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arXiv 0911.2402cond-mat.mes-hall
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一维超导结中的平衡和含时约瑟夫森电流

Equilibrium and time-dependent Josephson current in one-dimensional superconducting junctions

Enrico Perfetto, Gianluca Stefanucci, Michele Cini

摘要:

在紧束缚近似下研究了一维超导体-正常金属-超导体(S-N-S)系统的输运性质。我们计算了平衡直流约瑟夫森电流和随时间变化的振荡电流后,开关的恒定偏置。在第一种情况下,一个精确的嵌入程序来计算Nambu-Gorkov Keldysh格林函数,并用于推导连续和束缚态的贡献直流电流。本文还提出了一种获得超导导线上正常链的Andreev束缚态的一般形式。我们确定了一个制度,其中所有的约瑟夫森电流进行的ABS和获得的解析公式的电流相位关系的限制长链。在后一种情况下,完美的Andreev反射的条件表示的微观参数的模型,显示了所谓的宽带限(WBL)近似的限制。当在S-N-S结上施加有限偏压时,我们通过数值求解含时的Bogoliubov-deGennes方程来计算系统的精确时间演化。我们提供了一个微观描述的电子动力学不仅在正常区域内,而且在超导体,从而获得更多的信息,相对于基于WBL的方法。我们的计划使我们能够研究交流政权以及瞬态动力学的特征时间尺度是由多个Andreev反射的速度。

英文摘要:

We investigate the transport properties of a one-dimensional superconductor-normal metal-superconductor (S-N-S) system described within the tight-binding approximation. We compute the equilibrium dc Josephson current and the time-dependent oscillating current generated after the switch-on of a constant bias. In the first case an exact embedding procedure to calculate the Nambu-Gorkov Keldysh Green's function is employed and used to derive the continuum and bound states contributions to the dc current. A general formalism to obtain the Andreev bound states (ABS) of a normal chain connected to superconducting leads is also presented. We identify a regime in which all Josephson current is carried by the ABS and obtain an analytic formula for the current-phase relation in the limit of long chains. In the latter case the condition for perfect Andreev reflections is expressed in terms of the microscopic parameters of the model, showing a limitation of the so called wide-band-limit (WBL) approximation. When a finite bias is applied to the S-N-S junction we compute the exact time-evolution of the system by solving numerically the time-dependent Bogoliubov-deGennes equations. We provide a microscopic description of the electron dynamics not only inside the normal region but also in the superconductors, thus gaining more information with respect to WBL-based approaches. Our scheme allows us to study the ac regime as well as the transient dynamics whose characteristic time-scale is dictated by the velocity of multiple Andreev reflections.

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