Quantum phase transition triggering magnetic bound states in the continuum in graphene

Abstract

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, Δ∞|ε|3, which leads to the appearance of spin-degenerate bound states in the continuum (BICs) [Phys. Rev. B 92, 045409 (2015)PRBMDO1098-012110.1103/PhysRevB.92.045409]. 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 q0, 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 q0<qc1 (critical point) a mixed pseudogap Δ∞|ε|,|ε|2 appears yielding a phase with spin-degenerate BICs; (ii) near q0=qc1 when Δ∞|ε|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 q0>qc2 the cubic scaling of the pseudogap with energy Δ∞|ε|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.