STRUCTURE OF ELECTRON WAVES AT THE (111) SURFACE OF A NOBLE-METAL AS A CONSEQUENCE OF THE TOPOLOGY OF THE FERMI-SURFACE - QUANTUM ORDER INSTEAD OF QUANTUM CHAOS

Standing electron waves with a period d > 15 angstrom have been observed previously on (111) surfaces of single crystals of noble metals (Cu, Au, and Ag). These waves were observed by scanning tunneling microscopy. They were observed near adsorbed atoms (adatoms), near point defects (vacancies), and inside a ''quantum corral'' of 48 iron adatoms. It is shown here that these waves are not a consequence of a ''quantum chaos'' in a multiple scattering of electrons of 2D surface states by adatoms. These waves are instead a consequence of the topology of the Fermi surface of these metals. They arise as the result of the onset of a ''quantum order,'' i.e., the formation of long-wave Friedel and Rudermann-Kittel oscillations in the course of Coulomb and exchange interactions of adatoms with 3D bulk states of the metal.