Quantum Hall effect in an antidot lattice: Macroscopic limit

The quantum Hall effect in a 2D system with antidots is studied. The antido ts are assumed to be large compared with the quantum and relaxation lengths . In this approximation the electric field in the system can be described b y the continuity equation. It is found that the electric field in a system without conducting boundaries can be expressed in terms of the same system without a magnetic field. Specific problems of the electric field and curre nt in structures containing one or two antidots and in a circular disk with point contacts are solved. The effective Hall and longitudinal conductivit ies in a sample containing a large number of randomly distributed antidots are found. In the limit of zero local longitudinal conductivity, the effect ive longitudinal conductivity also vanishes, and the Hall conductivity is e qual to the local conductivity. The corrections to the conductivity tensor which are due to the finiteness of the local conductivity are obtained. Bre akdown of the quantum Hall effect in a lattice of antidots is studied on th e basis of the assumption that a high current density in narrow locations o f the system results in overheating of the electrons. Local and nonlocal mo dels of overheating are studied. The high-frequency effective conductivity of a system with antidots and the shift of the cyclotron resonance frequenc y are found. (C) 2000 MAIK "Nauka/Interperiodica".