Screening and Transport Properties in a Triangular Well

Abstract

Since dissipative transport properties always depend on matrix elements containing the screened or selfconsistent potential, there is a close connection between the form of the screened potential and the transport coefficients. In the quantum Hall regime the current may be dissipationless. However, the potential still plays a role because of the possibility of a metal insulator transition of the Mott type /1/. The condition for such a transition is eV^sc > kT where V^sc is the screened potential and kT may be interpreted as the thermal energy belonging to the guiding center of an electron. If the filling factor in the insulator regions have exact integer or fractional values then the quantum Hall effect (QHE) can be explained and its accuracy depends on the nature of the transition region between the insulator and the metallic domains. This problem is not understood.