Conductivity and Temperature Dependence

Electrical conductivity, represented by the letter σ , is a measure of a material's ability to conduct an electric current. Resistivity, represented by ρ , is the inverse quantity, ρ = 1 σ , and it quantifies how strongly the material opposes the flow of the current. In some contexts, such as experiments, it is more convenient to consider the resistivity, while in others, such as the theory presented in this project, it is useful to consider the conductivity. These values are temperature dependent. In metals the resistivity decreases as temperature is reduced, ρ T >0 . In other materials resistivity increases as temperature is reduced, ρ T <0 .
The following graph from the article by Bolotin et al in 2008 [6] shows the measured resistivity for graphene at different temperatures, as a function of the carrier density.
At low carrier density ( n< n * ) , the experimentally observed temperature dependance of conductivity in graphene is pronouncedly non metallic (the resistivity increases as temperature is reduced), while above the critical density n * it is metallic.
This peculiar behavior aroused much interest, and was investigated further, so far it is not completely understood. Here is a graph of resistance varies with temperature for different gate voltages (which is equivalent to density) from article [7].