Electronic flexoelectricity in low-dimensional systems

Symmetry breaking at surfaces and interfaces and the capability to support large strain gradients in nanoscale systems enable unusual forms of electromechanical coupling. Here, we introduce the concept of electronic flexoelectricity, a phenomenon that is manifested when the mechanical deformation of nonpolar quantum systems results in the emergence of net dipole moments and hence linear electromechanical coupling proportional to local curvature. The concept is illustrated in carbon systems, including polyacetylene and nanographitic ribbons. Using density functional theory calculations for systems made of up to 400 atoms, we determine the flexoelectric coefficients to be of the order of $\sim 0.1e$, in agreement with the prediction of linear theory. The implications of electronic flexoelectricity on electromechanical device applications and physics of carbon-based materials are discussed.

Figure 1

(Color online) (a) Schematics of polyacetylene chain for six different radii of curvature. (b) Variation of net dipole moment of the molecule as a function of radius of curvature. (c) Dependence of free energy (solid) for different electric fields as a function of radius of curvature. The amplitude of the applied electric field is given in the figure.

Figure 2

(Color online) [(a) and (c)] Schematics of flexed graphitic membranes with armchair and zigzag edges along the circumference. [(b) and (d)] Corresponding evolution of dipole moment dependence as a function of the radius of curvature $R$. Fit of the curves $f\sim 1∕R$ is shown by the solid line.

Figure 3

(Color online) Top panel represents the density distribution on an horizontal plane passing through top atoms of an armchair terminated rolled graphitic membrane at a radius of curvature of $6.5\mathrm{nm}$. Bottom: isosurface plot of the electronic charge density for the same system.