Real space imaging of the quantum-Hall incompressible states influenced by the strong disorder

Under the strong magnetic field, two-dimensional electron gas forms the quantum Hall insulating phase with the Fermi level lying between quantized Landau levels gap, i.e., incompressible state. This spatial configuration depends on the potential landscape comprised of edge confinement and bulk disorder potentials in a practical sample such as a Hall bar for transport measurements. Using a scanning gate method incorporated with the non-equilibrium transport technique, we explored the influence of potential disorder on the incompressible states inherent to the quantum Hall effect. At the magnetic field $\mathrm{B}=8\mathrm{T}$ near filling factor $v=1$ , we measured different mobility samples having different disorder potential. Incompressible strips observed in both the samples showed the same filling factor dependency: the incompressible strips shift from the Hall-bar edge to center as decreasing the filling factor. In contrast, we found, only in the low mobility sample, the strong modulation of the pattern such as bright and dark spots appearing in the incompressible strip. This pattern is related to the short-range potential disorder inherent to the low mobility sample.