Coulomb bound states and atomic collapse in tilted Dirac materials

Abstract

Searching for new states of matter and unusual quasi-particles in Dirac materials attracts a significant interest in condensed matter physics. Here we investigate the bound state formation in tilted Dirac materials in the presence of the one- and two-dimensional Coulomb potentials. Based on the exact solution of the Dirac equation, we obtain the energy spectrum of the bound states and the corresponding wave functions in the one-dimensional case. It is shown that the lower-energy bound states dive into the continuum below the band gap with the increase of the tilted parameter. The atomic collapse appears when the strength of the Coulomb potential exceeds the critical value. We show that the tilt of Dirac cone facilitates lowing the critical Coulomb potential strength where atomic collapse happens. Most notably, it is found that the bound states are absent for an overtilted Dirac dispersion. For the two-dimensional Coulomb potential, we perform the second-order perturbation theory to study the effect of band tilting on the bound state formation with a single point-like Coulomb impurity. The result indicates that the ground state becomes more unstable near the critical point for a stronger tilt parameter.