Atomic defects pin electrons in place inside a two-dimensional metal

In an ordinary metal, an electron with a given energy is usually free to roam. A team from Columbia University and Brookhaven National Laboratory now reports two electronic states in a layered metal that stay pinned in place even though their energies fall among those of the material's mobile electrons. Such oddities, known as bound states in the continuum, have already been built with light. According to the study, finding electronic versions embedded in a metal has remained an open challenge.

Quantum states come, broadly, in two kinds. Localised states are confined to a small region, like an electron held near a single atom. Extended states spread across a whole material. In a metal, the extended states form a continuum, an unbroken range of energies with no gaps. A localised state whose energy lies inside that range would normally leak away, mixing with its mobile neighbours and dissolving. A bound state in the continuum is the exception that stays put. Physicists have produced optical versions in photonic systems, which are structures engineered to guide light, but the electronic equivalent has been harder to come by.

The researchers turned to Pd₅AlI₂, a compound of palladium, aluminium and iodine. It is a van der Waals material, built from atomically thin sheets held together by weak forces, and the authors describe it as a two-dimensional metal. They examined it with a scanning tunnelling microscope, which scans a fine tip across a surface to map its electrons at the scale of individual atoms. With it they identified two electronic states created by defects in the crystal. Both remain localised despite sitting within the metal's continuum.

In the authors' account, the geometry of the crystal explains why these states do not leak away. Its atoms form what they call a decorated checkerboard lattice. Electrons move through a solid by hopping from atom to atom, and on this lattice the different hopping routes can interfere, cancelling one another out. The team's calculations suggest that this interference produces a flat or nearly flat band. This is a family of states whose energy hardly changes as the electron's momentum changes, built from electron waves trapped in small patches of the lattice. These trapped states are orthogonal to the continuum. In the mathematics of quantum mechanics, that means they are entirely independent of the mobile states and do not mix with them. Physicists call lattices like this frustrated, because competing paths cannot all be accommodated at once.

Defects supply the final ingredient. According to the study, atomic defects within the frustrated lattice shift the energies of the flat-band localised states so that they land inside the metallic continuum. There they persist as bound states in the continuum, which the authors describe as robust and symmetry-protected. In other words, their isolation rests on the symmetry of the lattice rather than on a delicate coincidence that small disturbances could undo.

The observation concerns two states in a single material. The mechanism behind them comes from calculations, which the authors present as suggestive. The abstract does not address whether the same interference effect can be found or engineered in other frustrated lattices, nor what electronic bound states of this kind might eventually be used for.