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

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.

6 pages; published version with a comparison to the exact diagonalization on a honeycomb lattice

References in corpus (14)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Two Dimensional Atomic Crystals
• The Coulomb impurity problem in graphene
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Atomic Collapse and Quasi-Rydberg States in Graphene
• Nonlinear screening of charge impurities in graphene
• Screening of a hypercritical charge in graphene
• Supercritical Coulomb Impurities in Gapped Graphene
• Atomic collapse, Lorentz boosts, Klein scattering, and other quantum-relativistic phenomena in graphene
• Screening of Coulomb Impurities in Graphene
• Coulomb impurity in graphene
• Polarization Charge Distribution in Gapped Graphene
• Electron-Electron Interactions in the Vacuum Polarization of Graphene

Cited by in corpus (8)

• Non-perturbative vacuum polarization effects in two-dimensional supercritical Dirac-Coulomb system. I. Vacuum charge density
• Non-perturbative vacuum polarization effects in two-dimensional supercritical Dirac-Coulomb system. II. Vacuum energy
• Tunable discrete scale invariance in transition-metal pentatelluride flakes
• Atomic Collapse in Graphene: Lost of Unitarity
• Discrete scale invariance of the quasi-bound states at atomic vacancies in a topological material
• Ferromagnetic phase in graphene-based planar heterostructures induced by charged impurity
• Atomic collapse of high-order singular potentials in graphene
• Anomalous Induced Density of Supercritical Coulomb Impurities in Graphene Under Strong Magnetic Fields