Quantum states and localisation of developable Moebius nanostructures

Abstract

The equilibrium equations for wide, developable, Moebius strips undergoing large deformations have recently been derived, and solved, numerically. We use these results to compute the eigenvalues and eigenstates of non-interacting electrons confined to Moebius strips of linking number up to 1.5 and of arbitrary width. The inverse participation ratio is used to show that electrons are increasingly localised to the higher curvature regions of the higher-width structures, where sharp creases could form channels for particle transport. Our geometric formulation could be used to study transport properties of Moebius strip and other components in nanoscale devices.