Edge capacitance of a two-dimensional topological insulator

We study capacitance of the two-dimensional topological insulator (TI) edge states. The total capacitance is combined as a serial circuit of three capacitors presenting geometrical ${C}_G$, quantum ${C}_Q$, and correlation ${C}_{\mathrm{corr}}$ contributions to the electron energy. If the Coulomb interaction is weak, they obey an inequality ${C}_G<{C}_Q<{C}_{\mathrm{corr}}$. Quantities ${C}_G$ and ${C}_Q$ are found in the case of a round TI dot. The quantum capacitance at the finite temperature is determined taking into account the edge states quantization with and without the magnetic field. We have concluded that, in the accepted approximations, ${C}_{\mathrm{corr}}^{\ensuremath{-}1}=0$.