Model estimates of the quantum capacitance of graphene-like nanostructures

Using simple models, analytical estimates of quantum capacitance C$_Q$ are obtained for an infinite sheet, a nanoribbon, and a chain of two-dimensional analogs of the A$_{N}$B$_{8-N}$ compounds with a hexagonal structure (graphene-like compounds). It is demonstrated that there is a nonmonotonic dependence of C$_Q$ on the electrostatic potential.