Geometry induced charge separation on a helicoidal ribbon

TL;DR

This paper calculates the quantum potential induced by geometry on a particle confined to a helicoidal ribbon, revealing localized states and an effective electric field analogous to the quantum Hall effect.

Contribution

It provides an exact calculation of the geometry-induced quantum potential for a helicoidal ribbon, highlighting the role of twist in creating localized states and effective fields.

Findings

Localized states appear at the rim of the helicoid.

The twist acts as an effective transverse electric field.

The phenomenon is reminiscent of the quantum Hall effect.

Abstract

We present an exact calculation of the effective geometry-induced quantum potential for a particle confined on a helicoidal ribbon. This potential leads to the appearance of localized states at the rim of the helicoid. In this geometry the twist of the ribbon plays the role of an effective transverse electric field on the surface and thus this is reminiscent of the quantum Hall effect.