Sample-to-sample fluctuations of electrostatic forces generated by quenched charge disorder

TL;DR

This paper investigates the sample-to-sample fluctuations of electrostatic forces caused by quenched charge disorder on surfaces, revealing both normal and lateral force fluctuations and their potential experimental implications.

Contribution

It provides an exact analysis of force fluctuations in various geometries, including the surprising presence of lateral force fluctuations with the same scaling as normal forces.

Findings

Normal force fluctuations are computed exactly.

Lateral forces exist with zero mean but similar fluctuation scaling.

Lateral force fluctuations can aid in characterizing charge disorder experimentally.

Abstract

It has been recently shown that randomly charged surfaces can exhibit long range electrostatic interactions even when they are net neutral. These forces depend on the specific realization of charge disorder and thus exhibit sample to sample fluctuations about their mean value. We analyze the fluctuations of these forces in the parallel slab configuration and also in the sphere-plane geometry via the proximity force approximation. The fluctuations of the normal forces, that have a finite mean value, are computed exactly. Surprisingly, we also show that lateral forces are present, despite the fact that they have a zero mean, and that their fluctuations have the same scaling behavior as the normal force fluctuations. The measurement of these lateral force fluctuations could help to characterize the effects of charge disorder in experimental systems, leading to estimates of their magnitudes that are complementary to those given by normal force measurements.