Electronic bound states in the continuum in a two-dimensional metal.

Bound states in the continuum (BICs) are quantum states that remain localized despite lying within a continuum of extended, delocalized states. Whereas optical BICs have been realized in photonic systems, achieving electronic bound states embedded in a metallic background remains an ongoing challenge. In this study, we used scanning tunneling microscopy to identify two defect-induced electronic states that remain localized within the metallic continuum of Pd5AlI2, a two-dimensional van der Waals metal. Our calculations suggest that electron-hopping interference on the decorated checkerboard lattice of Pd5AlI2 gives rise to a (quasi) flat band built from spatially localized eigenstates that are orthogonal to the dispersive continuum. Atomic defects within this frustrated lattice shift the associated flat-band localized states into the metallic continuum, forming robust, symmetry-protected BICs.