Localized defect states within the bands of bilayer graphene

Band structure engineering is crucial for creating materials that can host robust topological edge states, defect states, and correlated phases. This study unveils a remarkable new phenomenon: defect states in periodic systems that coexist within but separate from the continuum, specifically within Bernal stacked graphene. With the application of a localized potential, these states are localized and share energy with continuum states yet arise from fundamental algebraic conditions rather than system symmetries or topology. This is in contrast to AA-stacked graphene, where symmetries can give rise to such states, revealing that the Bernal-stacked case has a distinct, intriguing mechanism. These defect states, immune to energy-matching scattering, hold promise for a new avenue in band structure engineering.