Curvature-induced quantum behaviour on a helical nanotube

TL;DR

This paper explores how the curvature of a helical nanotube influences quantum particle behavior, revealing curvature-induced potential effects and energy band structures arising purely from geometry.

Contribution

It derives the Schrödinger equation for a quantum particle on a helical surface and analyzes the resulting curvature-induced quantum effects and energy band formation.

Findings

Curvature creates a periodic quantum potential.

Helical configuration is energetically favorable.

Energy bands originate from geometry.

Abstract

We investigate the effect of curvature on the behaviour of a quantum particle bound to move on a surface shaped as a helical tube. We derive and discuss the governing Schr\"odinger equation and the corresponding quantum effective potential which is periodic and points to the helical configuration as more energetically favorable as compared to the straight tube. The exhibited periodicity also leads to energy band structure of pure geometrical origin.