Alloying Control Study Of Topological Electronic Properties Of Multi-fermion CoSi System

Recently,the discovery of many topological quantum states has opened a new era in the development of condensed matter physics.Predicted in high energy physics,such as Majorana fermions,Dirac fermions and Weyl fermions have all found their counterparts in condensed matter systems.In condensed matter systems,fermions are not bound by Lorentz transformation.Due to the lower symmetry constraints of crystalline materials（230 space group symmetries）,more free fermion excitations have been found and classified in solid-state systems.Among them,the most famous example is the multiple fermions that go beyond conventional fermions.The solid-state realization of Dirac/Weyl fermions,as well as other topological fermions,not only provides new insights into particles in high-energy physics,but also provides a new platform for studying their unique topological features.Studying how the symmetry of materials strengthens or preserves multiple band degeneracy is an important approach to understanding and searching for new topological semimetals.We predict new quasiparticle excitations by finding the irreducible representation of the small group to which the high-symmetry points belong in the Brillouin zone（its dimension corresponds to the degeneracy of the band crossings of the high-symmetry points）.In particular,some brand-new quasiparticle excitations,such as spin-1 and charge-2 chiral fermions,have been recently predicted in the Co Si system.The most characteristic feature of these exotic topological semimetals is the non-zero topological charge number（Chern number）,and these topological fermions can be described by the effective spin Hamiltonian.Based on the multiple fermion Co Si system,we intend to effectively control its topological electronic states by alloying methods,in order to obtain new topological states.This paper firstly introduces the research progress of topological states,including the discovery of quantum Hall effect,the research status of topological insulators/semimetals and multiple fermion semimetals.Then the application of density functional theory（DFT）and Wannier-based tight-binding method and group theory（symmetry method）in topological physics is introduced.Finally,the main research contents of this paper are discussed.We first constructed Co Si_1-xA_x（A=Ge,Sn）and Co_1-xRh_xSi alloys by alloying engineering,and performed theoretical calculations by first-principles calculations combined with the Wannier-based tight-binding method.Then,in conjunction with point group representation theory,symmetry analysis is performed to study and explain related topological phenomena.When considering spin-orbit coupling,by analyzing the electronic band structure of the alloy and calculating the topological charge number（Chern number）,we determined that the transition from the multiple fermion semimetal phase（Co Si）to the Weyl semimetal phase is effectively achieved by alloying of Co Si_1-xA_x（A=Ge,Sn）.Furthermore,we also investigate the topologically protected surface states and Fermi arcs in them.The symmetry breaking caused by alloying changes the positions and energies of nodes（Weyl points）in the system,resulting in a more robust Fermi arc.Through alloying engineering,we finally achieved the goal of tuning the topological properties of multiple fermion semimetals.Finally,the summary and prospect of this research work are carried out.We expect to obtain more"ideal"topological materials through different control methods,which will provide a solid theoretical basis for guiding the design of topological functional devices and promoting the experimental exploration of multiple fermions.