The Kubo-Greenwood expression and 2d MIT transport

The 2d MIT in GaAs heterostructures (p- and n-type)features a mobility that drops continuously as the reduced density x= n/n$_{c}$-1 is decreased. The Kubo-Greenwood result [1] predicts $\mu$ = (e$\epsilon$$_{h}$/hn$_{c}$)$\alpha$$^{2}$(x) where $\alpha$ is a normalized DOS. $\alpha$(x)is obtained from the data [p-type, Gao et al. [2]; n-type Lilly et al. [3]]. Interact -ion corrections yield a Fermi energy E$_{F}$=E$_{c}$[x-A$_{HF}$ x$^{1/2}$/$\gamma$+A$_{CT,ic}$x$^{1/4}$/$\gamma$$^{3/2}$] where E$_{c}$ = n$_{c}$/a$_{2}$ with a$_{2}$ the noninteracting DOS and $\gamma$ = (2$\pi$n$_{c}$)$^{1/2}$a*, A$_{HF}$ is a Hartree -Fock term, while A$_{CT,ic}$ is a repulsive interaction term between the charged traps (CT) and the itinerant carriers (ic) that are confined in conducting filaments. N(E$_{F}$,x)is determined using N(E)dE=2kdk/2$\pi$ where k$_{F}$=(2$\pi$n$_{c}$ x)$^{1/2}$. The data determines the ``self-energy'' terms A$_{HF}$ and A$_{CT,ic}$. The effective mass m*(x) is given by m*(x)/m$_{b}$* = 1/$\alpha$(x) and diverges as x$^{-3/4}$ as x goes to zero at T=0. $\alpha$(x) goes to 1 for large x. The interaction approach will be compared with the percolation approach. [1] Mott and Davis, Elect. Prop. in Noncryst. Mat. [Clarendon Press 1971]; [2) Gao et al. PRL93,256402 (2004);[3] Lilly et al.PRL90,056806 (2003)