Curvature-induced electron localization in developable Möbius-like nanostructures

Abstract

We study curvature effects and localization of non-interacting electrons confined todevelopable one-sided elastic sheets motivated by recent nanostructured origami techniquesfor creating and folding extremely thin membrane structures. The most famous one-sidedsheet is the Möbius strip but the theory we develop allows for arbitrary linking number.Unlike previous work in the literature we do not assume a shape for the elasticstructures. Rather, we find the shape by minimizing the elastic energy, i.e., solving theEuler–Lagrange equations for the bending energy functional. This shape varieswith the aspect ratio of the sheet and affects the potential experienced by theparticles. Depending on the link there is a number of singular points on the edge ofthe structure where the bending energy density goes to infinity, leading to deeppotential wells. The inverse participation ratio is used to show that electronsare increasingly localized to the higher-curvature regions of the higher-widthstructures, where sharp creases radiating out from the singular points could formchannels for particle transport. Our geometric formulation could be used to studytransport properties of Möbius strips and other components in nanoscale devices.