Quantum capacitance,[1] also known as chemical capacitance[2] and electrochemical capacitance,[3] was first reported experimentally by Mead in 1961[4] and theoretically introduced by Serge Luryi (1988),[1] and is defined as the variation of electrical charge with respect to the variation of electrochemical potential , i.e., .[3]
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 .
Quantum capacitance is especially important for low-density-of-states systems, such as a 2-dimensional electronic system in a semiconductor surface or interface or graphene, and can be used to construct an experimental energy functional of electron density.[3]
^Cite error: The named reference Bisquert was invoked but never defined (see the help page).
^ abcMiranda, David A.; Bueno, Paulo R. (2016-09-21). "Density functional theory and an experimentally-designed energy functional of electron density". Phys. Chem. Chem. Phys. 18 (37): 25984–25992. Bibcode:2016PCCP...1825984M. doi:10.1039/c6cp01659f. ISSN 1463-9084. PMID 27722307.
^Mead, C. A. (1961). "Anomalous Capacitance of Thin Dielectric Structures". Phys. Rev. Lett. 6 (10). American Physical Society: 545–546. Bibcode:1961PhRvL...6..545M. doi:10.1103/PhysRevLett.6.545.
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