Drumhead Surface States in Topological Materials

• Drumhead surface states are two-dimensional modes localized on material surfaces, emerging from bulk nodal loops and stabilized by a π Berry phase.
• They exhibit nearly dispersionless behavior and large momentum-space extents, leading to enhanced correlation effects and robust transport phenomena.
• Their study spans electronic, magnonic, and phononic systems, with implications for exotic superconductivity, spintronics, and topological quantum materials.

A drumhead surface state is a two-dimensional, surface-localized electronic, magnonic, or phononic mode that fills the region bounded by the projection of a bulk nodal line (or ring) onto the surface Brillouin zone (BZ). These states are characterized by their nearly dispersionless (“flat band”) nature orthogonal to the loop, large momentum-space extent, and direct topological origin via a π Berry phase or related crystalline/topological invariant. Their realization spans electronic systems (nodal-line semimetals, Weyl loop materials), magnonic systems (pyrochlore ferromagnets), and phononic systems (e.g., distorted kagome RhPb), producing a diverse array of physical phenomena, from enhanced correlation effects and exotic superconductivity to protected spin and charge transport.

1. Topological Bulk Origin and Berry Phase Quantization

Drumhead surface states emerge when the bulk band structure of a 3D material hosts a one-dimensional nodal loop—a locus in momentum space along which two (or more) bands are degenerate. These nodal lines are stabilized