Finite-size nanowire at a surface: unconventional power laws of the van der Waals interaction

TL;DR

This paper investigates how the van der Waals interaction between a finite-size nanowire and a surface deviates from traditional power laws, revealing non-monotonic behavior influenced by nanowire properties and distance scales.

Contribution

It introduces a Luttinger liquid-based analysis of finite-size nanowire-surface interactions, uncovering unconventional power law modifications and non-monotonic dependencies.

Findings

Discovered non-monotonic power law behavior of van der Waals forces.

Identified the influence of spectral gap and temperature on interaction scaling.

Provided a framework for analyzing finite-size effects in nanowire-surface interactions.

Abstract

We study the van der Waals interaction of a metallic or narrow-gap semiconducting nanowire with a surface, in the regime of intermediate wire-surface distances $(v_{F}/c)L \ll d \ll L $ or $L \ll d \ll (c/v_{F})L $, where $L$ is the nanowire length, $d$ is the distance to the surface, and $v_{F}$ is the characteristic velocity of nanowire electrons (for a metallic wire, it is the Fermi velocity). Our approach, based on the Luttinger liquid framework, allows one to analyze the dependence of the interaction on the interplay between the nanowire length, wire-surface distance, and characteristic length scales related to the spectral gap and temperature. We show that this interplay leads to nontrivial modifications of the power law that governs van der Waals forces, in particular to a non-monotonic dependence of the power law exponent on the wire-surface separation.