Asymptotics of the dispersion interaction: analytic benchmarks for van der Waals energy functionals

TL;DR

This paper demonstrates that traditional $R^{-6}$ summation methods can produce qualitatively incorrect van der Waals interaction results for certain nanostructures, highlighting the need for revised energy functionals.

Contribution

It provides analytic microscopic calculations showing alternative power-law decay of van der Waals interactions in zero-gap nanostructures, challenging conventional models.

Findings

Traditional $R^{-6}$ summation can be qualitatively wrong for certain nanostructures.

The interaction decay follows a different power law than the conventional $R^{-6}$.

The new interaction behavior might be experimentally measurable at sub-micron scales.

Abstract

We show that the usual sum of $R^{-6}$ contributions from elements separated by distance $R$ can give \emph{qualitatively} wrong results for the electromagnetically non-retarded van der Waals interaction between non-overlapping bodies. This occurs for anisotropic nanostructures that have a zero electronic energy gap, such as nanowires, conducting nanotubes, and nano-layered systems including metals and graphene planes. In all these cases our analytic microscopic calculations give an interaction falling off with a power of separation different from the conventional value. We discuss implications for van der Waals energy functionals. The new nanotube interaction might be directly measurable at sub-micron separations.