Corner Dissipation in Quantum Hall Systems

A description of the onset of dissipation in the integer quantum Hall effect is given, where the electric field across the sample is expressed through a time dependent vector potential. This brings the essentially time dependent, non-stationary nature of the problem into focus. The electric field induces transitions between the levels of the disorder broadened Landau band. Above a critical electric field the particles are driven upwards in energy space beyond the Fermi level, which leads to dissipation since the accumulated energy is lost to the heat bath after τ$\text{}_{in}$, the time between two inelastic events. Thus the dissipated power is obtained without the use of the traditional (linear response) transport formulae. As an application we investigate the dissipation in the corner region of a Hall bar. The results are in reasonable accordance with recent experiments exploiting the fountain pressure effect.