The topological in-equivalence of Hall bar and Corbino geometries in coordinate space: Screening theory and direct transport experiments

Here we discuss the effect of topology on the quantum Hall effect taking into account the direct Coulomb interactions, considering two distinct geometries, namely the Hall bar and the Corbino disc. The consequences of interactions are underestimated in the standard approaches to explain the quantized Hall effect. However, the local distributions of the electron number density, the electrochemical potential, and current distributions depend on electron–electron interactions. Accounting for the direct Coulomb interaction and realistic boundary conditions results in local variations of compressibility—namely metal-like compressible and (topological) insulator-like incompressible regions. Within the framework of the screening theory, we show in the coordinate space that for both geometries, the bulk is compressible within most of the magnetic field interval corresponding to a quantized Hall plateau. The non-incompressible bulk throughout the plateau directly contrasts the standard explanation of the quantized Hall effect but is confirmed by our transport experiments. Our experimental results with two inner contacts within the Hall bar imply that the QHE plateaus scattering free transport along the sample edges even if the bulk of the sample is clearly in a compressible state. The scattering free transport is thereby supported by incompressible stripes. Our results confirm that the often promoted analogy in coordinate space between the quantized Hall effect and topological insulators is invalid throughout the entire plateau. We conclude that the equivalence of Hall and Corbino geometries is questionable. In addition, family relations of quantized Hall effect and topological insulators are doubtful. Finally, we propose experiments which will enable us to distinguish the topological properties of the two geometries in the coordinate space