The two-dimensional white noise problem and localisation in an inversion layer

The density of states in the two-dimensional white noise problem is calculated from the coherent potential approximation at high energy and from fluctuation theory at low energies; both the exponent and the power of E in the prefactor for the density of fluctuation states are evaluated. Comparison is made with the results of a tight binding simulation of the white noise problem, and good agreement between theory and calculation is obtained. Calculation of the conductivity of different sized samples enables the mobility edge to be determined, and it is found that the critical value of g=n(E_c)/n ₀ is more than 0.8, in contrast with much lower values suggested earlier. The metallic conductivity is compared with the CPA result, and found to be lower by a factor of 0.4. Some modifications are introduced into the theory when account is taken of orbital degeneracy. Comparison is made with Pollitt's experiments on the inversion layer.