Friedel oscillations of screening in nanotubes

TL;DR

This paper investigates how Friedel oscillations influence screening in nanotubes, revealing that unlike in 3D and 2D systems, the permittivity diverges and oscillations are not dominant at large distances.

Contribution

It demonstrates that in nanotubes, the permittivity diverges at singular points and Friedel oscillations are not the primary factor in long-distance screening, differing from lower-dimensional systems.

Findings

Permittivity becomes infinitely large at the singular point.

Friedel oscillations do not dominate screening at large distances.

Different screening mechanisms for zero and highest cylindrical harmonics.

Abstract

In 3D and 2D electronic systems the singular contribution to the static permittivity $\epsilon$ (Kohn singularity) is a small correction to the regular part of $\epsilon$ but it results in the leading term in asymptotic behavior of the screened potential (Friedel oscillations). In the present letter we show that for nanotubes quite different results are valid: $\epsilon$ becomes infinitely large at the singular point and the Friedel oscillations do not play the dominant role in the screening at the large distances. Moreover, the zero and highest cylindrical harmonics of the effective potential are screened by quite different mechanisms.