Efimov Effect in the Dirac Semi-metals

Abstract

Efimov effect refers to quantum states with discrete scaling symmetry and a universal scaling factor, and has attracted considerable interests from nuclear to atomic physics communities. In a Dirac semi-metal, when an electron interacts with a static impurity though a Coulomb interaction, the same scaling of the kinetic and interaction energies also gives rise to such a Efimov effect. However, even when the Fermi energy exactly lies at the Dirac point, the vacuum polarization of electron-hole pair fluctuation can still screen the Coulomb interaction, which leads to derivation from this scaling symmetry and eventually breakdown of the Efimov effect. This distortion of the Efimov bound state energy due to vacuum polarization is a relativistic electron analogy of the Lamb shift for the hydrogen atom. Motivated by recent experimental observations in two- and three-dimensional Dirac semi-metals, in this paper we investigate this many-body correction to the Efimov effect, and answer the question that under what condition a good number of Efimov-like bound states can still be observed in these condensed matter experiments.

7 pages, 5 figures

References in corpus (10)

• The electronic properties of graphene
• The Coulomb impurity problem in graphene
• Vacuum Polarization and Screening of Supercritical Impurities in Graphene
• Atomic Collapse and Quasi-Rydberg States in Graphene
• Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance
• Theory of a quantum critical phenomenon in a topological insulator: (3+1)-dimensional quantum electrodynamics in solids
• Vacuum polarization of graphene with a supercritical Coulomb impurity: Low-energy universality and discrete scale invariance
• Observing a scale anomaly and a universal quantum phase transition in graphene
• Renormalization group analysis of graphene with a supercritical Coulomb impurity
• Dynamic Super Efimov Effect

Cited by in corpus (6)

• Quantum Transport in Topological Semimetals under Magnetic Fields (II)
• Log-periodic quantum magneto-oscillations and discrete scale invariance in topological material HfTe5
• Tunable discrete scale invariance in transition-metal pentatelluride flakes
• Magnetic Manifestation of Discrete Scaling Symmetry in Dirac Semimetals
• The fractal geometry and the mapping of Efimov states to Bloch states
• Bound-like State in a 1D Self-Similar Delta-Barrier Array