Origin of the anomalous piezoelectric response in wurtzite Sc$_{x}$Al$_{1-x}$N alloys*

We present the theory that reveals the origin of the observed anomalous enhancement of piezoelectric response in wurtzite Sc$_{x}$Al$_{1-x}$N alloys [1]. Our first-principles calculations confirm that the 400{\%} increase of the piezoelectric constant is an intrinsic alloying effect. The energy surface topology is found to be strongly influenced by the alloying, being elongated around the global minimum along c=a direction. This leads to the large elastic softening along the crystal parameter c, and raises significantly the intrinsic sensitivity to axial strain resulting in the highly increased piezoelectric constant. The effect is particularly accentuated at intermediate compositions where the elongated double-minimum energy landscape is flattened due to the energy proximity of the wurtzite and so far experimentally unknown hexagonal phases of these alloys. Our observation provides a route for the design of materials with high piezoelectric response. \\[4pt] [1] F. Tasnadi, \textit{et al., }Phys. Rev. Lett. \textbf{104}, 137601 (2010).