Metallicity and its low-temperature behavior in dilute two-dimensional carrier systems

We theoretically consider the temperature-dependent and density dependent transport properties of semiconductor-based two-dimensional (2D) carrier systems within the RPA-Boltzmann (RPA, random-phase approximation) transport theory, taking into account realistic screened charged impurity scattering in the semiconductor. We derive a leading behavior in the transport property, which is exact in the strict 2D approximation and provides a zeroth-order explanation for the strength of metallicity in various 2D carrier systems. By carefully comparing the calculated full nonlinear temperature dependence of electronic resistivity at low temperatures with the corresponding asymptotic analytic form obtained in the ${T/T}_F\to 0$ limit, both within the RPA screened charged impurity scattering theory, we critically discuss the applicability of the linear temperature-dependent correction to the low-temperature resistivity in 2D semiconductor structures. We find quite generally that for charged ionized impurity scattering screened by the electronic dielectric function (within RPA or its suitable generalizations including local-field corrections), the resistivity obeys the asymptotic linear form only in the extreme low-temperature limit of ${T/T}_F<~\mathrm{0.05.}$ We point out the experimental implications of our findings and discuss in the context of the screening theory the relative strengths of metallicity in different 2D systems.