  In this work we investigate the electrostatic properties of two dimensional
electron system (2DES) in the integer quantum Hall regime. The alternating
screening properties of compressible and incompressible strips are formed due
to edge effects together with electron-electron interactions. As it is well
known, the Landau quantization emanates from strong perpendicular magnetic
fields. The (Landau) energy levels are broadened due to impurities, which we
embedded their effects in density of states (DOS). In a basic level DOS has two
different forms: the Gaussian and semi-elliptic descriptions. The second form
is calculated within the self consistent Born approximation (SCBA). Having in
hand the density of states, we obtain both the longitudinal and Hall
(transversal) conductivities ($\sigma_{l}, \sigma_{H}$) utilizing
Thomas-Fermi-Poisson approximation to calculate position dependent charge
density profile and use Drude formalism to obtain transport coefficients.
Since, the definition of capacitance is closely related with compressibility
via DOS, (local) screening properties of 2DES is extremely important to
understand local capacitances. Here we numerically simulate a translational
invariant Hall bar subject to high magnetic fields which is perpendicular to
the plane of the 2DES using realistic parameters extracted from the related
experiments. Using the above mentioned approaches the local capacitances are
calculated, numerically. Our findings are in perfect agreement with related
experimental results which are based on a dynamic scanning capacitance
microscopy technique.
