V. Kalmeyer et al., 2-DIMENSIONAL LOCALIZATION IN THE PRESENCE OF RANDOM FLUX AND THE QUANTUM HALL SYSTEM AT EVEN-DENOMINATOR FILLING FRACTIONS, Physical review. B, Condensed matter, 48(15), 1993, pp. 11095-11106
We present detailed numerical calculations of the two-dimensional loca
lization problem in the presence of random flux and discuss the implic
ations of these results to the nu = 1/2 anomaly in the quantum Hall sy
stems. In the case where flux disorder breaks the time-reversal symmet
ry, finite-size scaling of the localization length and the conductance
are consistent with a finite region of extended states above a critic
al energy E(c). For the special case of randomly distributed half-flux
quanta per plaquette, where time-reversal invariance is preserved, we
find no mobility edge at any nonzero E(c). We observe a crossover fro
m positive magnetoresistance to negative magnetoresistance as potentia
l disorder is increased. These results give qualitative explanation of
the striking magnetotransport data at even-denominator filling fracti
ons and suggest an experiment to observe the crossover behavior.