# Edge capacitance of a 2D topological insulator

## TL;DR

This paper investigates the capacitance contributions of edge states in a 2D topological insulator, analyzing geometrical, quantum, and correlation effects, and concludes that correlation capacitance is negligible under certain conditions.

## Contribution

It provides a detailed analysis of the different capacitance components in 2D topological insulator edge states, including temperature and magnetic field effects, with a novel focus on correlation capacitance.

## Key findings

- C_G < C_Q < C_corr when Coulomb interaction is weak
- C_G and C_Q are calculated for a round TI dot
- Correlation capacitance C_corr is found to be zero in the approximations used

## Abstract

We study capacitance of the 2D topological insulator (TI) edge states. The total capacitance is combined as a serial circuite of 3 capacitors presenting geometrical $C_G$, quantum $C_Q$ and correlation $C_{corr}$ contributions to the electron energy. If the Coulomb interaction is weak, they obey an inequality $C_G<C_Q<C_{corr}$. 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, $C_{corr}=0$.