We explore topological transitions in the type of propagation of surface electromagnetic modes in massive anisotropic tilted two-dimensional (2D) Dirac systems. The presence of tilting and mass gives rise to an indirect band gap that strongly modifies the joint density of states compared to the gapless system. New Van Hove singularities appear, and the interplay between intra- and interband transitions leads to an anisotropic optical conductivity with imaginary parts acquiring opposite signs in orthogonal directions, opening the possibility of having hyperbolic propagation of plasmons. Isofrequency contours and low plasmon losses, as obtained from the dispersion relation, show that transitions between purely anisotropic quasielliptical and well-defined, highly directional, hyperbolic modes are attainable only when tilt and mass coexist via frequency and Fermi level variation. This behavior could be probed in massive tilted 2D Dirac materials like the organic-layered compound $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ [BEDT-TTF = (bis-(ethylenedithio)tetrathiafulvalene)] or ${\mathrm{WTe}}_2$, in which hyperbolic plasmons were recently observed, through far-infrared absorption, optical nanoscopy, and similar current tools in graphene plasmonics.

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• Optical conductivity
• Plasma oscillations
• 2-dimensional systems
• Topological materials