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)].

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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.

The structure factor, pair distribution function, screened impurity potential, density of screening charge, and exchange and screened exchange energies have been theoretically investigated for a semiconductor quantum wire using an improved random phase approximation that takes into account the local field corrections within the Hubbard approximation. Our approach enabled us to obtain approximate analytical results on some of the aspects and to greatly simplify the computation task on others. However, computed results from our simple approach show very good agreement with those obtained by performing cumbersome numerical solutions for the structure factor, density–density response function and the static local field corrections, within the Singwi–Tosi–Land–Sjölander approximation. Our investigations suggest that: (i) the magnitude of the screened impurity potential and the average distribution of electrons about an electron at larger distances are enhanced on reducing the width of quantum wire, and (ii) the exchange interactions strengthen on narrowing the quantum wire and on increasing the carrier density. Friedel oscillations are seen in both our computed screened potential and the density of screening charge.

The electron–electron scattering rate (1/τee) in the presence of a random disorder potential has been computed, within the random phase approximation, as a function of excitation energy (ε) for a quantum well (QWL), a quantum wire (QWR) and a periodic quantum wire structure (QWS). It is found that: (i) 1/τee goes to zero when and (ii) the ε dependence as well as the magnitude of 1/τee are determined by the value of the inverse electron–impurity collision time (1/τ), the carrier density and the width of a QWR. The computed 1/τee exhibits its maximum value for and it decreases thereafter on increasing 1/τ, for all values of ε and other parameters. The computed 1/τee of a QWR declines monotonically with the width of the QWR and it reduces to 1/τee of a QWL at larger wire widths, for a given value of ε and the other intrinsic parameters. The 1/τee of a QWS differs from that of a QWR because of the added contribution from inter-wire electron–electron interactions in a QWS. For the given values of ε, 1/τ, carrier density and the width of a QWR, the 1/τee of a QWS is found to be smaller than that of a QWR and larger than that of a QWL. This suggests that the electron–electron scattering rate is enhanced on the reduction in the effective dimensionality of a system. Our theoretical study of 1/τee and its dependence on various intrinsic parameters of QWL, QWR and QWS suggests, in conclusion, that a quasi-particle Fermi liquid description can be applied to electron–electron scattering in the presence of an electron-disorder potential scattering, at zero temperature, in low-dimensional systems.