Atom assemblies on surfaces represent the ultimate lower size limit for electronic circuits, and their conduction properties are governed by quantum phenomena. A fundamental prediction for a line of atoms confining the electrons to one dimension is the Tomonaga-Luttinger liquid 1. Yet, astonishingly, this has not been observed in surface systems so far. Here we scrutinize self-organized chains of single-atom width by scanning tunnelling spectroscopy and photoemission. The lowenergy spectra univocally show power-law behaviour. Even more, the density of states obeys universal scaling with energy and temperature. This demonstrates paradigmatic Tomonaga-Luttinger liquid properties 2,3 encountered at the atomic scale, with bearing for the conductivity of wires and junctions. Local control enables us to study modified interactions due to defects or bridging atoms not previously possible. Arrays of single atoms on surfaces provide an environment for a rich variety of quantum phenomena, especially regarding the electron states responsible for conduction. Their properties can be probed locally with scanning tunnelling microscopy (STM). Key examples include the superposition of electron waves in quantum corrals, leading to new coherent states 4. A challenge remains the exotic correlated state predicted to occur when the electrons are squeezed into one dimension, as in a linear chain of atoms. Quantum theory describes this regime as a Tomonaga-Luttinger liquid 1 (TLL) with collective excitations of spin and charge. It reveals itself in characteristic power-law behaviour of the excitation spectra 2,3 , with markedly depressed density of states at the chemical potential (where conduction takes place). This state is highly fragile and collapses on slight coupling to the second dimension. Experimental indications of TLL low-energy spectra are scarce, consisting of one-dimensional (1D) crystals 5-7 , carbon nanotubes 8,9 and GaAs channels 10,11 (compiled in Supplementary Table S1). Surprisingly, and contrary to expectations, this phenomenon has not been found so far in atom chains at surfaces, although such behaviour will dramatically affect atomic leads and junctions 12. Creation of a TLL state in such chains would be highly intriguing because this promises local atom manipulations that tune the interactions. Concerning approaches to build suitable chains, artificial atom placement by an STM tip 13 leads to short arrays, which do not suffice for an extended 1D regime. Hence, our approach is to use self-organized chains of large extent formed by noble-metal atoms on the semiconducting Ge(001) surface 14,15. Here Au-induced chains show metallic tunnelling conductivity at room temperature 15. Self-organized formation of Au atom wires along the Ge(001) dimer rows leads to c(8 × 2) long-range order covering the

The one-dimensional (1D) model system Au/Ge(001), consisting of linear chains of single atoms on a surface, is scrutinized for lattice instabilities predicted in the Peierls paradigm. By scanning tunneling microscopy and electron diffraction we reveal a second-order phase transition at 585 K. It leads to charge ordering with transversal and vertical displacements and complex interchain correlations. However, the structural phase transition is not accompanied by the electronic signatures of a charge density wave, thus precluding a Peierls instability as origin. Instead, this symmetry-breaking transition exhibits three-dimensional critical behavior. This reflects a dichotomy between the decoupled 1D electron system and the structural elements that interact via the substrate. Such substrate-mediated coupling between the wires thus appears to have been underestimated also in related chain systems.

Atomic nanowires on the Au/Ge(001) surface are investigated for their structural and electronic properties using scanning tunneling microscopy (STM) and angle-resolved photoemission spectroscopy (ARPES). STM reveals two distinct symmetries: a c(8 × 2) describing the basic repeating distances, while the fine structure on top of the wires causes an additional superstructure of p(4 × 1). Both symmetries are long-range ordered as judged from low-energy electron diffraction. The Fermi surface is composed of almost perfectly straight sheets. Thus, the electronic states are one-dimensionally confined. Spatial dI/dV maps, where both topography and density of states (DOS) are probed simultaneously, reveal that the DOS at low energies, i.e. the conduction path, is oriented along the chain direction. This is fully consistent with the recently reported Tomonaga-Luttinger liquid phase of Au/Ge(001), with the density of states being suppressed by a power-law towards the Fermi energy.

Self-organized atomic nanowires of noble metals on Ge(001): atomic structure and electronic properties Abstract. Atomic structures of quasi-one-dimensional (1D) character can be grown on semiconductor substrates by metal adsorption. Significant progress concerning study of their 1D character has been achieved recently by condensing noble metal atoms on the Ge(001) surface. In particular, Pt and Au yield high quality reconstructions with low defect densities. We report on the self-organized growth and the long-range order achieved, and present data from scanning tunneling microscopy (STM) on the structural components. For Pt/Ge(001), we find hot substrate growth is the preferred method for self-organization. Despite various dimerized bonds, these atomic wires exhibit metallic conduction at room temperature, as documented by low-bias STM. For the recently discovered Au/Ge(001) nanowires, we have developed a deposition technique that allows complete substrate coverage. The Au nanowires are extremely well separated spatially, exhibit a continuous 1D charge density, and are of solid metallic conductance. In this review, we present structural details for both types of nanowires, and discuss similarities and differences. A perspective is given for their potential to host a 1D electron system. The ability to condense different noble metal nanowires demonstrates how atomic control of the structure affects the electronic properties.

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