Non-local dielectric functions on the nanoscale: electronic polarization and fluctuations

Abstract

In this work, we use a non-local dielectric theory to describe the electronic polarization induced by perturbing fields, and to characterize spontaneous, quantum mechanical fluctuations in the polarization. The theory holds on the intramolecular length scale, within the Born-Oppenheimer approximation. A non-local dielectric function ε d ( r , r ′) acts as an integral kernel that gives the dielectric displacement D( r) at point r within a molecule, in terms of the electric field E( r′) acting at other points r ′. Due to the inhomogeneity of the intramolecular environment, ε d ( r , r ′) differs from the non-local dielectric function ε v ( r , r ′) that characterizes the screening of applied potentials; however, the longitudinal component of the spatial Fourier transform ε d ( k , k ′) is completely determined by k, k′, and ε v ( k , k ′). For a molecule in equilibrium with a radiation bath at a fixed temperature, the fluctuation-dissipation theorem relates correlations of the spontaneous polarization fluctuations to the imaginary part of the non-local polarizability density. From this result, we derive a relation between the correlations of the fluctuating electronic polarization and the dielectric function ε d ( r , r ′;iω).