS = m*/(πℏ²), so C_Q is roughly constant except near band edge.
Graphene: linear Dirac dispersion → DOS = 2|E|/(πℏ²v_F²) vanishes at the Dirac point → C_Q dips sharply near V_g = 0.
Total gate capacitance: 1/C_total = 1/C_geo + 1/C_Q — quantum effects dominate when C_Q ≪ C_geo.