ShockleyZustände

Shockley-Zustände, or Shockley surface states, are electronic states that are localized at the surface or interface of a crystalline solid. They arise when the periodic potential of a crystal ends at a boundary, allowing solutions of the Schrödinger equation that decay into the bulk and whose energies lie within the projected bulk band gap.

The concept was introduced by William Shockley in 1939 as part of the theory of surface states in crystals. In simple models, such as a semi-infinite lattice or a tight-binding chain, the termination alters the boundary conditions for electron wavefunctions, enabling bound states that do not extend far into the interior.

Shockley states are often contrasted with Tamm states. Tamm states are typically associated with an additional surface potential barrier or defect at the termination, while Shockley states arise primarily from the bulk band structure and the lattice boundary itself. In many materials, both types of surface states can be present, and their identification may depend on the specific surface preparation and experimental conditions.

Practically, Shockley surface states occur in metals and semiconductors and are observed as two-dimensional states with dispersion parallel to the surface. They are localized near the surface, with wavefunctions decaying into the interior, and their energies typically lie within a bulk band gap when projected onto the surface Brillouin zone. They can be studied by angle-resolved photoemission spectroscopy and scanning tunneling spectroscopy, and are particularly notable on noble metal surfaces such as Cu(111) and Au(111).

See also: surface states, Tamm states, topological surface states.