Intriguing topological phases may appear in both insulating and semimetallic states. Topological insulators exhibit topologically nontrivial band inversion, while topological Dirac/Weyl semimetals show “relativistic” linear band crossings. Here, we report an unusual topological state of ${\mathrm{Pt}}_3\mathrm{Sn}$, where the two topological features appear simultaneously. Based on first-principles calculations, we show that ${\mathrm{Pt}}_3\mathrm{Sn}$ is a three-dimensional weak topological semimetal with topologically nontrivial band inversion between the valence and conduction bands, where the band structure also possesses type-II Dirac points at the boundary of two electron pockets. The formation of the Dirac points can be understood in terms of the representations of relevant symmetry groups and the compatibility relations. The topological surface states appear in accordance with the nontrivial bulk band topology. The unique coexistence of the two distinct topological features in ${\mathrm{Pt}}_3\mathrm{Sn}$ enlarges the material scope in topological physics, and is potentially useful for spintronics.

• Received 6 March 2017
• Revised 19 October 2017

DOI:https://doi.org/10.1103/PhysRevB.96.205107