Defect bound states in the continuum of bilayer electronic materials without symmetry protection

Abstract: We analyze a class of bound defect states in the continuum electronic spectrum of bilayer materials, which emerge independent of symmetry protection or additional degrees of freedom. Taking graphene as a prototypical example, our comparative analysis of AA- and AB-stacked bilayer graphene demonstrates that these states originate from the intrinsic algebraic structure of the tight-binding Hamiltonian when trigonal warping is neglected rather than any underlying symmetry. Inclusion of trigonal warping and higher-order hoppings broaden the bound states into long-lived resonances. This discovery provides a pathway to previously unexplored approaches in defect and band-structure engineering. We conclude with a proposed protocol for observing these states in scanning tunneling microscopy experiments.