Artificial atoms in graphene hosting a series of quasibound states can serve as an excellent platform to explore atomic collapse and become a basis to design novel graphene nanodevices. We theoretically study behaviors of massless Dirac fermions in singular potentials with a general form of $1/r^{\gamma }$. Different from the Coulomb potential that demands a supercritical charge $Z>Z_c$, a high-order singular potential ($\gamma >1$) is found to, in principle, induce atomic collapse with an infinitesimal charge $Z$. The energies of atomic collapse states (ACSs) within these potentials are arranged roughly as a power sequence. We also show that some special ACSs can exist even above the bulk Dirac point, which cannot appear in the Coulomb potential. These findings uncover the anomalies of massless Dirac fermions in diverse charge potentials and provide guidance for further experiments and graphene nanodevice applications.

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• Density of states
• Dirac fermions
• Graphene
• Semiclassical methods