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.

在狄拉克材料中寻找新的物质状态和不寻常的准粒子引起了凝聚态物理学的极大兴趣。在这里，我们研究了一维和二维库仑势存在下倾斜狄拉克材料中束缚态的形成。基于狄拉克方程的精确解，我们得到了一维情况下束缚态的能谱和相应的波函数。结果表明，低能束缚态潜入连续体随着倾斜参数的增加，带隙低于带隙。当库仑势的强度超过临界值时，就会出现原子坍缩。我们表明，狄拉克锥的倾斜有助于降低发生原子坍缩的临界库仑势强度。最值得注意的是，发现过度倾斜的狄拉克色散不存在束缚态。对于二维库仑势，我们使用二阶微扰理论来研究带倾斜对具有单点状库仑杂质的束缚态形成的影响。结果表明，对于更强的倾斜参数，基态在临界点附近变得更加不稳定。