Gold-induced nanowires on the Ge(100) surface yield a 2D and not a 1D electronic structure

Atomic nanowires on semiconductor surfaces induced by the adsorption of metallic atoms have attracted a lot of attention as possible hosts of the elusive, one-dimensional Tomonaga-Luttinger liquid. The Au/Ge(100) system in particular is the subject of controversy as to whether the Au-induced nanowires do indeed host exotic, 1D (one-dimensional) metallic states. In light of this debate, we report here a thorough study of the electronic properties of high quality nanowires formed at the Au/Ge(100) surface. The high-resolution ARPES data show the low-lying Au-induced electronic states to possess a dispersion relation that depends on two orthogonal directions in k space. Comparison of the E(k(x), k(y)) surface measured using high-resolution ARPES to tight-binding calculations yields hopping parameters in the two different directions that differ by approximately factor of two. Additionally, by pinpointing the Au-induced surface states in the first, second, and third surface Brillouin zones and analyzing their periodicity in k(parallel to), the nanowire propagation direction seen clearly in STM can be imported into the ARPES data. We find that the larger of the two hopping parameters corresponds, in fact, to the direction perpendicular to the nanowires (t(perp)). This proves that the Au-induced electron pockets possess a two-dimensional, closed Fermi surface, and this firmly places the Au/Ge(100) nanowire system outside potential hosts of a Tomonaga-Luttinger liquid. We combine these ARPES data with scanning tunneling spectroscopic measurements of the spatially resolved electronic structure and find that the spatially straight-wirelike-conduction channels observed up to energies of order one electron volt below the Fermi level do not originate from the Au-induced states seen in the ARPES data. The former are rather more likely to be associated with bulk Ge states that are localized to the subsurface region. Despite our proof of the 2D (two-dimentional) nature of the Au-induced nanowire and subsurface Ge-related states, an anomalous suppression of the density of states at the Fermi level is observed in both the STS and ARPES data, and this phenomenon is discussed in the light of the effects of disorder.