The coupling between two atomically sharp nanocontacts provides tunable access to a fundamental underlying interaction: the formation of the bond between two atoms as they are brought into contact. Here we report a detailed experimental and theoretical analysis of the relation between the chemical force and the tunneling current during bond formation in atom-scale metallic junctions and their dependence on distance, junction structure, and material. We found that the short-range force as well as the conductance in two prototypical metal junctions depend exponentially on the distance and that they have essentially the same exponents. In the transition regime between tunneling and point contact, large short-range forces generate structural relaxations which are concomitant with modifications of the surface electronic structure and the collapse of the tunneling barrier.

The $\mathrm{In}/\mathrm{Si}(111)\mathrm{\text{−}}(4\times 1)$ surface is a paradigmatic example of a quasi-one-dimensional system showing a reversible structural and electronic (metal-insulator) phase transition when the temperature is lowered. In this work, we use first-principles simulation techniques to uncover the atomic and electronic origin of this controversial transition. Our calculations show that the ground state consists of insulating ($4\times 2$) indium chains with a weak interchain coupling that induces opposite shear distortions in alternate chains. First-principles molecular dynamics simulations show that the $(4\times 1)\leftrightarrow (8\times 2)$ phase transition is due to the “dynamical fluctuations” the system undergoes when, at high temperature, it fluctuates chaotically between degenerate ground states. The metallicity of the $\mathrm{In}/\mathrm{Si}(111)\mathrm{\text{−}}(4\times 1)$ surface is related to the low energy cost for the shear distortion.

The operation of the STM on metallic surfaces from the tunneling to the contact regime has been explored with a combination of first-principles total energy methods and a calculation of the electronic currents based on nonequilibrium Keldish-Green’s function techniques. Our calculations for the behavior of the total energy, forces, atomic relaxations, and currents for an Al tip on an Al(111) surface as a function of the tip-sample distance indicate that atomic relaxations and saturation effects become relevant in a similar distance range where the onset of a short-range chemical interaction between the tip apex and the surface atoms is taking place. These two factors, that have an opposite influence in the current, lead to corrugations of the order of $0.2\mathrm{\AA }$, similar to the ones found experimentally in other (111) metal surfaces, for the closer distances (around $4.25\mathrm{\AA }$) where stable operation can be achieved.

Different S and Mo vacancies as well as their corresponding antisite defects in a free-standing MoS ₂ monolayer are analysed by means of scanning tunnelling microscopy (STM) simulations. Our theoretical methodology, based on the Keldysh nonequilibrium Green function formalism within the density functional theory (DFT) approach, is applied to simulate STM images for different voltages and tip heights. Combining the geometrical and electronic effects, all features of the different STM images can be explained, providing a valuable guide for future experiments. Our results confirm previous reports on S atom imaging, but also reveal a strong dependence on the applied bias for vacancies and antisite defects that include extra S atoms. By contrast, when additional Mo atoms cover the S vacancies, the MoS ₂ gap vanishes and a bias-independent bright protrusion is obtained in the STM image. Finally, we show that the inclusion of these point defects promotes the emergence of reactive dangling bonds that may act as efficient adsorption sites for external adsorbates.

First-principles calculations show that the rich variety of image patterns found in carbon nanostructures with the atomic force and scanning tunneling microscopes can be rationalized in terms of the chemical reactivity of the tip and the distance range explored in the experiments. For weakly reactive tips, the Pauli repulsion dominates the atomic contrast and force maxima are expected on low electronic density positions as the hollow site. With reactive tips, the interaction is strong enough to change locally the hybridization of the carbon atoms, making it possible to observe atomic resolution in both the attractive and the repulsive regime although with inverted contrast. Regarding STM images, we show that in the near-contact regime, due to current saturation, bright spots correspond to hollow positions instead of atomic sites, providing an explanation for the most common hexagonal pattern found in the experiments.