Magnetic-Field Metal Insulator Transitions in Modulation-Doped Multiple-Quantum Structures.

A systematic study of far infrared spectroscopy and electrical transport measurement have been carried out on three set of modulation-doped rm GaAs/Al _{0.3}Ga_{0.7}As multiple-quantum-well structures at low temperatures 0.4 -30K and in magnetic fields up to 11T. A range of metal -insulator behavior is observed depending upon sample doping and magnetic field. For very low doping densities, transport results show that sample is a Mott insulator (impurity -band-insulator) and the optical transitions are essentially those of isolated impurities. When the doping density is increased, the results of transport measurement show metallic behavior, e.g., the carrier concentration is independent upon temperature at low magnetic fields, but the results of optical measurement still show the impurity-related transitions even at fields where the transport measurement exhibits the metallic behavior. This proves that this transition takes place within the impurity band, and the Mott insulator becomes an impurity-band-metal. When the doping concentration is increased further, electrons in the sample become a 2D electron gas at low fields due to strong screening from the self consistently electron-electron and electron-positive ion interaction. The integer quantum Hall effect and Shubnikov-de Hass oscillations are observed from two heavily doped samples and one lightly doped sample with wide barrier width (the fractional quantum Hall effect is not observed in these samples because of the large disorder created by interface roughness and some other disorders). One sample enters another insulating phase when magnetic field is so high that filling factor nu<1. The optical transitions for this insulating phase are no longer CR, but rather transitions between Landau level -like states localized in long range potential fluctuations created by the randomly distributed positive impurity ions. These "localized" states are completely unrelated to the original impurity states.