安德烈夫过程对石墨烯-超导体-石墨烯（GSG）结中古斯-汉欣（GH）位移的影响
Effect of Andreev Processes on the Goos-Hänchen (GH) shift in the Graphene-Superconductor-Graphene (GSG) junctions
AI总结：
本文研究石墨烯-超导体-石墨烯结中电子和空穴的古斯-汉欣位移及微分电导，分析安德烈夫反射的影响及其随超导区域宽度的变化。
摘要：
本文研究了石墨烯-超导体-石墨烯（GSG）异质结的输运性质，其中超导区域位于石墨烯片的中部，这与广泛研究的超导体-石墨烯-超导体（SGS）型约瑟夫森结的输运性质形成对比。我们特别详细分析了在这种结中，由于正常反射和安德烈夫反射，电子和空穴在GS界面处的古斯-汉欣位移，采用基于转移矩阵的方法。此外，我们评估了作为偏压函数的归一化微分电导，该电导表征了通过这种结的输运，并指出了它们如何受到安德烈夫反射和正常反射的影响。在文章的后续部分，我们展示了电子和空穴的GH位移如何随超导区域的宽度变化。在这种结中，微分电导作为偏压函数的行为，在由安德烈夫反射和正常反射主导的区域，也被展示和分析。
英文摘要：
In this article, we study the transport properties of Graphene-Superconductor-Graphene (GSG) heterojunction where the superconducting region is created in the middle of a graphene sheet, as contrasted to widely studied transport properties through a Superconductor-Graphene-Superconductor (SGS) type of Josephson junction. We particularly analyse in detail the Goos-Hänchen shift of the electron and the hole at the GS interface in such a junction, due to normal as well as Andreev reflection, using a transfer matrix-based approach. Additionally, we evaluate the normalised differential conductance as a function of bias voltage that characterises the transport through such junction and point out how they are influenced by Andreev and normal reflection. In the subsequent parts of the article we demonstrate how the GH shift for both electron and hole changes with the width of the superconducting region. The behavior of the differential conductance in such junctions as a function of the bias voltage in the region, dominated by Andreev and normal reflection, is also presented and analysed.
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