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.

arXiv comment6 pages; published version with a comparison to the exact diagonalization on a honeycomb lattice

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Cited by in corpus (19)

• Realization of a Tunable Artificial Atom at a Supercritically Charged Vacancy in Graphene
• Discovery of Log-Periodic Oscillations in Ultra-Quantum Topological Materials
• Observing a scale anomaly and a universal quantum phase transition in graphene
• Log-periodic quantum magneto-oscillations and discrete scale invariance in topological material HfTe5
• Essentially non-perturbative and peculiar polarization effects in planar QED with strong coupling
• Renormalization group analysis of graphene with a supercritical Coulomb impurity
• Non-perturbative vacuum polarization effects in two-dimensional supercritical Dirac-Coulomb system. I. Vacuum charge density
• Efimov Effect in the Dirac Semi-metals
• Plane density of induced vacuum charge in a supercritical Coulomb potential
• Non-perturbative vacuum polarization effects in two-dimensional supercritical Dirac-Coulomb system. II. Vacuum energy
• Tunable discrete scale invariance in transition-metal pentatelluride flakes
• Collapse of the vacuum in hexagonal graphene quantum dots: a comparative study between the tight-binding and the mean-field Hubbard models
• Atomic Collapse in Graphene: Lost of Unitarity
• Magnetic Manifestation of Discrete Scaling Symmetry in Dirac Semimetals
• 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
• Bosonization approach for "atomic collapse" in graphene