Valley relaxation in graphene due to charged impurities

Abstract

Monolayer graphene is an example of materials with multivalley electronic structure. In such materials, the valley index is being considered as an information carrier. Consequently, relaxation mechanisms leading to loss of valley information are of interest. Here, we calculate the rate of valley relaxation induced by charged impurities in graphene. A special model of graphene is applied, where the p z orbitals are two-dimensional Gaussian functions, with a spatial extension characterized by an effective Bohr radius a eB . We obtain the valley relaxation rate by solving the Boltzmann equation, for the case of noninteracting electrons, as well as for the case when the impurity potential is screened due to electron-electron interaction. For the latter case, we take into account local-field effects and evaluate the dielectric matrix in the random phase approximation. Our main findings are as follows: (i) The valley relaxation rate is proportional to the electronic density of states at the Fermi energy. (ii) Charged impurities located in the close vicinity of the graphene plane, at distance d 0.3Å, are much more efficient in inducing valley relaxation than those farther away, the effect of the latter being suppressed exponentially with increasing graphene-impurity distance d. (iii) Both in the absence and in the presence of electron-electron interaction, the valley relaxation rate shows pronounced dependence on the effective Bohr radius a eB . The trends are different in the two cases: In the absence (presence) of screening, the valley relaxation rate decreases (increases) for increasing effective Bohr radius. This last result highlights that a quantitative calculation of the valley relaxation rate should incorporate electron-electron interactions as well as an accurate knowledge of the electronic wave functions on the atomic length scale.

Electric Field and Light Field Modulated Josephson Effect in Silicene-Based SNS Josephson Junction: Andreev Reflection and Free Energy

“…q is the scattering wave vector and Π(q, ω) is the dynamical polarization within the random-phaseapproximation (RPA) which contains the screening effect by the high energy state with large charge density of state (DOS) D = W |f 1 |/(π v F ) where W is the width of the silicene ribbron. For the case that the screening is ignored, the relaxation time has a simply relation wih the distance to the impurity, τ ∝ e d/ℓ [18], where ℓ = 0.47Åfor silicene. For ballistic Josephson junction, the diffusive effect is not considered, however, due to the existence of the screened (or unscreened) charged impurities in the substrate, the diffusive effect (e.g., to the conductivity or the valley-polarization) need to be taken into accout.…”

“…For the case that the screening is ignored, the relaxation time has a simply relation wih the distance to the impurity, τ ∝ e d/ℓ [18], where ℓ = 0.47 Åfor silicene. For ballistic Josephson junction, the diffusive effect is not considered, however, due to the existence of the screened (or unscreened) charged impurities in the substrate, the diffusive effect (e.g., to the conductivity or the valley-polarization) need to be taken into accout.…”

Microscopic nonlinear quantum theory of absorption of strong electromagnetic radiation in doped graphene

“…Among the important processes induced by external radiation fields the multiphoton stimulated bremsstrahlung (SB) is a basic mechanism of energy exchange between the charged particles and plane monochromatic wave in plasmalike media to provide the energy-momentum conservation law for real absorption-emission processes that has been revealed immediately after the invention of lasers [21]. What concerns the electrons elastic scattering on impurity ions in graphene, there are many papers with consideration of this basic scattering effect which have been described mainly within the framework of perturbation theory by electrostatic potential (see, e.g., [22][23][24][25][26][27][28][29][30]). Regarding the SB process in graphene at moderate intensities of stimulated radiation, in case of its linear absorption by electrons (or holes), at the present time there are extensive investigations carried out in the scope of the linear theory, see, e.g.…”

The properties of strong couple bound polaron in monolayer graphene

“…The problem of screening of an electrically charged impurity and the rate of valley relaxation induced by charged impurities in graphene have been also considered and calculated. When Coulomb interaction is neglected, a special model of graphene is applied, the screening charge has a sign opposite to that of the impurity;the valley relaxation rate by solving the Boltzmann equation can be obtained [4,5]. The effects of spin-orbit © 2016.…”