Novel Piezoelectricity in Two-Dimensional Metallic/Semimetallic Materials with Out-of-Plane Polarization.

Normally, the good conductivity of metals and semimetals is incompatible with the piezoelectricity since the internal electric current will dismiss any polarization. However, here, we reveal that the out-of-plane piezoelectric effect can exist in two-dimensional (2D) metallic/semimetallic materials due to their giant anisotropy. A method is developed to calculate the out-of-plane polarization in 2D systems, where the modern theory of polarization based on a Berry-phase approach is not applicable. Detailed calculation and analysis on a Dirac material, the FeB monolayer, show that it has an out-of-plane polarization of 8.3 pC/m and the piezoelectric coefficient of = -59.3 pC/m and = -0.25 pm/V. This work provides a formalism to discover more piezoelectric materials within the vast 2D metallic/semimetallic materials.