Landau Level to Efimov-like Bound State Crossover in Two-dimensional Dirac Semimetals

Abstract

In two-dimensional Dirac semimetals, massless Dirac fermions can form a series of Efimov-like quasibound states in an attractive Coulomb potential. In an applied magnetic field, these quasibound states can become bound states around the Dirac point, due to the energy gap between two successive Landau levels. Through the calculation of the energy spectrum directly, we show that there exists a crossover from the Landau level to the bound state as the magnetic field increases. Because of the decreasing magnetic length, the deep quasibound states are pushed up to the Dirac point relatively and transformed into bound states gradually. Furthermore, the magnetic positions of the emerging bound states in the crossovers obey a geometric scaling law, which can be regarded as an analogy of the radial law in the Efimov effect. We extend our analysis to massless three-component fermions, which also demonstrate this phenomenon. Our results show the universality of fermions with linear dispersion in two dimension and pave a way for the future experimental exploration.