Conductivity Sum Rule in the Nearly Free Two-Dimensional Electron Gas in an Uniaxial Potential

We report an investigation of the conductivity sum rule in the two-dimensional system of free electrons in a weak uniaxial potential. The sum rule is defined through the integration of a real part of a multiband conductivity tensor and separates between the intraband and interband charge transport concentrations. It is shown how the relative direction of the electric field and the uniaxial potential defines the transport concentrations of the nearly free electron system and why the sum rule is obeyed.