Computational Study Of A New Topological Semimetallic Germanium Allotrope

As a new quantum state,topological semimetals have many strange physical properties,including ultra-high speed,low energy consumption quantum transport,Fermi arc surface states,high carrier mobility,negative reluctance,etc.At present,it has become a hot topic in condensed matter physics to explore this novel topological quantum state and find the corresponding real stable materials.With the development of new algorithms,thousands of topological semimetallic materials have been found in existing 3D crystal databases.However,most of them are composed of toxic heavy elements,which are very bad for practical applications.In view of this,in this paper,environment-friendly Ge element is the research object,using first-principles method to explore the low-density Ge allotrope phase with the structural characteristics of zeolite,and two ideal topological semimetals with compatible characteristics with traditional semiconductor materials are obtained.Specific research contents and conclusions are as follows:(1)In this paper,the Ge allotrope,ABW-Ge₄,with the structural characteristics of zeolite ABW is studied.The calculated results of E-V curve,elastic constant,phonon spectrum and molecular dynamics show that ABW-Ge₄has good energy,mechanical,kinetic and thermodynamic(500 K)stability.By analysing electronic properties,it can be seen that the Dirac states are linearly intersected along??X and G₀?X directions near the Fermi energy level.The intersecting nodes are continuously distributed in the Brillouin region and form a closed node ring.Topological analysis shows that the nodal ring is protected by the mirror M_x[(k_x,k_y,k_z)?(-k_x,k_y,k_z)],and the projection on the(100)surface presents a tympanic topological surface state.Therefore,ABW-Ge₄ is a typical topological node-line semimetallic.In addition,the Fermi velocities of band dispersion near the special nodes are also calculated.The minimum and maximum values are 0.2×10⁵m/s and 13.2×10⁵m/s,respectively(the Fermi velocities are larger than that of graphite 9.42×10⁵m/s),which show strong anisotropy.In addition,it is worth noting that the ABW-Ge₄ intersection opens an energy gap of 100me V(HSE06)and becomes a topological insulator conducting on the internal insulating surface under the action of considering the spin orbit coupling(SOC).(2)The Dirac state of ABW-Ge₄ is unstable under SOC,so is there a topological semimetallic under SOC in the germanium isomer phase?Therefore,in this paper,based on the zeolite structure database,systematic screening is carried out,and it is found that the Ge isomeric phase with GIS structure characteristics(GIS-Ge₈)is a stable Dirac topological semimetallic under SOC.Specifically,we first verify the energy,mechanical,kinetic,and thermal(500 K)stability of GIS-Ge₈.Because of its small volume modulus,GIS-Ge₈ shows good mechanical ductility.Different from ABW-Ge₄ topological node-line semimetals,the low energy states of GIS-Ge₈form discontinuous isolated Dirac points in the whole Brillouin region.More importantly,because it is protected by the symmetry of the C₄ axis of rotation,the Dirac point located on the z axis(??M path)is SOC resistant--considering the SOC effect,the intersection does not open a band gap.In addition,we also study the(010)topological surface states of GIS-Ge₈,whose closed Fermi arc further confirms its topological properties.