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 observ ed previously on (111) surfaces of single crystals of noble metals (Cu , Au, and Ag). These waves were observed by scanning tunneling microsc opy. They were observed near adsorbed atoms (adatoms), near point defe cts (vacancies), and inside a ''quantum corral'' of 48 iron adatoms. I t 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 o f a ''quantum order,'' i.e., the formation of long-wave Friedel and Ru dermann-Kittel oscillations in the course of Coulomb and exchange inte ractions of adatoms with 3D bulk states of the metal.