Quantum capacitance

Quantum capacitance, also known as chemical capacitance and electrochemical capacitance , was first theoretically introduced by Serge Luryi (1988), and is defined as the variation of electrical charge with respect to the variation of electrochemical potential , i.e., . In the simplest example, if you make a parallel-plate capacitor where one or both of the plates has a low density of states, then the capacitance is not given by the normal formula for parallel-plate capacitors, . Instead, the capacitance is lower, as if there was another capacitor in series, . This second capacitance, related to the density of states of the plates, is the quantum capacitance and is represented by . The equivalent capacitance is called electrochemical capacitance .

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