Quantum flexoelectric nanobending

Abstract

The aim of this article is twofold. First, to develop a clear quantum theoretical playground where questions about the connection between strain fields and electric fields could be unambiguously explored. Second, as an application, to derive a criterion that establishes the length scale below which bent molecules, in particular, carbon nanotubes, display flexoelectricty. To this end, we consider a model molecule that displays the basic elements necessary to support flexoelectricity. Due to its simplicity, a full quantum mechanical solution is possible, providing analytical expressions for the energy bands and for the electronic states and their corresponding strain gradient-induced charge density. This charge density is in turn used to evaluate the appearance of electric fields. Finally, we investigate the consequences of applying our model to real organic ring systems, in particular, answering the question of whether flexoelectricity found in the theory should be present in experiments.