| As a kind of emerging two-dimensional carbon material,Graphene has been drawing much attention since the first successful fabrication of experimental sample of graphene monolayer in the end of 2004.In terms of the layer number and stacking manner between the adjacent layers,Graphene materials have formed a large family,including the graphene monolayer,bilayer and few-layer(< 10 layers)and multiplelayer(>10 layer but with quasi-2D property).Recently,the twisted graphene bilayer and few-layer come into being,intriguing the graphene research community.These graphene materials distinguish from one another in their electronic properties,depending on their layer number and stacking manner.It is necessary to study in-depth the electronic transport properties of these graphene materials,in order to facilitate the applications of graphene,in particular,in the field of a new era of electronics.The resistivity of graphene at room temperature is an important electronic transport property which is dominated by the electron-phonon(e-ph)scattering process.Owing to the ubiquitous occurrence of e-ph scattering even in a perfect graphene crystalline sample,the resistivity of graphene arsing from the e-ph scattering is called the intrinsic resistivity.This work aims to perform a first-principles calculations on the intrinsic resistivity of two kind of graphene triple layers with ABA and ABC stackings respectively.Our calculation indicates that the two kinds of graphene triple layers has obviously different resistivities owing to the different structure symmetry.It is always a challenging task to calculate the intrinsic resistivity of any actual material on the level of first-principles calculations,namely,without any semiempirical approximations,considering both difficulties in the physical approaches and unaffordable computational burden.Our theoretical approach consists of three steps to obtain the first-principles calculation results of the intrinsic resistivity of graphene triple layers.At first,we perform the DFT and DFPT calculations to obtain the electronic band structure and wavefunction,the phonon spectrum and eigen-vectors,and more importantly,the e-ph interaction matrix elements.Such a calculation is realized by means of the quantum espresso(QE)code package.However,such a calculation has to be performed in two relatively coarse k-and q-meshes(the BZ samplings of the electronic and phononic wavevectors)owing to the huge computational cost.Secondly,we employ the Wannier interpolation technique to obtain the physical quantities essential for the calculation of the intrinsic resistivity on much fine k-and q-meshes,based on the corresponding values on the coarse meshes.Finally,we setup a program to calculate numerically the intrinsic resistivity of graphene triple layers within the theoretical framework of semiclassical Boltzmann transport theory.We obtain the numerical results about the electronic band structures and the phononic spectrum of the two kinds of graphene triple layers.Some results are consistent with those in previous literature.Therefore,some new results about the electronic and phononic dispersions of the graphene triple layers which have never been reported previously are believable.As for the intrinsic resistivity,we find that at room temperature,ABAstacking graphene triple layer has smaller value than that of ABC-stacking structure.This is due to that the ABA stacking triple layer has mirror symmetry in the vertical direction.Therefore,the Z(out-plane)phonon mode is forbidden to couple to the electronic states in both of the valence and conduction bands.In contrast,such a mirror symmetry is absent in the ABC-stacking graphene triple layer,in which the coupling between the out-plane vibration mode and the carrier is allowed.Consequently,the the ABC-stacking graphene triple layer has a relatively large intrinsic resistivity,in comparison with the ABA stacking triple layer structure.More detailed study on the intrinsic resistivity of two kinds of graphene triple layer is in progress. |
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