Quantum Hall-like effect on strips due to geometry

TL;DR

This paper demonstrates that a helicoidal strip's geometry induces localized electronic states analogous to the quantum Hall effect, with the twist acting like a magnetic field, potentially stabilizing the structure at low temperatures.

Contribution

It provides an exact calculation of the effective potential on a helicoidal strip, revealing geometry-induced localized states similar to quantum Hall phenomena.

Findings

Localized states appear at a distance from the central axis.

The twist acts like a magnetic field influencing electronic states.

Twisted configurations may be stabilized at low temperatures.

Abstract

In this Letter we present an exact calculation of the effective potential which appears on a helicoidal strip. This potential leads to the appearance of lcalized states at a distance \xi_0 from the central axis. The twist \omega of the strip plays the role of a magnetic field and is responsable for the appearance of these localized states and an effective transverse electric field thus this is reminiscent of the quantum Hall effect. At very low temperatures the twisted configuration of the strip may be stalilized by the electronic states.