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Using evolutionary algorithm for crystal structure prediction, we present anew stable two-dimensional (2D) carbon allotrope composed of polymerizedas-indacenes (PAI) in a zigzag pattern, namely PAI-graphene whose energy islower than most of the reported 2D allotropes of graphene. Crucially, thecrystal structure realizes a nonsymmorphic layer group that enforces anontrivial global topology of the band structure with two Dirac cones lyingperfectly at the Fermi level. The absence of electron/hole pockets makesPAI-graphene a pristine crystalline topological semimetal having anisotropicFermi velocities with a high value of $7.0 \times 10^{5}$ m/s. We show thatwhile the semimetallic property of the allotrope is robust against theapplication of strain, the positions of the Dirac cone and the Fermi velocitiescan be modified significantly with strain. Moreover, by combining strain alongboth the x- and y-directions, two band inversions take place at $\Gamma$leading to the annihilation of the Dirac nodes demonstrating the possibility ofstrain-controlled conversion of a topological semimetal into a semiconductor.Finally we formulate the bulk-boundary correspondence of the topological nodalphase in the form of a generalized Zak-phase argument finding a perfectagreement with the topological edge states computed for differentedge-terminations.

PAI-graphene: a new topological semimetallic two-dimensional carbon allotrope with highly tunable anisotropic Dirac cones