Vacuum polarization of graphene with a supercritical Coulomb impurity: Low-energy universality and discrete scale invariance

TL;DR

This paper investigates the universal low-energy behavior of massless Dirac fermions in supercritical Coulomb potentials in graphene, revealing discrete scale invariance and its connection to atomic collapse resonances, with potential experimental tests.

Contribution

It introduces a universal low-energy parameter for supercritical Coulomb channels in graphene and links vacuum polarization to atomic collapse resonances, highlighting discrete scale invariance.

Findings

Vacuum polarization exhibits a power-law tail with log-periodic modulation.

The low-energy physics is characterized by a universal length-scale parameter.

Predictions can be tested through graphene experiments with charged impurities.

Abstract

We study massless Dirac fermions in a supercritical Coulomb potential with the emphasis on that its low-energy physics is universal and parametrized by a single quantity per supercritical angular momentum channel. This low-energy parameter with the dimension of length is defined only up to multiplicative factors and thus each supercritical channel exhibits the discrete scale invariance. In particular, we show that the induced vacuum polarization has a power-law tail whose coefficient is a sum of log-periodic functions with respect to the distance from the potential center. This coefficient can also be expressed in terms of the energy and width of so-called atomic collapse resonances. Our universal predictions on the vacuum polarization and its relationship to atomic collapse resonances shed new light on the longstanding fundamental problem of quantum electrodynamics and can in principle be tested by graphene experiments with charged impurities.