Analog of atomic collapse for adatoms on rhombohedral multilayer graphene

We propose that a multigraphene of ABC-type stacking yields virtual bound states lying within the Coulomb insulating gap of an Anderson-like adatom. Wondrously, a virtual state constitutes the counterpart of the atomic collapse phenomenon proposed in relativistic atomic physics, while the second emerges as its particle-hole symmetric, analogous to a positron state. Thus, we introduce the effect as the adatomic collapse, which occurs due to a flat band with a dispersionless state and a divergent density of states similar to|epsilon - epsilon F|2/J-1 near the Fermi energy epsilon F for J 3, where J pi is the Berry phase. We conclude this scenario based on the Kramers-Kronig transformation of the quasiparticle broadening, from where we observe that the aforementioned van Hove singularity induces virtual bound states. Counterintuitively, near the singularity, we find these states above and below the Fermi energy correlated to the existence of the bottom and top edges of the Coulomb insulating region, respectively. As such a behavior rises without a twist, the system is known as moireless and the phenomenon emerges also assisted by the adatom Coulomb correlations. Similarly to Science 340, 734 (2013) we find the effective critical atomic number Zc similar to 0.96 in contrast to an ultraheavy nucleus. Thus, we point out that multigraphene is a proper playground for testing a predicted phenomenon of the relativistic atomic physics in the domain of the condensed matter physics.