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We study in detail the properties of pi-fluxes embedded in a state with afinite density of anyons that form either a Fermi liquid or a Bose-Einsteincondensate. By employing a recently developed exact lattice bosonization in 2D,we demonstrate that such pi-flux remains a fully deconfined quasiparticle witha finite energy cost in a Fermi liquid of emergent fermions coupled to a Z2gauge field. This pi-flux is accompanied by a screening cloud of fermions,which in the case of a Fermi gas with a parabolic dispersion binds exactly 1/8of a fermionic hole. In addition there is a long-ranged power-law oscillatorydisturbance of the liquid surrounding the pi-flux akin to Friedel oscillations.These results carry over directly to the pi-flux excitations in orthogonalmetals. In sharp contrast, when the pi-flux is surrounded by a Bose-Einsteincondensate of particles coupled to a Z2 gauge field, it binds a superfluidhalf-vortex, becoming a marginally confined excitation with a logarithmicenergy cost divergence.

Anatomy of Z2 fluxes in anyon Fermi liquids and Bose condensates