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arXiv 0809.3536cond-mat.mes-hallcond-mat.str-el
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无序和相互作用下石墨烯中的量子振荡

Quantum oscillations in graphene in the presence of disorder and interactions

Pallab Goswami, Xun Jia, Sudip Chakravarty

摘要:

讨论了石墨烯中的量子振荡。相互作用的影响由关于de Haas-van Alphen振荡的Kohn定理解决,该定理指出,只要忽略无序并且系统被充分屏蔽,电子-电子相互作用就不会影响振荡频率,这对于化学势不太接近狄拉克点应该是有效的。通过精确的转移矩阵和有限尺寸对角化计算,我们确定了存在势无序时朗道能级的位置。即使对于中度无序,位置也未移位;然而,更强的无序可以导致移位,但即使对于石墨烯晶格上的裸跳跃矩阵元素的一半那么大的无序宽度,这也似乎是最小的。电导率的Shubnikov-de Haas振荡在杂质散射的自洽玻恩近似下解析计算。电导率的振荡部分遵循广泛调用Lifshitz-Kosevich形式时,某些质量和频率参数得到适当的解释。

英文摘要:

Quantum oscillations in graphene is discussed. The effect of interactions are addressed by Kohn's theorem regarding de Haas-van Alphen oscillations, which states that electron-electron interactions cannot affect the oscillation frequencies as long as disorder is neglected and the system is sufficiently screened, which should be valid for chemical potentials not very close to the Dirac point. We determine the positions of Landau levels in the presence of potential disorder from exact transfer matrix and finite size diagonalization calculations. The positions are shown to be unshifted even for moderate disorder; stronger disorder, can, however, lead to shifts, but this also appears minimal even for disorder width as large as one-half of the bare hopping matrix element on the graphene lattice. Shubnikov-de Haas oscillations of the conductivity are calculated analytically within a self-consistent Born approximation of impurity scattering. The oscillatory part of the conductivity follows the widely invoked Lifshitz-Kosevich form when certain mass and frequency parameters are properly interpreted.

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