Edge States and Capacitance of a 2D Topological Insulator

The planar capacitance of the 2D topological insulator (TI) based on HgTe layer is studied. It is assumed that the width of the HgTe layer is close to the critical value corresponding to zero energy gap. The developed width fluctuations lead to the formation of internal edge states at the interfaces between ordinary and topological insulating phases. The edge states energies cover the entire energy gap. These states are recharging under applied voltage. The geometric capacitance C_G is found in the percolation approach. Besides, the quantum capacitance has been calculated. At last, the problem of non-local capacitance in a random network of the edge states is considered.