On composites of the type: metal - dielectrics and superconductor - dielectrics

TL;DR

This paper models the dielectric response of metal-dielectric and superconductor-dielectric composites using spectral functions, analyzing percolation effects, shape influences, and low-frequency behaviors in the quasistatic approximation.

Contribution

It introduces a spectral function approach to describe dielectric properties of composites, including effects of shape, concentration, and Josephson junctions in superconductors, highlighting percolation transitions.

Findings

Percolation transition at x_c=1/3 causes metallic-like behavior.

Dielectric constant increases with superconducting particle concentration.

Low-frequency divergence persists above percolation threshold.

Abstract

Composites of the type: metal - dielectrics and superconductor - dielectrics are studied in the quasistatic approximation. The dielectric response is described by the spectral function $G(n,x)$, which contains effects of the concentration x (of metallic resp. superconductive particles) on the dielectric function,and effects of the shape. The parameter n plays the role of the depolarisation factor for dielectric materials, in metals it is a factor which includes effects like shape, and a topology of the composite. There exists a percolation transition at $ x_{c}= \frac{1}{3} $ which leads to a metallic-like for the composite with the concentration $ x > x_{c}$. At low frequencies divergence with frequency remains even when there are present dielectric particles above the percolation concentration. In superconductor case the spectral function $G(n,x)$ may include also Josephson junction effects. We assume in both cases of composites two types of spheroidal particles, metal (superconducting) ones and dielectric ones. A dielectric function is constant in both cases for the dielectric material, and a dielectric function for the metal and for the superconductor are used with well known form for metals and a classical superconductor. A percolation transition at $ x_{c}$ leads to a metallic-like absorption for the composite with $x>x_{c}$. Note that at low frequencies divergence in frequency remains even when there are present dielectric particles above $x_{c}$. Below the percolation threshold dielectric properties are modified by metalic particles. We obtain at very low temperatures and low concentrations x of the superconductor the effective dielectric constant. The absorption part is zero in our simple case. The real part of the dielectric function increases with the concentration of the superconducting spheres. The frequency dependence is quadratic, it gives low frequency tail.