We explore the unusual electromagnetic response of ultrathin anisotropic σ-near-zero uniaxial metasurfaces, demonstrating extreme topological transitions--from closed elliptical to open hyperbolic--for surface plasmon propagation, associated with a dramatic tailoring of the local density of states. The proposed metasurfaces may be implemented using nanostructured graphene monolayers and open unprecedented venues for extreme light confinement and unusual propagation and guidance, combined with large tunability via electric bias.
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