Flexural and acoustic phonon-drag thermopower and electron energy loss rate in silicene.

We have performed a comprehensive numerical and analytical examination of two crucial transport aspects in silicene: the phonon-drag thermopower,Sp, and the electron's energy loss rate,Fe. Specifically, our investigation is centered on their responses to out-of-plane flexural phonons and in-plane acoustic phonons in silicene, a two-dimensional allotrope of silicon as a function of electron temperature,T,and electron concentration,n,upto the room temperature. It is found that the calculated quantities have a non-monotonic dependence for the phonon modes for both parameters(T and n)considered while analytical results predict definite dependencies up to the complete low-temperature Bloch-Gruneisen (BG) regime. To provide a more comprehensive picture, we contrast the complete numerical outcomes with the approximated analytical BG results, revealing a convergence within a specific range of temperature and carrier concentration. In light of this convergence, we put forth suggestions to elucidate the underlying factors responsible for this behavior. A comparison based on the magnitude of the calculated quantities can be made from the figures between the two considered phonon modes, which clearly shows that the out-of-plane flexural phonons are effective throughout the considered temperature range. This observation leads us to posit that the dominating contribution of the out-of-plane flexural phonon modes hinges upon the deformation potential constant and phonon energy associated with the phonon mode. Our study carries significant implications for estimating the electrical and thermal properties of silicene and provides valuable insights for the development of devices based on silicene-based technologies.

Electron single flexural phonon relaxation, energy loss and thermopower in single and bilayer graphene in the Bloch-Gruneisen regime.

The flexural phonons serve as one of the important modes of interaction in graphene that can inhibit carrier mobility. For the estimation of scattering due to flexural phonons a two-phonon scattering process had been in place, as due to symmetry constraints out-of-plane deformations modulate electron hopping only in the second order. But recently it has been shown that electrostatic gating can break the planar mirror symmetry and activate single flexural phonon scattering processes (Gunst et al 2017 Phys. Rev. Lett. 118 046601). Motivated by this we perform single flexural phonon mechanism based analytical and numerical calculations of the electron phonon relaxation rate, energy loss rate and thermopower in single and bilayer graphene and obtain the power exponents of these quantities in the Bloch Gruneisen regime using the non-equilibrium Boltzmann transport equation. We find that the scattering by flexural phonons substantially changes the temperature dependencies from that observed due to in-plane phonons but the carrier concentration dependencies remain the same as of the in-plane phonons for all the three investigated quantities.