Frequency-dependent conductivity of a finite disordered metal

Abstract

We derive a real-space formula for the ac conductivity tensor of a disordered electronic system. It applies both to the conductor in an insulating matrix and in a circuit through the appropriate boundary conditions. Using a field-theoretical approach, we show that the explicit enforcement of the gauge invariance leads to the decoupling of the Drude and diffusion contributions. The ac conductivity complies with the conductivity sum rule, confirming the consistent incorporation of the particle-number conservation in our method. We obtain a closed-form analytical solution for the conductivity and the dielectric function of a metallic particle which enables us to explain the anomalous far-infrared absorption and the plasmon broadening and red shift in a small-metallic-particle–insulator composite.