Electron states confined within nano-steps on metal surfaces.

To elucidate electron states confined within steps on metal surfaces, we demonstrated a new point of view that a linear step on a noble metal surface can be treated as a dipole potential composed of delta functions. For an electron confined by two pairs of dipole potentials, we derived quasi-stationary eigenstates whose eigenenergies are complex numbers which lead to the lifetime of the electron. To derive the local density of states (LDOS), scanning tunneling microscopy (STM) images and scanning tunneling spectra (STS) for stepped surfaces, we incorporated the lifetime effect on them and clarified the relation between the LDOS and the STM current by applying the expression for the STM current derived by Selloni et al (1985 Phys. Rev. B 31 2602). Although, in previous studies, the Fabry-Pérot interference mechanism has been used to explain electron states confined within two steps, it requires four fitting parameters, in contrast our method requires one fitting parameter which specifies the height of the delta functions. Our results for LDOS images, topographical images and STS are consistent with experimental ones for both the cases where electrons stay on a terrace confined by two steps and on a wide terrace outside the step, which confirms the validity of our model.