▎ 摘　　要

Graphene hosting a pair of collinear adatoms in the phantom atom configuration has density of states vanishing in the vicinity of the Dirac point which can be described in terms of the pseudogap scaling as cube of the energy, Delta proportional to vertical bar epsilon vertical bar(3), which leads to the appearance of spin-degenerate bound states in the continuum (BICs) [Phys. Rev. B 92, 045409 (2015)]. In the case when adatoms are locally coupled to a single carbon atom the pseudogap scales linearly with energy, which prevents the formation of BICs. Here, we explore the effects of nonlocal coupling characterized by the Fano factor of interference q(0), tunable by changing the slope of the Dirac cones in the graphene band structure. We demonstrate that three distinct regimes can be identified: (i) for q(0) < q(c1) (critical point) a mixed pseudogap Delta proportional to vertical bar epsilon vertical bar, vertical bar epsilon vertical bar(2) appears yielding a phase with spin-degenerate BICs; (ii) near q(0) = q(c1) when Delta proportional to vertical bar epsilon vertical bar(2) the system undergoes a quantum phase transition (QPT) in which the new phase is characterized by magnetic BICs, and (iii) at a second critical value q(0) > q(c2) the cubic scaling of the pseudogap with energy Delta proportional to vertical bar epsilon vertical bar(3) characteristic to the phantom atom configuration is restored and the phase with nonmagnetic BICs is recovered. The phase with magnetic BICs can be described in terms of an effective intrinsic exchange field of ferromagnetic nature between the adatoms mediated by graphene monolayer. We thus propose a new type of QPT resulting from the competition between two ground states, respectively characterized by spin-degenerate and magnetic BICs.