是否存在稳定的高原子序数原子?——狄拉克材料中的原子塌缩现象

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

相对论量子力学预言当原子序数超过某一特定值时,原子会发生塌缩现象.然而这一重要理论预言仍未得到实验的直接证实.狄拉克材料中的准粒子满足相对论性方程,并且体系的精细结构常数远大于真空中取值,因而可以用来探究原子塌缩现象.最近在狄拉克半金属中发现一种全新的以磁场对数为周期的磁阻振荡,表明体系中准粒子存在原子塌缩现象和伴随出现的离散标度不变性.

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 veloc- ity 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 col- lapse 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 phys- ics, generating immediate interest throughout related fields. Recently, a novel type of quantum magneto-resistance oscil- lations 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 （logB）. The logB 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 cartier density at the Fermi level and thus leads to the observable signatures in the magne- to-resistance. This mechanism leads to the discrete scale invariance under the magnetic fields, which behaves as a novel type of logB periodic magneto-resistance oscillations beyond the Landau level physics in the electrical transport meas- urements. Thus, the discovery of the exotic logB 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 investiga- tions 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.