Majorana-Fano干涉器量子输运性质的理论研究

Majorana fermion has become a hot topic in the field of condensed matter physics because of its important underlying physics and potential applications. It should be emphasized that to further understand the nature of Majorana fermion, its quantum transport behaviors should be studied. In this project, we would like to take the Majorana-Fano interferometer as an example to investigate the quantum transport behaviors assisted by the Majorana bound state. First, we aim to choose the Fano interferometer whose resonant channel is formed by the coupling between the Majorana bound state and the leads. After discussing the influence of Fano interference on the respective tunneling mechanisms, we will summarize the properties of the Fano effect in this kind of setup. With the researches above, we would like to study the Majorana bound state how to modify the transport behaviors in the quantum-dot Fano interferometer. If exotic Majorana-assisted results were found in this setup, which we believe firmly, we will propose schemes to examine the existence of Majorana fermion...By investigating the conductance, Fano parameter, electron correlation, noise, and Fano factor, we would like to present a comprehensive description about the special Fano interference induced by Majorana bound state in this project. We believe that our research can provide some helpful information for the further understanding about the characteristics of the Majorana fermion and the Fano effect in mesoscopic systems. Meanwhile, it can provide theoretical supports for the development of relevant experiments.

Majorana费米子因其重要的物理内涵和潜在应用价值已成为凝聚态物理中的研究热点。然而，要深入理解Majorana费米子的物理性质，就必须对其量子输运行为进行研究。本项目拟选择Majorana-Fano干涉器这一典型介观体系，来研究其中由Majorana束缚态驱动及调节的量子输运行为。首先，针对以Majorana束缚态与引线耦合为共振通道的Fano干涉器件，分析Fano干涉对不同隧穿机制的影响，进而总结其中Fano效应的表现规律。接下来，研究Majorana束缚态如何改变量子点Fano干涉器的输运性质，并分析利用此类Fano干涉器来实现对Majorana费米子有效探测的可行性。相信本项目的研究能够为理解Majorana费米子的输运特性提供帮助，为介观体系的Fano效应注入新的内涵，也可以为相关实验工作的开展提供理论支持。

Majorana费米子因其重要的物理内涵一直是物理学各领域的研究重点。随着凝聚态物理中理论和实验的不断突破，研究者能够在拓扑超导体系中成功制备出Majorana费米子束缚态，为深入理解Majorana费米子的性质提供了重要途径。值得强调的是，Majorana零模式在容错拓扑量子计算方面具有巨大的潜在应用价值。因此，近年来Majorana束缚态吸引了科学工作者的高度关注。.然而，要深入理解Majorana束缚态的物理性质，就必须对其量子输运行为进行研究，同时也能为其在量子计算方面的应用提供有力支撑。本项目基于该思路，选择Majorana-Fano干涉器这一典型介观体系，来研究其中由Majorana束缚态驱动及调节的量子输运行为。首先，针对以Majorana束缚态与引线耦合为共振通道的Fano干涉器件，分析了Fano干涉对不同隧穿机制的影响，如：局域和交叉Andreev反射以及电子隧穿，发现各输运过程均能收到Fano干涉调节，在此基础上总结了其中Fano效应的表现方式。接下来，研究了Majorana束缚态如何改变量子点Fano干涉器的输运性质，并讨论了利用此类Fano干涉器来实现对Majorana费米子有效探测的可行性。根据这些研究，得出结论：在Majorana束缚态导致的复杂量子干涉条件下，Fano效应仍有机会出现，但是完全不同于单电子隧穿的情况，主要表现为Fano反共振的弱化。同时，也可以发现，由于Fano 效应的存在，Andreev反射也能以新的方式实现调控。.通过上述几个方面的研究，本项目加深了对Majorana费米子束缚态输运特性的理解，为介观体系的Fano效应注入新的内容，也可以为Majorana束缚态的实验探测和后续应用提供新的思路。