The communication of the electron system with the outside world at low excitation transport experiments happens by exchanging electrons at the Fermi level. We argue that the locations where this is possible in the quantum Hall effect regime are the so-called edge channels. We explain that these channels can be understood as a more general representation of the many-particle quantum Hall (QH) system close to equilibrium that allows describing transport due to non-equilibrium on a very fundamental level. Based on fundamental principles of quantum physics, a transfer matrix formulation for the local non-equilibrium electrochemical potential in a network of interconnected directed quantum channels can be used to solve the lateral distribution of the non-equilibrium excitation potentials. Instead of using the Landauer formula or other tools like the Kubo formula for addressing conductance’s just a transfer matrix formulation for the transfer of electrochemical potentials is used to find the self-consistent lateral distribution of the non-equilibrium electrochemical potentials. Currents and potentials that are measured at contacts are only calculated as a post-processing step right at the contacts, and they allow calculating all the resistances and conductance’s like known from QH experiments. The interplay between transport and the many-particle system is of general interest when dealing with accessing information about quantum systems. Our approach allows modeling electron systems in the QH regime for realistic sample geometries, including inhomogeneities, like present in real samples or that are forced by gate electrodes as well as the random disorder potential. We combine our network model for transport with the Hartree–Fock method that allows the inclusion of realistic screening effects as well as the magnetic field-dependent enhanced g-factor.
Part of the book: Research Advances in Quantum Dynamics