LOCALIZATION PHASE-DIAGRAM FOR A DISORDERED SYSTEM IN A MAGNETIC-FIELD IN 2 DIMENSIONS

A phase diagram for the localization-delocalization transition of a tw o-dimensional disordered semiconducting system in a perpendicular magn etic field B is investigated with a numerical method. Disorder origina tes from a random distribution of shallow impurities, measured in unit s of the impurity concentration c. Starting with a tight-binding Hamil tonian and an impurity state basis, the localization criterion is defi ned by means of the quantum connectivity of impurities. Finite-size sc aling is employed to study the transition in the B-c parameter space. On this footing a phase diagram of the localization-delocalization tra nsition in the B-c parameter space is calculated. At low concentration s c < c1 almost-equal-to 0.246a-2, where a is the impurity radius, all states are localized. Above c1 two nose-shaped areas of a phase of de localized states exist, the tips of which are found at (c1, B1) = (0.2 46 +/- 0.004a-2, 0.013 +/- 0.001) and (c3, B3) = (0.67 +/- 0.03a-2, 0. 76 +/- 0.07) with the magnetic field given in terms of a2l-2, where l is the Lamor length. Both areas join at (c2, B2) = (1.2 +/- 0.2a-2, 0. 233 +/- 0.009). States are well localized at B = 0. An estimate of the localization length exponent is given. The transition is discussed in terms of orbital shrinking and interference effects, which are safely distinguished. The latter mechanism can account for a re-entrant beha viour with respect to the magnetic field. The metal-insulator transiti on is discussed as a function of the electron density in conjunction w ith the phase diagram. Results are compared with previous calculations within the zero differential overlap approximation.