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

Abstract

We present analytical results for the static conductivity of the two-dimensional electron gas at low temperature. The conductivity is expressed as \ensuremath{\sigma}(T)=\ensuremath{\sigma}(0)[1-C(\ensuremath{\alpha},n)T/${\ensuremath{\varepsilon}}_{F}$ -D(\ensuremath{\alpha},n)(T/${\ensuremath{\varepsilon}}_{F}$${)}^{3/2}$+O(${T}^{2}$ )]. Analytical expressions for \ensuremath{\sigma}(0) in the case of impurity and surface roughness scattering are given. C(\ensuremath{\alpha},n) and D(\ensuremath{\alpha},n) are universal functions, depending on the ${q}^{2\ensuremath{\alpha}}$ dependence of the scattering potential via C(\ensuremath{\alpha}) 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.