Boundary conditions and many-body effects in the quantised Hall effect

It is shown that the edges of a quasi-two-dimensional electron gas yield a considerable influence on the shape of the magneto-quantum oscillations of the channel resistance. In the Hall geometry, necessary for the investigation of the Hall effect, both types of front and lateral edges are of different importance for the formation of sigma xx (or rho xx) gaps and sigma xy (or rho xy) plateaus in sufficiently high magnetic fields and for the deduction of a high precision value for e2/h. In the first case, the gate-overlapped source capacitor (e.g. of a silicon MOS device) determines the equipotentials of the gate and the silicon surface allowing the chemical potential to occupy values between the broadened quantum levels of the channel. The latter effect, yielding a possibility for an accurate determination of the Sommerfeld fine-structure constant, indicates that, owing to the self-energy of the electron gas, scattering of the electrons at the lateral channel edges is completely impeded at low temperatures. Both ideas should be valid for arbitrary quasi-two-dimensional systems because of the universality of the arguments discussed.