The anderson transition in the presence of a magnetic field

The Anderson problem in the presence of a magnetic field is investigated. For 2 + ε. dimensions we compute the conductivity by means of a two-cut-off scaling procedure. We find the following behaviour. If for zero magnetic field the system is an insulator, the presence of the magnetic field gives rise to an insulator-metal transition. Upon increasing the magnetic field, we find that the conductivity increases. Upon further increase in the magnetic field, a second transition occurs leading to an insulating state. We find a series of such transitions. For the tight- binding Anderson model we find that the conductivity is periodic with the increase in magnetic field. The period is half a fluxon φ₀/2, (φ₀= hc/e). The conductivity is minimal for φ = (φ₀/2)n, n = 0,1,2.,. and maximal for φ = (φ₀/4)(4n + 1), n = 0, 1,2.,. (φ is flux per unit cell).