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arXiv 1606.01249cond-mat.mes-hallcond-mat.supr-con
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Dirac材料中超导邻近效应的准经典理论

Quasiclassical theory for the superconducting proximity effect in Dirac materials

Henning G. Hugdal, Jacob Linder, Sol H. Jacobsen

摘要:

我们推导出一阶准经典非平衡Eilenberger和Usadel方程,其量小于费米能,适用于具有自旋动量锁定的Dirac边缘和表面电子,与拓扑绝缘体相关。我们详细讨论了几个关键的技术点和假设的推导,并提供了一个Riccati参数化的方程。首先求解S/N和S/F双层膜以及约瑟夫森结的平衡方程,研究了狄拉克材料中的超导邻近效应。与相关工作类似,我们发现交换场的作用强烈依赖于场的方向。只有垂直于输运方向的分量导致F中库珀对波函数的衰减。平行于输运方向的场导致S/F/S结中充电电流和态密度对超导相位差的依赖性发生相移。此外,我们还计算了S/N和S/F双层膜在外加偏压下的微分电导,并确定了N区和F区的长度以及交换场对微分电导的依赖关系。

英文摘要:

We derive the quasiclassical non-equilibrium Eilenberger and Usadel equations to first order in quantities small compared to the Fermi energy, valid for Dirac edge and surface electrons with spin-momentum locking, as relevant for topological insulators. We discuss in detail several of the key technical points and assumptions of the derivation, and provide a Riccati-parametrization of the equations. Solving first the equilibrium equations for S/N and S/F bilayers and Josephson junctions, we study the superconducting proximity effect in Dirac materials. Similarly to related works, we find that the effect of an exchange field depends strongly on the direction of the field. Only components normal to the transport direction lead to attenuation of the Cooper pair wavefunction inside the F. Fields parallel to the transport direction lead to phase-shifts in the dependence on the superconducting phase difference for both the charge current and density of states in an S/F/S-junction. Moreover, we compute the differential conductance in S/N and S/F bilayers with an applied voltage bias, and determine the dependence on the length of the N and F regions and the exchange field.

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