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arXiv 0706.1391cond-mat.mes-hallcond-mat.mtrl-sci
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石墨烯的弹性散射理论与输运

Elastic scattering theory and transport in graphene

D. S. Novikov

摘要:

石墨烯的电子性质描述的狄拉克费米子。本文详细地介绍了轴对称势场中二维有质量狄拉克费米子的弹性散射理论。虽然无质量极限与原始石墨烯相关,但保持有限质量允许将两个亚晶格之间的对称性破缺的情况推广,并提供了与抛物线带中电子的散射理论的联系。我们证明,狄拉克理论需要短距离正则化的潜力,这是更奇异的1/r。然后将该方法应用于光滑短程势的散射。接下来,我们考虑库仑势散射,狄拉克理论是一致的点散射只有有效杂质强度低于1/2。从散射相移,我们得到了精确的库仑输运截面的杂质强度。结果是相关的运输在石墨烯中的杂质的存在下,不诱导散射之间的狄拉克点的布里渊区。

英文摘要:

Electron properties of graphene are described in terms of Dirac fermions. Here we thoroughly outline the elastic scattering theory for the two-dimensional massive Dirac fermions in the presence of an axially symmetric potential. While the massless limit is relevant for pristine graphene, keeping finite mass allows for generalizations onto situations with broken symmetry between the two sublattices, and provides a link to the scattering theory of electrons in a parabolic band. We demonstrate that the Dirac theory requires short-distance regularization for potentials which are more singular than 1/r. The formalism is then applied to scattering off a smooth short-ranged potential. Next we consider the Coulomb potential scattering, where the Dirac theory is consistent for a point scatterer only for the effective impurity strength below 1/2. From the scattering phase shifts we obtain the exact Coulomb transport cross-section in terms of the impurity strength. The results are relevant for transport in graphene in the presence of impurities that do not induce scattering between the Dirac points in the Brillouin zone.

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