Scaling for the frequency-dependent conductivity in disordered electronic systems

The scaling theory of Abrahams et al. is extended to the dynamical conductivity σ(ω) and Hall conductivity σH(ω). It is shown, by means of a self-consistent scaling argument, that at the mobility edge σ(ω)~ω^(d-2)d and σH(ω)~ω^2(d-2)d (the dimensionality $d>2$). Thus, at $d=3$, the frequency-dependent part of the conductivity, Δσ(ω)≡σ(ω)-σdc, exhibits a crossover near the mobility edge from ω1/2 to ω1/3 behavior. Similarly, the frequency-dependent part of the Hall conductivity crosses over from ω1/2 to ω2/3 behavior.