Study Of Majorana Zero Mode Lattice And Topological Electronic States In Topological Quantum Materials

In the field of condensed matter physics,the exploration and tunning of novel quantum states in topological systems has always been a very important research direction.Since the experimental discovery of quantum Hall effect（QHE）,the concept of topology has been introduced into condensed matter physics,which has become a new paradigm for the classification of matter phases.The topological quantum state of a system is defined by its topological invariant,which has become another phase classification method in condensed matter physics after Landau’s symmetry breaking phase transition theory.Majorana zero mode（MZM）can be realized in a system simultaneously hosting topology and superconductivity.MZM is a novel quasi-particle state which obeys non-Abelian statistics.Braiding MZM in real space can realize non-local quantum states,which is expected to solve the decoherence problem in quantum computing,and plays a key role in future topological quantum computation.Therefore,MZM has been widely studied and has become an important frontier in condensed matter physics research in recent years.In recent years,the research of topological physics has expanded from the original topological insulator to topological metal/semi-metal and topological superconducting systems.With the establishment of topological material database,the solid-state theory has been further improved.However,although great progress has been made in the study of topological phase classification,it is still a great challenge to modulate the topological state of a system by controllable means.In view of the above research background,this thesis takes ultra-low temperature and high magnetic field scanning tunneling microscopy/spectroscopy（STM/S）measurements and carries the research work as follows:1.The topological band structure tuned by external magnetic field in magnetic Weyl semimetal Eu B₆ has been systematically studied.It is found that the existence of unconventional anomalous Hall effect（UAHE）and the variation of electron density of states are related to the change of Berry curvature in this system.This study marks the realization of artificial control of topological energy states,and has implications for the practical applications of spintronics,magnetic sensors and future quantum devices.In addition,the spectral features related to phonon modes have been found in the STM/S study in Eu B₆ system,which resulted from the opening of additional inelastic tunneling channels.By means of inelastic electronic tunneling spectroscopy,phonon modes with energies of about 11 me V,32 me V,54 me V and 90 me V are determined,which are derived from the vibration of Eu atoms and the vibration and deformation of octahedral B cages,respectively.Due to its unique magnetic and topological properties,Eu B₆system may be applied to the study of the interaction between phonons and spins,providing a good platform for the exploration and tuning of more abundant topological electronic states in the future.2.Systematically investigated a new type of charge density wave（CDW）induced by natural strain in Li Fe As.The existence of natural stress in Li Fe As causes strain in the system,resulting in lattice distortion and further inducing the peculiar biaxial CDW.The two types of CDW present in the system are oriented along the Fe-Fe lattice direction and As-As lattice direction,with an angle of about 45°and periods of～2.7nm and～24.3 nm,respectively.The two types of CDW have different effects on the superconducting properties of Li Fe As system.CDW_Fe-Fe has no obvious modulation effect on the superconducting gap size,while CDW_As-As has obvious periodic modulation effect on the superconducting gap size.The results show that CDW_As-Asmodulates the superconducting strength of the system and provides a basis for the generation of ordered vortex lattice.3.The artificial control of large scale and highly ordered MZM lattice is successfully realized in Li Fe As system with biaxial CDW,which provides an ideal platform for the realization of MZM braiding and the construction of topological qubits.Li Fe As system has simple crystal structure,homogeneous composition,tunable chemical potential and abundant topological superconducting surface electronic structures,which is an ideal platform for the study of MZM.Different from the conventional unstrained Li Fe As system,the strained Li Fe As system goes through a phase transition from the mixed state of topological/trivial bands to the strong topological insulating state due to the change of symmetry and renormalization of band structure,and accommodates robust and high-proportion topological vortices.Combined with the modulation of superconducting by CDW_As-As and the strong topological insulating band structure,the biaxial CDW system realizes a large scale,highly ordered and tunable MZM lattice.This work has changed the research status of iron-based superconducting MZM system,such as material inhomogeneity,low proportion of topological vortices and disordered and uncontrollable vortex lattice,providing an ideal platform for the research of MZM,and is of great significance for the realization of MZM braiding and the construction of topological qubits.The work in this thesis systematically studied the MZM lattice and the tuning of topological electronic states of Weyl semimetal in topological quantum material systems,which is of great significance for the future development of topological quantum computation and topological electronics.