Are there stable high-atomic-number elements? —Atomic collapse in Dirac materials

Abstract

One fundamental problem of quantum electrodynamics is the fate of the superheavy atomic nucleus, which is proposed to collapse when the atomic number Z exceeds certain value. However, this intriguing supercritical collapse phenomenon remains elusive in experiments. The quasi-particle in Dirac materials obeys the relativistic equation, and the Fermi velocity is much smaller than the speed of light in vacuum. Thus, the value of the fine-structure constant in Dirac materials is much larger than the value in vacuum, which provides a promising platform to investigate the supercritical atomic collapse phenomenon. Such Dirac materials include the three-dimensional topological semimetal materials and the two-dimensional graphene system, which obey the massless Dirac equation. Owing to the large value of the fine-structure constant in these solid state systems, the Coulomb attraction can give rise to supercritical atomic collapse in analogy to the phenomenon proposed to exist in superheavy atoms. Moreover, the massless Dirac equation with Coulomb attraction preserves the scale invariance, in contrast to the scaling symmetry breaking in massive Dirac equation of superheavy atoms. The scale invariance has a profound impact on the physical characteristic of the system, which goes beyond the original theoretical scenario of atomic collapse phenomenon. The scale invariance in combination with the quantization effect results in a novel feature—the discrete scale invariance, which is a rarely observed trait in quantum systems. Up to now, the discrete scale invariance confirmed in quantum systems only exists in the Efimov trimers and the related physics, generating immediate interest throughout related fields. Recently, a novel type of quantum magneto-resistance oscillations has been observed in a topological Dirac material through the electrical transport measurements in an ultrahigh magnetic field. The quantum oscillations obey a new law with the property periodic in the logarithmic magnetic field (log B ). The log B periodicity is a hallmark of the intriguing discrete scale invariance. The supercritical atomic collapse in the Dirac semimetals can give rise to quasi-bound states, which are in analogous to the Efimov bound states. Without any magnetic field, these quasi-bound states obey the discrete scale invariance in both energy space and real space. Under the appearance of the magnetic field, such quasi-bound states can be broken in sequence, with the corresponding magnetic field value obeys the geometric progression. The breakdown of the Efimovian-like quasi-bound states under the magnetic field influences the mobile carrier density at the Fermi level and thus leads to the observable signatures in the magneto-resistance. This mechanism leads to the discrete scale invariance under the magnetic fields, which behaves as a novel type of log B periodic magneto-resistance oscillations beyond the Landau level physics in the electrical transport measurements. Thus, the discovery of the exotic log B periodic oscillations could virtually represent the atomic collapse and the discrete scale invariance for the quasi-particles in Dirac semimetals. It would be interesting to extend the investigations of the atomic collapse and the discrete scale invariance phenomena to various Dirac systems and other types of measurements, such as the magnetic susceptibilities measurements and the scanning tunneling spectroscopy.