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The electric field inside typical conductors drops down exponentially withthe screening length determined by an intrinsic length scale of the system suchas the density of mobile carriers. We show that in a classically conformalsystem with boundaries, where the intrinsic length scale is absent, thescreening of an external electric field is governed by the quantum conformalanomaly associated with the renormalization of the electric charge. Theelectric field decays algebraically with a fractional power determined by thebeta function of the system. We argue that this `anomalous conformal screeningeffect' is an indirect manifestation of the Schwinger pair production inrelativistic field theory. We discuss the experimental feasibility of theproposed phenomenon in Dirac and Weyl semimetals what would allow directexperimental access to the beta function.

Direct measurement of a beta function and an indirect check of the Schwinger effect near the boundary in Dirac-Weyl semimetals