Temperature dependence of the conductivity for the two-dimensional electron gas: Analytical results for low temperatures

We present analytical results for the static conductivity of the two-dimensional electron gas at low temperature. The conductivity is expressed as σ(T)=σ(0)[1-C(α,n)T/${\varepsilon }_F$ -D(α,n)(T/${\varepsilon }_F$ ${)}^{3/2}$+O($T^2$ )]. Analytical expressions for σ(0) in the case of impurity and surface roughness scattering are given. C(α,n) and D(α,n) are universal functions, depending on the $q^{2\alpha }$ dependence of the scattering potential via C(α) and the density n of electrons via C(n). It is shown that the energy-dependent conductivity at temperature zero has a singularity at the Fermi energy. Our results are compared with other theoretical results and with experiments in Si-MOS (metal-oxide-semiconductor) systems.