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

## TL;DR

This paper demonstrates that in boundary-lacking conformal systems like Dirac-Weyl semimetals, electric field screening is governed by the quantum conformal anomaly, providing a new way to measure the beta function and indirectly observe the Schwinger effect.

## Contribution

It introduces the concept of anomalous conformal screening in boundary-free conformal systems and proposes a method to measure the beta function experimentally in Dirac-Weyl semimetals.

## Key findings

- Electric field decays algebraically with a fractional power
- Screening governed by the system's beta function
- Feasibility of experimental measurement in Dirac/Weyl semimetals

## Abstract

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