Phonon drag thermopower and energy loss rate in single and bilayer graphene due to piezoelectric surface acoustic phonons in Bloch-Gruneisen regime

Abstract

In this report, we have both numerically and analytically calculated the phonon drag thermopower, Spz and, energy loss rate, Fpz due to piezoelectric surface acoustic phonons present in the underlying piezoelectric substrate at a distance, d apart from single and bilayer graphene as a function of carrier's temperature, concentration and phonon mean free path. The numerical results are then reduced to analytical results in the Bloch-Gruneisen regime and the corresponding power dependency of the quantities described above are obtained. We have also included the effect of Thomas-Fermi and Random Phase Approximation screening into account in these calculations. The obtained unscreened results are further reduced in much simpler form for a particular case having no distance between the graphene samples and the underlying substrate or at larger values of distances. The temperature dependency in Spz and Fpz for both SLG and BLG systems is found to be one order less than the in-plane acoustic phonons dependency, which is directly related to the matrix element of electron-in plane acoustic phonon interaction having a linear dependence on the phonon wave vector, q. Furthermore, a comparison of these calculations is made between the in-plane and piezoelectric surface acoustic phonon modes. One finds a crossover between these phonons modes depicting these are important in providing effective scattering channels for energy relaxation in typical experimental situations at different temperatures.