Confinement-Induced Nonlocality and Casimir Force in Transdimensional Systems

TL;DR

This paper investigates how confinement-induced nonlocality affects the Casimir force in transdimensional systems, revealing weakened attraction and altered distance dependence, with implications for nanoscale material interactions.

Contribution

It introduces a theoretical analysis of nonlocal effects on Casimir forces in ultrathin slabs, including anisotropic and isotropic cases, using Lifshitz theory and nanotube arrays.

Findings

Nonlocality weakens Casimir attraction in ultrathin slabs.

Distance dependence of force changes from 1/l to 1/√l due to nonlocal effects.

Anisotropic nanotube arrays exhibit strong orientation-dependent Casimir forces.

Abstract

We study within the framework of the Lifshitz theory the long-range Casimir force for in-plane isotropic and anisotropic free-standing transdimensional material slabs. In the former case, we show that the confinement-induced nonlocality not only weakens the attraction of ultrathin slabs but also changes the distance dependence of the material-dependent correction to the Casimir force to go as $\sim\!1/\!\sqrt{l}$ contrary to the $\sim\!1/l$ dependence of that of the local Lifshitz force. In the latter case, we use closely packed array of parallel aligned single-wall carbon nanotubes in a dielectric layer of finite thickness to demonstrate strong orientational anisotropy and crossover behavior for the inter-slab attractive force in addition to its reduction with decreasing slab thickness. We give physical insight as to why such a pair of ultrathin slabs prefers to stick together in the perpendicularly oriented manner, rather than in the parallel relative orientation as one would customarily expect.