Abstract
Low temperature carrier transport properties in 2D semiconductor systems can be theoretically well-understood within RPA-Boltzmann theory as being limited by scattering from screened Coulomb disorder arising from random quenched charged impurities in the environment. In this work, we derive a number of analytical formula, supported by realistic numerical calculations, for the relevant density, mobility, and temperature range where 2D transport should manifest strong intrinsic (i.e., arising purely from electronic effects) metallic temperature dependence in different semiconductor materials arising entirely from the 2D screening properties, thus providing an explanation for why the strong temperature dependence of the 2D resistivity can only be observed in high-quality and low-disorder 2D samples and also why some high-quality 2D materials manifest much weaker metallicity than other materials. We also discuss effects of interaction and disorder on the 2D screening properties in this context as well as compare 2D and 3D screening functions to comment why such a strong intrinsic temperature dependence arising from screening cannot occur in 3D metallic carrier transport. Experimentally verifiable predictions are made about the quantitative magnitude of the maximum possible low-temperature metallicity in 2D systems and the scaling behavior of the temperature scale controlling the quantum to classical crossover.
Highlights
The observation of a strong apparent metallic temperature dependence of the 2D electrical resistivity in high-quality semiconductor systems at low carrier densities has become fairly routine[1,2,3,4,5] during the last 20 years ever since the first experimental report of such an effective metallic behavior in high-mobility n-Si MOSFETs6,7
Decreasing amount of quenched disorder in the system. This low-temperature density-driven crossover behavior across nc in going from an effective strongly insulating phase (n < nc) to an effective metallic phase (n > nc), which is sometimes quite sharp, is often referred to[1,2,3] as the two-dimensional metal-insulator-transition (2D MIT) – a terminology we will use in the current work in our picture this is not a quantum phase transition at all, but is a sharp crossover from a strongly-localized insulating phase to a weakly-localized metallic phase the weak localization behavior may not manifest itself until the temperature is unrealistically low[8]
Using a physically motivated mean-field model of random phase approximation (RPA)-Boltzmann transport theory, where the carrier resistivity arises entirely from scattering off random quenched charged impurities in the environment, we have argued that the strong temperature dependence of 2kF-screening in 2D systems could by itself produce a metallic temperature dependence in qualitative agreement with experimental findings in many 2D systems
Summary
Independent 2D density of states, fails completely for the calculation of 2D resistivity at finite temperatures since it predicts a very weak temperature-dependent 2D resistivity for T ≪ TF whereas the full wave vector dependent polarizability, which includes the anomalous T/T F suppression of screening around q ≈ 2kF, predicts a strong linear-in-T/TF increase of the metallic 2D resistivity at low temperatures[15,16,17,18,19,20] This strong temperature-dependence of the 2D 2kF screening function is the mechanism underlying strong metallicity in 2D semiconductor systems at intermediate densities where the value of T/TF is not necessarily small leading to a substantial screening dependent thermal effect. Within a physical mean field approximation, the 2D charge carriers (electrons or holes) are scattered from the screened Coulomb disorder, and any strong temperature dependence in the screening function, for 2kF-scattering which dominates transport at lower temperatures, must necessarily be reflected in the 2D resistivity
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