Department of Science of Bijar, University of Kurdistan, Bijar, Iran.
J Phys Condens Matter. 2010 Jun 23;22(24):245503. doi: 10.1088/0953-8984/22/24/245503. Epub 2010 Jun 1.
In this paper, we first evaluate the electronic transmission of Dirac fermions into a p-n junction of gapped graphene and show that the final result depends on the sign of the refractive index, n. We also, by considering the appropriate wavefunctions in the region of the electrostatic potential, show that both transmission and the reflection probability turn out to be positive and less than unity instead of the negative transmission and higher than unity reflection coefficient commonly referred to as the Klein paradox. We then obtain the transmission probability corresponding to a special p-n junction for which there exists a region in which the low energy excitations of graphene acquire a finite mass and, interestingly, find that in this case the transmission is independent of the index of refraction, in contrast with the corresponding result for gapped graphene. We then discuss the validity of the solutions reported in some of the papers cited in this work which, considering the Büttiker formula, turn out to lead to the wrong results for conductivity.
在本文中，我们首先评估了狄拉克费米子在带隙石墨烯的 p-n 结中的电子输运，并表明最终结果取决于折射率 n 的符号。我们还通过在静电势区域中考虑适当的波函数，表明透射率和反射概率都为正且小于 1，而不是通常称为 Klein 悖论的负透射率和大于 1 的反射系数。然后，我们得到了对应于特殊 p-n 结的透射率，其中存在一个区域，其中石墨烯的低能激发获得有限的质量，有趣的是，我们发现在这种情况下，透射率与折射率无关，与带隙石墨烯的对应结果形成对比。然后，我们讨论了在这项工作中引用的一些论文中报告的解的有效性，这些解考虑了 Büttiker 公式，导致电导率的错误结果。
