Observing a scale anomaly and a universal quantum phase transition in graphene

Abstract

One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale free quantum system is broken into a discrete scale symmetry for a critical value of a control parameter. This is an example of a (zero temperature) quantum phase transition. Such an anomaly takes place for the quantum inverse square potential known to describe 'Efimov physics'. Broken continuous scale symmetry into discrete scale symmetry also appears for a charged and massless Dirac fermion in an attractive $1/r$ Coulomb potential. The purpose of this article is to demonstrate the universality of this quantum phase transition and to present convincing experimental evidence of its existence for a charged and massless fermion in an attractive Coulomb potential as realised in graphene.

7 pages and 6 figures + 7 pages and 5 figures of supplementary material

References in corpus (8)

• The Coulomb impurity problem in graphene
• Electronic properties of graphene: a perspective from scanning tunneling microscopy and magneto-transport
• Atomic Collapse and Quasi-Rydberg States in Graphene
• Observation of universality in ultracold 7Li three-body recombination
• Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance
• Radio Frequency Association of Efimov Trimers
• Supercritical Coulomb Impurities in Gapped Graphene
• Vacuum polarization of graphene with a supercritical Coulomb impurity: Low-energy universality and discrete scale invariance

Cited by in corpus (22)

• Tuning a Circular p-n Junction in Graphene from Quantum Confinement to Optical Guiding
• Discovery of Log-Periodic Oscillations in Ultra-Quantum Topological Materials
• Quantum scale anomaly and spatial coherence in a 2D Fermi superfluid
• Log-periodic quantum magneto-oscillations and discrete scale invariance in topological material HfTe5
• Scale anomaly of a Lifshitz scalar: a universal quantum phase transition to discrete scale invariance
• Vacancies in Graphene : Dirac Physics and Fractional Vacuum Charges
• Efimov Effect in the Dirac Semi-metals
• Time fractals and discrete scale invariance with trapped ions
• Spectral Properties of the Symmetry Generators of Conformal Quantum Mechanics: A Path-Integral Approach
• Defects in Graphene : A Topological Description
• Tunable discrete scale invariance in transition-metal pentatelluride flakes
• Duality between the quantum inverted harmonic oscillator and inverse square potentials
• $\mathcal{N}=2$ supersymmetry and anisotropic scale invariance
• On the landscape of scale invariance in quantum mechanics
• Magnetic Manifestation of Discrete Scaling Symmetry in Dirac Semimetals
• Discrete scale invariance of the quasi-bound states at atomic vacancies in a topological material
• Polarization Charge around Impurities in Two-Dimensional Anisotropic Dirac Systems
• Fall-to-the-centre as a $\mathcal{P}\mathcal{T}$ symmetry breaking transition
• Efimov effect for two particles on a semi-infinite line
• Geometry-induced wavefunction collapse
• Atomic collapse of high-order singular potentials in graphene
• The fractal geometry and the mapping of Efimov states to Bloch states