Topological nonsymmorphic metals from band inversion

We expand the phase diagram of two-dimensional, nonsymmorphic crystals at integer fillings that do not guarantee gaplessness. In addition to the trivial, gapped phase that is expected, we find that band inversion leads to a class of topological, gapless phases. These topological phases are exemplified by the monolayers of MT_e2 (M = W; Mo) if spin-orbit coupling is neglected. We characterize the Dirac band touching of these topological metals by theWilson loop of the non-Abelian Berry gauge field. Furthermore, we develop a criterion for the proximity of these topological metals to 2D and 3D ℤ2 topological insulators when spinorbit coupling is included; our criterion is based on nonsymmorphic symmetry eigenvalues, and may be used to identify topological materials without inversion symmetry. An additional feature of the Dirac cone in monolayer MT_e2 is that it tilts over in a Lifshitz transition to produce electron and hole pockets-a type-II Dirac cone. These pockets, together with the pseudospin structure of the Dirac electrons, suggest a unified, topological explanation for the recently reported, nonsaturating magnetoresistance in WTe2, as well as its circular dichroism in photoemission. We complement our analysis and first-principles band structure calculations with an ab-initio-derived tight-binding model for the WT_e2 monolayer.