A Dirac semimetal with surface hourglass fermions: BaHgSn

We proposed that BaHgSn is a Dirac semimetal which hosts hourglass-like surface states protected by glid symmetry. Compared with the topological crystalline insulators (TCI) KHgSb, BaHgSn has the similar crystal structure, but it has an additional band inversion induced by the stronger bonding and antibonding state splitting at Γ point, which leads to the bulk Dirac point on AΓ path. Due to this addtional band inversion, BaHgSn has the M_z mirror Chern number C±_i=±3, while KHgSb has Z^'₂=(0;000) and C^'±_i=±2. BaHgSn has the same hourglass-like states as KHgSb along the $\tilde{X}\tilde{U}$ path on (010) surface, but it has bulk Dirac cone projection along $\tilde{Z}\tilde{\Gamma}$ path and zigzag surface states protected by C±_i=±3 along $\tilde{\Gamma}\tilde{X}$ path. When 5% pression is applied along the y axis, the bulk Dirac point is gapped, and BaHgSn becomes a strong topological insulator (TI) with Z₂=(1;000). The change of surface states is that bulk Dirac cone projection opens a gap and nontrival zigzag surface states protected by nontirvial Z₂ appear along $\tilde{Z}\tilde{\Gamma}$ path. We also calculate the Wilson-loop spectral for (010) surface, the results are consistent with the surface states.