First-principle Study On Topological Properties Of Superconducting Crystalline Materials

Research on superconducting properties and band topology of solid materials is current topics in condensed matter physics.In superconducting compounds with nontrivial band topology,the superconducting proximity effect could induce superconductivity in the topological surface states,resulting an equivalent spinless p+ip type superconductor.Connate topological superconductors provide a potential platform to study the novel properties of Majorana zero modes（MZMs）.Owing to MZMs obey non-Abelian statistics and can form building blocks of topological qubits for fault-tolerant quantum computers,connate topological superconductors thus have bright application prospect in topological quantum computation.Therefore,it is of great significance in basic physics research and application to discovery and research superconductor with nontrivial band topology.Superconducting compounds with symmetry protected Dirac point near the Fermi level can sustain an exotic quasi-particle along the cores of superconducting vortices,namely,a gapless one-dimensional helical MZM.Due to the lack of proper realistic material,there have been no reports on the experimental realization of one-dimensional helical MZM so far.Using first-principle calculation method,this thesis screened out several possible superconducting Dirac compounds from noncentrosymmetric superconductors,Ti₂O based superconductors,and van der waals superconductors.These superconducting Dirac materials may provide potential platform for experimental verification of the one-dimensional helical MZM.Besides,this thesis also studied the recently discovered superconductor LaCoSi,which provides guidance and ideas for understanding its superconducting properties.The main research contents and results are summarized as follows:Noncentrosymmetric superconductors LaPtSi and LaPtGe have very similar electronic structure:strong spin-orbital coupling（SOC）effect induces the band inversion at theΓpoint,thus leading to the coexistence of type III Dirac semimetal state,type II Dirac semimetal state and topological insulator state.Distinct to the Dirac point in the centrosymmetric compounds,where the twofold Dirac cone degeneracy is reserved at any k point in momentum space,the Dirac points in these two superconductors have two nondegenerate Weyl cones.There are multiple topological nontrivial surface states on the（001）surface.The Dirac type surface states corresponding to the type III Dirac point show large energy dispersion and lead the Fermi level crossing.These predicted compounds provide realistic platforms for the interplay of bulk Dirac points and superconductivity in noncentrosymmetric superconductors.The Ti₂O based quasi-two-dimensional（2D）superconductor BaTi₂Bi₂O exhibits a quasi-two-dimensional multiband character and has a band inversion between Bad_x2-y2and Bi p_xy orbitals at theΓpoint.In the absence of SOC effect,the band inversion leads to a triple point along theΓ-Z directions.Because of the strong SOC effect of Bi element,there appears a type I Dirac point protected by C₄ rotational symmetry along theΓ-Z directions,when SOC is considered.The Dirac point in BaTi₂Bi₂O is 48 me V lower than the Fermi level,which make it is easier to be confirmed by angle-resolved photoemission spectroscopy（ARPES）.The coexistence of bulk superconductivity and Dirac point near the Fermi level,make BaTi₂Bi₂O a promising platform for experimental realization of the one-dimensional helical MZM.The electronic structure of van der Waals（vdW）type superconductor Nb₂S₂C shows highly anisotropic with the low energy states dominated by Nb 4d and S 3p orbitals.The band inversion between Nb d_z2 and S p_xy orbitals at theΓpoint leads to a triple point along theΓ-A path.Upon including SOC effect,the band with S p_xy character splits into two bands.One band crosses the Nb d_z2 band,resulting in a type I Dirac point protected by C₃rotational symmetry.Meanwhile,another band hybrids with the Nb d_z2 band,generating a topological insulator state.The type I Dirac point can be exactly turned to the Fermi level by applying proper external pressure.These results may provide realistic material and idea for experimental investigation of the superconducting Dirac semimetal.The electronic structure,magnetic behavior,and topological nature of newly discovered Co-based superconductor LaCoSi were studied.The density of states closes to the Fermi level feature a narrow peak,which arises from the dispersionless flat bands formed by Co d_x2-y2 orbital.The large density of states at the Fermi level resulting from the narrow peak promotes LaCoSi close to the Stoner ferromagnetic instability.The predicted ground state of LaCoSi favors ferromagnetic order,rather than the experimental determined Pauli paramagnetic state.Such overestimate magnetic tendency within calculations indicates this system nearness to a ferromagnetic quantum critical point.Intriguingly,the band crossings around the Fermi level form two groups of open nodal lines along k_z direction.The nodal lines are constrained to lie in the k_x=y=0 and k_x=±k_yplanes and protected by nonsymmorphic mirror crystal symmetries.Nodal lines induced surface states are observed in the（010）surface Brillouin zone.These results are useful for understanding the superconducting behavior of LaCoSi and suggest it is a potential connate topological superconductor.