Piezoelectric Substrate Effect on Electron-Acoustic Phonon Scattering in Bilayer Graphene

We have studied the effect of piezoelectric scattering as a function of electron temperature and distance between the sample and the substrate on electron-acoustic phonon scattering rate in Bilayer Graphene sitting on a piezoelectric substrate. We obtain approximate analytical result by neglecting the chiral nature of carriers and then proceed to obtain unapproximated numerical results for the scattering rate incorporating chirality of charge carriers. We find that on the incorporation of full numerical computation the magnitude as well as the power exponent both is affected with the power exponent changed from T-3 to T-3.31 in the low temperature range and to T-6.98 dependence in the temperature range (>5K). We also find that the distance between the sample and substrate begins to strongly affect the scattering rate at temperatures above 10K. These calculation not only suggest the influencing effect of piezoelectric substrate on the transport properties of Dirac Fermions at very low temperatures but also open a channel to study low dimension structures by probing piezoelectric acoustical phonons.