Summary of disorder and interaction effects

Abstract

In an over all picture the conductivity of a two-dimensional electron gas at zero temperature can be characterized by the interplay of disorder and interactions. The former can be described using the dimensionless parameter k _F l _D, where k _F is the Fermi wave vector and l _D is the transport mean free path of the electrons at zero temperature. The interactions are quantified by the interaction parameter conventionally defined as ${r_s} = 1/\sqrt {\pi {n_s}a{{_B^*}^2}}$ in two dimensions, where n _s is the sheet density of electrons (or holes) and a ^*_B is the effective Bohr radius. For two-dimensional systems with no valley degeneracy, r _s coincides with the ratio of the Coulomb interaction between carriers and the Fermi energy, i.e., r _s = E _C/E _F := r̄_s. For systems with a valley degeneracy g _v (e.g., g _v = 2 for Si-MOSFETS, whereas g _v = 1 for p-SiGe), this energy ratio becomes larger by a factor of g _v as compared to the standard definition of r _s, i.e.,

$${\bar{r}_{s}} = \frac{{{E_{C}}}}{{{E_{F}}}} = {g_{v}}{r_{s}} $$

.