安德列夫反射效应可以被用来探测拓扑超导体的配对形式和超导体的拓扑性质以及马约拉纳零能模的存在，对理解和认识拓扑超导体有重要应用价值。本文主要介绍了我在攻读博士学位期间已经发表的两方面研究工作：（1）马约拉纳零能模诱导的含有自旋选择性的安德列夫反射过程的输运性质，以及（2）Bi/Ni双层膜中自旋三重态的安德列夫反射谱。此外，我们也探讨了马约拉纳零能模的磁学性质以及拓扑p波超导体的拓扑性质。本文的主要内容有：

我们研究了包含马约拉纳零能模以及低能激发态的涡旋态与铁磁针尖之间发生含有自旋选择性的安德列夫反射效应时的电导及散粒噪声等输运性质。首先，我们计算了马约拉纳零能模在涡旋中的磁矩分布。随后我们计算了涡旋态与铁磁针尖发生含有自旋选择性的安德列夫反射时的电导以及散粒噪声。我们发现在针尖偏离涡旋中心时，激发态会在其本征能量处诱导出电导峰，马约拉纳零能模则贡献出零能电导峰。接着我们研究了这一效应的散粒噪声和Fano 因子。我们发现散粒噪声和Fano因子在零温时为0，而普通的金属-s波超导体弱透射率隧道结中安德列夫反射过程的Fano 因子为2。

我们研究了Bi/Ni双层膜中可能存在的超导态如ABM态p波超导态以及其与s波混合后的超导态的安德列夫电导谱以及局域态密度。首先，我们计算了ABM态p波超导体在二维隧道结中的安德列夫电导谱，发现ABM态可以解释Bi/Ni双层膜的点接触实验结果。接着我们进一步研究了ABM态的表面态密度。我们发现零能处的电导峰主要来源于两个外尔点间的表面态在入射面上的投影。然而，纯ABM态只能解释点接触实验的结果，却不能解释太赫兹光谱实验中发现的无节点超导态。所以我们进一步研究了ABM态和s波超导态混合型超导态的电导谱以及能谱。我们发现当s波分量较小时，混合型超导体的电导可以解释点接触实验的结果，却无法解释太赫兹光谱实验的结果。但是在s波分量较大时，混合型超导态的能谱可以解释太赫兹光谱的实验结果，其电导却无法解释点接触实验的结果。

The Andreev reflection can be used to detect the pairing form of the topological superconductors and its topological properties as well as the existence of Majorana zero mode. It has important application value in understanding topological superconductors. This paper mainly introduces the research work in two aspects that have been published during my doctoral study: (1) the transport properties of the spin selective Andreev reflection induced by the Majorana zero mode and (2)Andreev spectroscopy of the triplet superconductivity state in Bi/Ni bilayer systeml. In addition,we also discuss the magnetic properties of Majorana zero mode and the topological properties of topological p-wave superconductors. The main contents of this paper are:
We have studied the transport properties such as conductance and shot noise when the spinselective Andreev reflection effect occurs between the ferromagnetic tip and the vortex state including the Majorana zero mode and the low-energy excited states. First of all, we calculate the magnetic moment distribution of the Majorana zero mode mode in the vortex. Subsequently, we calculate the conductance and shot noise of the spin selective Andreev reflection between the vortex state and the ferromagnetic tip. We find that when the STM tip deviates from the center of the vortex, the excited state induces a conductance peak at its intrinsic energy, and the Majorana zero mode contributes a zero energy conductance peak. In addition, we study the shot noise power and Fano factor of this effect. We find that the shot noise power and Fano factor are zero at zero  temperature, while the Fano factor of the normal Andreev reflection process in weakly transparent Normal metal/s-wave superconductor junctions is two.
We study the Andreev conductance spectroscopy and local density of states of superconducting state that may exist in the Bi/Ni bilayer i.e. the ABM state and the ABM state mixture with S-wave pairing. Firstly, we calculate the Andreev conductance spectroscopy of ABM state p-wave superconductors in two-dimensional tunnel junction and find that ABM states can explain the point contact experimental results of Bi/Ni bilayers. Then we further study the surface density of states of the ABM state. We find that the conductance peak at zero energy mainly comes from the projection of the surface state between two Weyl points on the incident plane. However, the pure ABM state can only explain the results of the point contact experiment, but can not explain the nodeless superconducting state found in the terahertz spectrum experiment. Therefore, we further study the conductance and energy spectra of mixed superconductors consist of ABM state and s-wave superconducting state. We find that the conductance of the mixed superconductor with small s-wave component can explain the results of the point contact experiment, but can not explain the results of the terahertz spectrum experiment. However, when the s-wave component is large, the energy spectrum of the mixed superconducting state can explain the terahertz spectrum, but the conductance can not explain the results of the point contact experiment.