Symmetry-breaking phase transition without a Peierls instability in conducting monoatomic chains

Electric Field-Induced Phase Transition of Nanowires on Germanium(001) Surfaces

The manipulation of conductive nanowires (NWs) on semiconductor platforms provides important insights into the fabrication of nanoscale electronic devices. In this work, we directly observed the electric field-induced phase transitions in atomic Au-NWs self-assembled on Ge(001) surfaces using scanning tunneling microscopy (STM). The tunneling electrons and electric fields underneath a STM tip apex can effectively trigger a phase transition in Au-NWs on Ge(001) surfaces. Such phase transitions are associated with a remarkable atomic rearrangement in the Au-NWs, thereby modifying their band structures. Moreover, directly monitoring the dynamic reconstruction of Au-NWs on Ge(001) surfaces helps us to understand the NWs' intricate atomic configurations and their electronic properties. The spatially controlled phase transition at the nanometer scale using STM shows the possibility of modulating NWs' properties at an atomic scale.

Phonon Dispersion and the Competition between Pairing and Charge Order

The Holstein model describes the interaction between fermions and a collection of local (dispersionless) phonon modes. In the dilute limit, the phonon degrees of freedom dress the fermions, giving rise to polaron and bipolaron formation. At higher densities, the phonons mediate collective superconducting (SC) and charge-density wave (CDW) phases. Quantum Monte Carlo (QMC) simulations have considered both these limits but have not yet focused on the physics of more general phonon spectra. Here we report QMC studies of the role of phonon dispersion on SC and CDW order in such models. We quantify the effect of finite phonon bandwidth and curvature on the critical temperature T_{cdw} for CDW order and also uncover several novel features of diagonal long-range order in the phase diagram, including a competition between charge patterns at momenta q=(π,π) and q=(0,π) which lends insight into the relationship between Fermi surface nesting and the wave vector at which charge order occurs. We also demonstrate SC order at half filling in situations where a nonzero bandwidth sufficiently suppresses T_{cdw}.

Surface electronic states of Au-induced nanowires on Ge(0 0 1)

The electronic states of Au-induced atomic nanowires on Ge(0 0 1) (Au/Ge(0 0 1) NWs) have been studied by angle-resolved photoelectron spectroscopy with linearly polarized light. We have found three electron pockets around the [Formula: see text] line, where the Fermi surfaces are closed in a surface Brillouin zone (SBZ). The results indicate 2D Fermi surfaces of Au/Ge(0 0 1) NWs whereas the atomic structure is 1D. On the basis of the polarization-dependent spectra, the relation between SBZ and the direction of the atomic NW, and the symmetry of the surface state are clarified. These are very useful for further studies on the atomic structure of NWs.

One-dimensional quantum matter: gold-induced nanowires on semiconductor surfaces

Interacting electrons confined to only one spatial dimension display a wide range of unusual many-body quantum phenomena, ranging from Peierls instabilities to the breakdown of the canonical Fermi liquid paradigm to even unusual spin phenomena. The underlying physics is not only of tremendous fundamental interest, but may also have bearing on device functionality in future micro- and nanoelectronics with lateral extensions reaching the atomic limit. Metallic adatoms deposited on semiconductor surfaces may form self-assembled atomic nanowires, thus representing highly interesting and well-controlled solid-state realizations of such 1D quantum systems. Here we review experimental and theoretical investigations on a few selected prototypical nanowire surface systems, specifically Ge(0 0 1)-Au and Si(hhk)-Au, and the search for 1D quantum states in them. We summarize the current state of research and identify open questions and issues.

Gold deposited on a Ge(0 0 1) surface: DFT calculations

The atomic geometry, stability and electronic properties of self-organized Au induced nanowires on a Ge(0 0 1) surface are investigated based on the density-functional theory in the generalized gradient approximation and the stoichiometry of Au. According to the formation energy and the simulated STM image, the Ge atoms substituted by the Au atoms have been confirmed as occurring at a Au coverage lower than 0.25 Ml. The STM image with single and double dimer vacancies looks like the Au atoms have penetrated the subsurface. The energetically favorable dimer-row arrayed structures at 0.50 Ml and 0.75 Ml Au coverages have a 4  ×  1, 4  ×  2 or c(8  ×  2) transition symmetry, which comprise a flat Au-Au homodimer row and an alternating various buckling phase Ge-Ge or Au-Ge dimer row. The c(8  ×  2) zigzag-shaped protruding chains of shallow-groove STM images are highly consistent with the observations, but a long-range order dimer-row arrayed structure formation requires sufficient mobile energy to complete mass transport of the substituted Ge atoms in order to avoid the re-adsorption of these atoms; otherwise a deep-groove structure reconstruction is sequentially formed. A quasi-1D electron-like energy trough aligns in the direction perpendicular to the nanowire of the dimer-row arrayed structure in the c(8  ×  2) phase on a 0.75 Ml Au/Ge(0 0 1) surface, which is contributed by the Au-Ge dimer rows and the subsurface Ge atoms below them. The bottom energy of the energy trough is consistent with angle-resolved photo-emission spectroscopy studies (Schäfer et al 2008 Phys. Rev. Lett. 101 236802, Meyer et al 2011 Phys. Rev. B 83 121411(R)).

Quasi-One-Dimensional Metal-Insulator Transitions in Compound Semiconductor Surfaces

Existing examples of Peierls-type 1D systems on surfaces involve depositing metallic overlayers on semiconducting substrates, in particular, at step edges. Here we propose a new class of Peierls system on the (101[over ¯]0) surface of metal-anion wurtzite semiconductors. When the anions are bonded to hydrogen or lithium atoms, we obtain rows of threefold coordinated metal atoms that act as one-atom-wide metallic structures. First-principles calculations show that the surface is metallic, and below a certain critical temperature the surface will condense to a semiconducting state. The idea of surface scaffolding is introduced in which the rows are constrained to move along simple up-down and/or sideways displacements, mirroring the paradigm envisioned in Peierls's description. We predict that this type of insulating state should be visible in the partially hydrogenated (101[over ¯]0) surface of many wurtzite compounds.

Coverage-dependent geometries of nanowires on Ge(0 0 1)-Au surfaces: modification of trenches

Despite intense research the microscopic atomic structure of Au-induced nanowires on Ge(0 0 1) substrates is still under discussion. We analyse a variety of structural models for Au-induced nanowires on the Ge(0 0 1) surface using first-principles calculations. Here we focus on subridge modifications at higher Au coverages and study geometries based on the giant missing row model with Ge-Ge dimers in the grooves between the nanowires due to replacing them by Ge-Au heterodimers or Au-Au homodimers. Stable geometries are predicted for higher Au coverages, which however have only a minor influence on the electronic structure. The findings are interpreted that the Au coverage and the actual geometry may vary in the various experiments according to the preparation conditions.

Probing the electronic transport on the reconstructed Au/Ge(001) surface

By using scanning tunnelling potentiometry we characterized the lateral variation of the electrochemical potential µec on the gold-induced Ge(001)-c(8 × 2)-Au surface reconstruction while a lateral current flows through the sample. On the reconstruction and across domain boundaries we find that µec shows a constant gradient as a function of the position between the contacts. In addition, nanoscale Au clusters on the surface do not show an electronic coupling to the gold-induced surface reconstruction. In combination with high resolution scanning electron microscopy and transmission electron microscopy, we conclude that an additional transport channel buried about 2 nm underneath the surface represents a major transport channel for electrons.

Modeling 1D structures on semiconductor surfaces: synergy of theory and experiment

Atomic scale nanowires attract enormous interest in a wide range of fields. On the one hand, due to their quasi-one-dimensional nature, they can act as an experimental testbed for exotic physics: Peierls instability, charge density waves, and Luttinger liquid behavior. On the other hand, due to their small size, they are of interest not only for future device applications in the micro-electronics industry, but also for applications regarding molecular electronics. This versatile nature makes them interesting systems to produce and study, but their size and growth conditions push both experimental production and theoretical modeling to their limits. In this review, modeling of atomic scale nanowires on semiconductor surfaces is discussed, focusing on the interplay between theory and experiment. The current state of modeling efforts on Pt- and Au-induced nanowires on Ge(001) is presented, indicating their similarities and differences. Recently discovered nanowire systems (Ir, Co, Sr) on the Ge(001) surface are also touched upon. The importance of scanning tunneling microscopy as a tool for direct comparison of theoretical and experimental data is shown, as is the power of density functional theory as an atomistic simulation approach. It becomes clear that complementary strengths of theoretical and experimental investigations are required for successful modeling of the atomistic nanowires, due to their complexity.

Au-induced quantum chains on Ge(001)-symmetries, long-range order and the conduction path

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.