Transversal flexoelectric coefficient for nanostructures at finite deformations from first principles

We present a formulation for calculating the transversal flexoelectric coefficient of nanostructures at finite deformations from first principles. Specifically, we introduce the concept of radial polarization to make the coefficient a well-defined quantity for uniform bending deformations. We use the framework to calculate the flexoelectric coefficient for group IV atomic monolayers using density functional theory. We find that graphene's coefficient is significantly larger than previously reported, with a charge transfer mechanism that differs from other members of its group.