## Calculations of Quantum Capacitance of The Two Dimensional Electron System

**Afif Sıddıki**

* Mimar Sinan Fine Arts University, Physics Department*

13 April 2016, Wednesday, 13:40

Cavid Erginsoy Seminar Room, Physics Department, 3rd floor

**Abstract:**
In this work we investigate the electrostatic properties of two dimensional electron system (2DES) in the integer quantum Hall regime and the alternating properties of the compressible and the incompressible strips formed due to the edge effects. We consider the effect of impurities on the two dimensional via density of states calculations. As it is well known the Landau Levels emerge due to high perpendicular magnetic field and are broadened which stem from impurities. At a first order approximation the density of state takes two different form when considering impurities, these are the Gaussian and the semi-elliptic forms calculated within the self consistent Born approximation (SCBA). Having in hand the density of states, we calculate both the longitudinal and Hall (transversal) conductivities ($\sigma_{L}, \sigma_{H}$) utilising Thomas-Fermi-Poisson approximation. Since the definition of capacitance is closely related with the charging energy once the compressibility properties of the 2DES is numerically and experimentally obtained, one can predict the (local) capacitance. Using the Thomas-Fermi-Poisson approximation and granted density of states we calculate numerically the local capacitances of a 2DES subject to perpendicular magnetic field. Our findings are in perfect agreement with the experiment which is based on a dynamic scanning capacitance microscopy.