First-principles' Study Of Dirac Semimetal

Dirac semimetal is a new kind of quantum matter with nontrivial topological prop-erties.There are three-dimensional Dirac nodes near the Fermi level in the bulk band structure,around which the dispersions are linear along three directions.The four-fold degeneracy at the Dirac node is often protected by time-reversal symmetry and crystal symmetry.As far as the nontrivial topology,it is related to either the non-zero Z₂topo-logical invariant defined in certain two-dimensional plane,or the possible topologically nontrivial gap exactly at the Dirac nodes with symmetry-breaking perturbations.Based on the first-principles'calculations,we mainly predict and investigate two Dirac semimetal materials,which have not been identified in experiments.Group IVA elements have been widely used in conventional semiconductors and microelectronics,so the realization of Dirac semimetal in group IVA elements will prompt the commercial application of this new quantum matter.Our studies reveal that one layered allotrope of Ge and Sn could be a good candidate.We find the three-dimensional Dirac points along the C₃rotation axis in the bulk band structure,and the parity of the occupied states at the time-reversal invariant points and the surface states demonstrate the nontrivial topology.In addition,our theoretical calculations show that the quasi-2D film of the new allotrope of Ge is a quantum spin Hall insulator when the thickness is properly tuned.This could be an important progress in the integration of topologically nontrivial materials into Ge-based electronic devicesRecently,the hexagonal ABC compounds come into sight as a new kind of ferro-electrics.Their lattice structure is simple and they have similar polarizations as those of well-known ferroelectrics?such as BaTiO₃?.On the other hand,combining nontrivial topology and traditional properties of semiconductors?such as ferroelectrics and fer-romagnetism?has application potentials in spintronics and thus has attracted people's attention.In one of the hexagonal ABC compounds-LiZnBi,we find that its low-energy bands near the?point and the related topological properties are strongly dependent on the strain.Under suitable strains,LiZnBi can be turned into Dirac semimetal,where the Z₂topological invariant is nonzero and there are Fermi arcs in the surface states connecting the projections of the bulk Dirac nodes.Furthermore,we study how the strain affects the low-energy band structure in detail and draw a conclusion that both biaxial compressive in-plane strain and tensile out-of-plane strain favor the Dirac semimetal phase in LiZnBi.Besides the Dirac semimetal phase,we also explore other topologically nontrivial phases.In the graphene/topological insulator heterostructure,we discover a gapless Dirac Fermion with a much depressed Fermi velocity in the interface.The anomalously small linear terms are attributed to the interaction between the Dirac Fermions in the two materials.Moreover,based on the mean-field approximations,we predict that with a weak electron-electron interaction,the Dirac Fermion with small Fermi velocity will open a topologically nontrivial gap and the half quantum Hall effect is expected.