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Tilted Dirac Fermions

We introduce the notion of a band-inverted, topological semimetal in two-dimensional nonsymmorphic crystals. This notion is materialized in the monolayers of MTe$_2$ (M $=$ W, Mo) if spin-orbit coupling is neglected. We characterize the Dirac band touching topologically by the Wilson loop of the non-Abelian Berry gauge field. An additional feature of the Dirac cone in monolayer MTe$_2$ 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, non-saturating magnetoresistance in WTe$_2$, as well as its circular dichroism in photoemission. We complement our analysis and first-principle bandstructure calculations with an $\textit{ab-initio}$-derived-derived tight-binding model for the WTe$_2$ monolayer.