In this talk, I will discuss that both the two-body Weyl Hamiltonian with Coulomb attraction and the three-body Schrödinger Hamiltonian with 2-body resonant scattering condition can give rise to Efimov bound states with discrete scale invariance. In both cases, the magnetic field introduces a new length scale and breaks the discrete scale invariance of the system down to approximate discrete scale invariance. The formation and dissolution of Efimov bound states largely change the densities of mobile carriers, and further give rise to log-B periodic magneto-resistance oscillations beyond the quantum limit. Due to the ultralow carrier density and small Fermi velocity of recent Dirac semimetal materials, the results of two-body Weyl model are more relevant to the experimental results.

Refs: arXiv:1704.00995