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arXiv 0802.4062cond-mat.mes-hallcond-mat.supr-con
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石墨烯约瑟夫森结中的临界电流

Critical currents in graphene Josephson junctions

J. Gonzalez, E. Perfetto

摘要:

我们研究了石墨烯中的超导相关性,当它被放置在两个超导体之间时,特别关注由2D系统支持的超导电流。为了这个目的,我们使用的形式主义,把重点放在多体方面的问题,与调查的相关变量,如超导接触之间的距离L,温度和掺杂水平的临界电流的依赖关系的目的。因此,我们表明,尽管在未掺杂的石墨烯中费米能级处的态密度消失,但在零温度下可能存在超电流,并且在大的L下具有1/L^3的自然依赖性。当考虑到温度效应时,超导电流在热长度L_T(~ v_F / k_B T,以石墨烯的费米速度v_F表示)之外被进一步抑制,进入衰减为1/L^5的状态。另一方面,由于费米能级从电荷中性点移动了化学势μ,因此掺杂可以增强超电流。这就引入了一个新的交叉长度L* ~ v_F / μ,在这个长度处,有限电荷密度的效应开始显现,标志着超电流从短距离的1/L^3行为转变为大L时较软的1/L^2衰减。事实证明,临界电流的衰减一般由幂律行为给出,这可以被视为狄拉克理论应用于石墨烯低能描述的完美标度的结果。

英文摘要:

We study the superconducting correlations induced in graphene when it is placed between two superconductors, focusing in particular on the supercurrents supported by the 2D system. For this purpose we make use of a formalism placing the emphasis on the many-body aspects of the problem, with the aim of investigating the dependence of the critical currents on relevant variables like the distance L between the superconducting contacts, the temperature, and the doping level. Thus we show that, despite the vanishing density of states at the Fermi level in undoped graphene, supercurrents may exist at zero temperature with a natural 1/L^3 dependence at large L. When temperature effects are taken into account, the supercurrents are further suppressed beyond the thermal length L_T (~ v_F / k_B T, in terms of the Fermi velocity v_F of graphene), entering a regime where the decay is given by a 1/L^5 dependence. On the other hand, the supercurrents can be enhanced upon doping, as the Fermi level is shifted by a chemical potential μfrom the charge neutrality point. This introduces a new crossover length L* ~ v_F / μ, at which the effects of the finite charge density start being felt, marking the transition from the short-distance 1/L^3 behavior to a softer 1/L^2 decay of the supercurrents at large L. It turns out that the decay of the critical currents is given in general by a power-law behavior, which can be seen as a consequence of the perfect scaling of the Dirac theory applied to the low-energy description of graphene.

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