Research Progress Of The Fe-based Superconductor Majorana-zero-mode Materials

Due to the potential application of fault-tolerant topological quantum computing,the research of Majorana zero-energy mode（MZM）attracts intensive interest in the field of condensed matter physics.In recent years,clear MZM signals have been observed in the center of superconducting vortices in Fe-based superconductors with topological surface states,which opens a new chapter for MZM carriers.Earlier proposals of MZM carrier,such as p-wave superconductors and the superconductivity-proximity hetero-junction system,were plagued by technical difficulties such as experimental observation and sample growth.The Fe-based MZM-carrier materials（abbreviation:Fe-Majorana Materials）are considered to be one of the key carrier systems for further exploration about Majorana physics and realization of topological quantum computing,with un-precedented advantages including the mature sample-growth method and the clear ex-perimental phenomenon with unambiguous physics.In the past,the research of Fe-Majorana Materials is mainly based on the Fe（Te,Se）single crystal and other Fe-selenium superconductors.However,because most of these systems require doping to generate nontrivial topological band structures,such materials are inevitably bothered by the spontaneous inhomogeneity,which makes the existence of MZMs in the superconducting vortices uncertain and becomes the roadblocks to the further research of MZM and braiding for this new platform.At the same time,Fe-Arsenic superconductors,another major material family of Fe-based superconductors,have been absent from the research feast of MZM for a long time,which may lead to the doubt of the universal verification about the vortex-MZM physics mainly derived from the Fe（Te,Se）-single-crystal experiments.As a try of solving the problems mentioned above,this thesis will introduce a series of research progress of MZM based on Fe-arsenic superconductor materials,which will keep on the research of Fe-Majorana Materials and gradually promote the MZM research to the quantum-engineering field.As the beginning,we will briefly review the background of Fe-Majorana Materi-als;Combined with experimental observation and theoretical calculation,we next will illustrate the universal existence of topological band structures in the Fe-based super-conductor family;By summarizing the previous experimental results of vortex MZM in Fe（Te,Se）single crystal,we introduce the physical cognition of vortex MZM,which will help to understand the subsequent experimental progress.As the reflection of”the common problems of Fe-Selenium MZM-carrier materials”,this thesis will draw out our MZM-related studies in Fe-Arsenic superconductors:Firstly,the experimental re-sult of Ca KFe₄As₄single crystal,a new material of Fe-based MZM carrier,is introduced to declare the great potential of Fe-arsenic materials in the construction of homogeneous Fe-Majorana Materials;Secondly,we will elaborate the recent works of Li Fe As single crystal about manipulation of MZM vortex states;Finally,we will summarize and fore-cast the research work of Fe-Majorana Material system.Following the physical thinking of Fe-Majorana Materials,this paper aims to perform the important experimental break-throughs after the series work of Fe（Te,Se）single crystal,and tries to play a connecting role of MZM research in the Fe-Majorana Material system.