We investigate the energy dependent electron-phonon relaxation rate, energy loss rate, and phonon drag thermopower in single layer graphene (SLG) and bilayer graphene (BLG) under the Bloch-Gruneisen (BG) regime through coupling to acoustic phonons interacting via the Deformation potential in the Boltzmann transport equation approach. We find that the consideration of the chiral nature of electrons alters the temperature dependencies in two-dimensional structures of SLG and BLG from that shown by other conventional 2DEG system. Our investigations indicate that the BG analytical results are valid for temperatures far below the BG limit (∼TBG/4) which is in conformity with a recent experimental investigation for SLG [C. B. McKitterick et al., Phys. Rev. B 93, 075410 (2016)]. For temperatures above this renewed limit (∼TBG/4), there is observed a suppression in energy loss rate and thermo power in SLG, but enhancement is observed in relaxation rate and thermopower in BLG, while a suppression in the energy loss rate is observed in BLG. This strong nonmonotonic temperature dependence in SLG has also been experimentally observed within the BG limit [Q. Ma et al., Phys. Rev. Lett. 112, 247401 (2014)].

No abstract

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.

No abstract

The acoustic, optic, and surface polar optic phonons are the three important intrinsic and extrinsic phononic modes that increasingly populate graphene on a substrate with rising temperatures; the coupling of the three phononic modes with photoexcited hot carriers in the equipartition regime provides significant pathways for electron-phonon relaxation. In this paper, we theoretically investigate the relative significance of the three phononic modes in electron scattering and cooling phenomena in single layer graphene, including their comparison with supercollision driven power loss, and obtain analytical formulas on the energy dependence of electron–phonon scattering rates and cooling power in the Boltzmann transport formalism. The obtained analytical solutions not only closely reproduce the results for scattering rates and cooling power, as that obtained from the earlier reported numerically tractable integral forms, but also enable us to derive closed-form formulas of the cooling time and thermal conductance. The important role of Pauli blocking that prevents transition to filled energy states has also been elucidated in the estimation of the scattering rate and cooling power density for all three modes. The obtained formulas provide better insight into the dynamics of hot electron phenomena giving an explicit view of the interplay of the different variables that affect the transport quantities under investigation. The formulas can also be potentially useful for performance optimization of transport quantities in numerical optimization methods since the first and second-order derivatives are easily deducible from these formulas.