Quantum capacitance is a concept in condensed matter physics and nanotechnology that describes the capacitance associated with the density of states of a material at the quantum level. It is particularly relevant in systems where the electronic states are quantized, such as in quantum dots, two-dimensional electron gases, and other nanostructures. In classical capacitance, the capacitance (\(C\)) is defined as the ability of a system to store charge per unit potential difference.
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The electronic contribution to differential capacitance arising from a change of chemical potential as particles are added. For noninteracting Electrons at zero temperature, it is times the density of states of the whole sample at the Fermi energy. The quantum capacitance of a graphene cone gives a worked example.