Origin of atomic resolution on metal surfaces in scanning tunneling microscopy

Scanning tunneling microscopy has repeatedly resolved individual atoms on a number of metal surfaces with atomic distances 2.5--3 {}. This is in sharp contradiction to the resolution limits previously predicted, 6--9 {}. We present a theory of such atomic resolution in terms of actual tip states, for example, dz² tip states on tungsten tips. Quantitative interpretation of the observed images is obtained with no adjustable parameters. We predict that to achieve atomic resolution, the tip material should be either a d-band metal or certain semiconductor.