Renormalization group analysis of graphene with a supercritical Coulomb impurity

Abstract

We develop a field-theoretic approach to massless Dirac fermions in a supercritical Coulomb potential. By introducing an Aharonov--Bohm solenoid at the potential center, the critical Coulomb charge can be made arbitrarily small for one partial-wave sector, where a perturbative renormalization group analysis becomes possible. We show that a scattering amplitude for reflection of particle at the potential center exhibits the renormalization group limit cycle, i.e., log-periodic revolutions as a function of the scattering energy, revealing the emergence of discrete scale invariance. This outcome is further incorporated in computing the induced charge and current densities, which turn out to have power-law tails with coefficients log-periodic with respect to the distance from the potential center. Our findings are consistent with the previous prediction obtained by directly solving the Dirac equation and can in principle be realized by graphene experiments with charged impurities.

7 pages; published version

References in corpus (8)

• The Coulomb impurity problem in graphene
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• Atomic Collapse and Quasi-Rydberg States in Graphene
• Screening of Coulomb Impurities in Graphene
• Coulomb impurity in graphene
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• On the landscape of scale invariance in quantum mechanics
• Magnetic Manifestation of Discrete Scaling Symmetry in Dirac Semimetals
• Ferromagnetic phase in graphene-based planar heterostructures induced by charged impurity
• Atomic collapse of high-order singular potentials in graphene
• Effect of resonant impurity scattering of carriers on Drude peak broadening in uniaxially strained graphene
• Renormalization group analysis of weakly interacting van der Waals Fermi system