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The combination of a strong pump and a weak probe has been widely applied to investigate both optical and nanomechanical devices. Such pump-probe measurements allows for the exploration of nonlinear dynamics, driven by the large pump tone, by measuring the system response to a probe tone. In contrast, here we report on the dynamics of a mechanical Duffing resonator driven with a combination of two large tones at different frequencies. Our results indicate the presence of various distinct regimes with very different dynamics. We systematically investigate the impact of the relative strength and detuning between the two drives on the dynamical response. This provides an illustrative example of dynamical phase transitions in out-of-equilibrium systems.

Magnetic Resonance Force Microscopy (MRFM) describes a range of approaches to detect nuclear spins with mechanical sensors. MRFM has the potential to enable magnetic resonance imaging (MRI) with near-atomic spatial resolution, opening up exciting possibilities in solid state and biological research. In many cases, the spin-mechanics coupling in MRFM is engineered with the help of periodic radio-frequency pulses. In this paper, we report that such pulses can result in unwanted parametric amplification of the mechanical vibrations, causing misinterpretation of the measured signal. We show how the parametric effect can be cancelled by auxiliary radio-frequency pulses or by appropriate post-correction after careful calibration. Future MRFM measurements may even make use of the parametric amplification to reduce the impact of amplifier noise

In topology, one averages over local geometrical details to reveal robust global features. This approach proves crucial for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials. Moving beyond linear Hamiltonian systems, the study of topology in physics strives to characterize open (non-Hermitian) and interacting systems. Here, we establish a framework for the topological classification of driven-dissipative nonlinear systems. Specifically, we define a graph index for the Floquet semiclassical equations of motion describing such systems. The graph index builds upon topological vector analysis theory and combines knowledge of the particle-hole nature of fluctuations around each out-of-equilibrium stationary state. To test this approach, we divulge the topological invariants arising in a micro-electromechanical nonlinear resonator subject to forcing and a time-modulated potential. Our framework classifies the complete phase diagram of the system and reveals the topological origin of driven-dissipative phase transitions, as well as that of under- to over-damped responses. Furthermore, we predict topological phase transitions between symmetry-broken phases that pertain to population inversion transitions. This rich manifesting phenomenology reveals the pervasive link between topology and nonlinear dynamics, with broad implications for all fields of science.

The new generation of strained silicon nitride resonators harbors great promise for scanning force microscopy, especially when combined with the extensive toolbox of cavity optomechanics. However, accessing a mechanical resonator inside an optical cavity with a scanning tip is challenging. Here, we experimentally demonstrate a cavity-based scanning force microscope based on a silicon nitride membrane sensor. We overcome geometric constraints by making use of the extended nature of the mechanical resonator normal modes, which allows us to spatially separate the scanning and readout sites of the membrane. Our microscope is geared towards low-temperature applications in the zeptonewton regime, such as nanoscale nuclear spin detection and imaging.

Many experimental techniques aim at determining the Hamiltonian of a given system. The Hamiltonian describes the system's evolution in the absence of dissipation, and is often central to control or interpret an experiment. Here, we theoretically propose and experimentally demonstrate a method for Hamiltonian reconstruction from measurements over a large area of phase space, overcoming the main limitation of previous techniques. A crucial ingredient for our method is the presence of dissipation, which enables sampling of the Hamiltonian through ringdown-type measurements. We apply the method to a driven-dissipative system -- a parametric oscillator -- observed in a rotating frame, and reconstruct the (quasi-)Hamiltonian of the system. Furthermore, we demonstrate that our method provides direct experimental access to the so-called symplectic norm of the stationary states of the system, which is tied to the particle- or hole-like nature of excitations of these states. In this way, we establish a method to unveil qualitative differences between the fluctuations around stabilized minima and maxima of the nonlinear out-of-equilibrium stationary states. Our method constitutes a versatile approach to characterize a wide class of driven-dissipative systems.

Considering the growing interest in magnetic materials for unconventional computing, data storage, and sensor applications, there is active research not only on material synthesis but also characterisation of their properties. In addition to structural and integral magnetic characterisations, imaging of magnetization patterns, current distributions and magnetic fields at nano- and microscale is of major importance to understand the material responses and qualify them for specific applications. In this roadmap, we aim to cover a broad portfolio of techniques to perform nano- and microscale magnetic imaging using SQUIDs, spin center and Hall effect magnetometries, scanning probe microscopies, x-ray- and electron-based methods as well as magnetooptics and nanoMRI. The roadmap is aimed as a single access point of information for experts in the field as well as the young generation of students outlining prospects of the development of magnetic imaging technologies for the upcoming decade with a focus on physics, materials science, and chemistry of planar, 3D and geometrically curved objects of different material classes including 2D materials, complex oxides, semi-metals, multiferroics, skyrmions, antiferromagnets, frustrated magnets, magnetic molecules/nanoparticles, ionic conductors, superconductors, spintronic and spinorbitronic materials.

The field of nanoscale magnetic resonance imaging (NanoMRI) was started 30 years ago. It was motivated by the desire to image single molecules and molecular assemblies, such as proteins and virus particles, with near-atomic spatial resolution and on a length scale of 100 nm. Over the years, the NanoMRI field has also expanded to include the goal of useful high-resolution nuclear magnetic resonance (NMR) spectroscopy of molecules under ambient conditions, including samples up to the micron-scale. The realization of these goals requires the development of spin detection techniques that are many orders of magnitude more sensitive than conventional NMR and MRI, capable of detecting and controlling nanoscale ensembles of spins. Over the years, a number of different technical approaches to NanoMRI have emerged, each possessing a distinct set of capabilities for basic and applied areas of science. The goal of this roadmap article is to report the current state of the art in NanoMRI technologies, outline the areas where they are poised to have impact, identify the challenges that lie ahead, and propose methods to meet these challenges. This roadmap also shows how developments in NanoMRI techniques can lead to breakthroughs in emerging quantum science and technology applications.

Nanoscale magnetic resonance imaging (NanoMRI) is an active area of applied research with potential use in structural biology and quantum engineering. The success of this technological vision hinges on improving the instrument's sensitivity and functionality. A particular challenge is the optimization of the magnetic field gradient required for spatial encoding, and of the radio-frequency field used for spin control, in analogy to the components used in clinical MRI. In this work, we present the fabrication and characterization of a magnet-in-microstrip device that yields a compact form factor for both elements. We find that our design leads to a number of advantages, among them a fourfold increase of the magnetic field gradient compared to those achieved with traditional fabrication methods. Our results can be useful for boosting the efficiency of a variety of different experimental arrangements and detection principles in the field of NanoMRI.

The vision of building computational hardware for problem optimization has spurred large efforts in the physics community. In particular, networks of Kerr parametric oscillators (KPOs) are envisioned as simulators for finding the ground states of Ising Hamiltonians. It was shown, however, that KPO networks can feature large numbers of unexpected solutions that are difficult to sample with the existing deterministic (i.e., adiabatic) protocols. In this work, we experimentally realize a system of two classical coupled KPOs, and we find good agreement with the predicted mapping to Ising states. We then introduce a protocol based on stochastic sampling of the system, and we show how the resulting probability distribution can be used to identify the ground state of the corresponding Ising Hamiltonian. This method is akin to a Monte Carlo sampling of multiple out-of-equilibrium stationary states and is less prone to become trapped in local minima than deterministic protocols.

Long and thin scanning force cantilevers are sensitive to small forces, but also vulnerable to detrimental non-contact interactions. Here we present an experiment with a cantilever whose spring constant and static deflection are dominated by the interaction between the tip and the surface, a regime that we refer to as ``overcoupled''. The interactions are an obstacle for ultrasensitive measurements like nanoscale magnetic resonance imaging (nanoMRI). We discuss several strategies to overcome the challenges presented by the overcoupling, and demonstrate proton nanoMRI measurements of individual influenza virus particles.

We report spatially resolved measurements of static and fluctuating electric fields over conductive (Au) and non-conductive (SiO2) surfaces. Using an ultrasensitive `nanoladder' cantilever probe to scan over these surfaces at distances of a few tens of nanometers, we record changes in the probe resonance frequency and damping that we associate with static and fluctuating fields, respectively. We find that the two quantities are spatially correlated and of similar magnitude for the two materials. We quantitatively describe the observed effects on the basis of trapped surface charges and dielectric fluctuations in an adsorbate layer. Our results provide direct, spatial evidence for surface dissipation in adsorbates that affects nanomechanical sensors, trapped ions, superconducting resonators, and color centers in diamond.

Networks of coupled parametric resonators (parametrons) hold promise for parallel computing architectures. En route to realizing complex networks, we report an experimental and theoretical analysis of two coupled parametrons. In contrast to previous studies, we explore the case of strong bilinear coupling between the parametrons, as well as the role of detuning. We show that the system can still operate as an Ising machine in this regime, even though careful calibration is necessary to ensure that the correct solution space is available. Apart from the formation of split normal modes, new states of mixed symmetry are generated. Furthermore, we predict that systems with $N>2$ parametrons will undergo multiple phase transitions before arriving at a regime that can be equivalent to the Ising problem.

We report the development of a scanning force microscope based on an ultra-sensitive silicon nitride membrane transducer. Our development is made possible by inverting the standard microscope geometry - in our instrument, the substrate is vibrating and the scanning tip is at rest. We present first topography images of samples placed on the membrane surface. Our measurements demonstrate that the membrane retains an excellent force sensitivity when loaded with samples and in the presence of a scanning tip. We discuss the prospects and limitations of our instrument as a quantum-limited force sensor and imaging tool.

Since the invention of the solid-state transistor, the overwhelming majority of computers followed the von Neumann architecture that strictly separates logic operations and memory. Today, there is a revived interest in alternative computation models accompanied by the necessity to develop corresponding hardware architectures. The Ising machine, for example, is a variant of the celebrated Hopfield network based on the Ising model. It can be realized with artifcial spins such as the `parametron' that arises in driven nonlinear resonators. The parametron encodes binary information in the phase state of its oscillation. It enables, in principle, logic operations without energy transfer and the corresponding speed limitations. In this work, we experimentally demonstrate flipping of parametron phase states on a timescale of an oscillation period, much faster than the ringdown time \tau that is often (erroneously) deemed a fundamental limit for resonator operations. Our work establishes a new paradigm for resonator-based logic architectures.

The parametron, a resonator-based logic device, is a promising physical platform for emerging computational paradigms. When the parametron is subject to both parametric pumping and external driving, complex phenomena arise that can be harvested for applications. In this paper, we experimentally demonstrate deterministic phase switching of a parametron by applying frequency tuning pulses. To our surprise, we find different regimes of phase switching due to the interplay between a parametric pump and an external drive. We provide full modeling of our device with numerical simulations and find excellent agreement between model and measurements. Our result opens up new possibilities for fast and robust logic operations within large-scale parametron architectures.

Force detectors rely on resonators to transduce forces into a readable signal. Usually these resonators operate in the linear regime and their signal appears amidst a competing background comprising thermal or quantum fluctuations as well as readout noise. Here, we demonstrate that a parametric symmetry breaking transduction leads to a novel and robust nonlinear force detection in the presence of noise. The force signal is encoded in the frequency at which the system jumps between two phase states which are inherently protected against phase noise. Consequently, the transduction effectively decouples from readout noise channels. For a controlled demonstration of the method, we experiment with a macroscopic doubly-clamped string. Our method provides a promising new paradigm for high-precision force detection.

We present a "nanoladder" geometry that minimizes the mechanical dissipation of ultrasensitive cantilevers. A nanoladder cantilever consists of a lithographically patterned scaffold of rails and rungs with feature size $\sim$ 100 nm. Compared to a rectangular beam of the same dimensions, the mass and spring constant of a nanoladder are each reduced by roughly two orders of magnitude. We demonstrate a low force noise of $158 (+62)(-42)\,$zN and $190 (+42)(-33)\,$zN in a one-Hz bandwidth for devices made from silicon and diamond, respectively, measured at temperatures between 100--150 mK. As opposed to bottom-up mechanical resonators like nanowires or nanotubes, nanoladder cantilevers can be batch-fabricated using standard lithography, which is a critical factor for applications in scanning force microscopy.

Charge transport in nanostructures and thin films is fundamental to many phenomena and processes in science and technology, ranging from quantum effects and electronic correlations in mesoscopic physics, to integrated charge- or spin-based electronic circuits, to photoactive layers in energy research. Direct visualization of the charge flow in such structures is challenging due to their nanometer size and the itinerant nature of currents. In this work, we demonstrate non-invasive magnetic imaging of current density in two-dimensional conductor networks including metallic nanowires and carbon nanotubes. Our sensor is the electronic spin of a diamond nitrogen-vacancy center attached to a scanning tip. Using a differential measurement technique, we detect DC currents down to a few uA above a baseline current density of 2e4 A/cm2. Reconstructed images have a spatial resolution of typically 50 nm, with a best-effort value of 22 nm. Current density imaging offers a new route for studying electronic transport and conductance variations in two-dimensional materials and devices, with many exciting applications in condensed matter physics.

Much of the physical world around us can be described in terms of harmonic oscillators in thermodynamic equilibrium. At the same time, the far from equilibrium behavior of oscillators is important in many aspects of modern physics. Here, we investigate a resonating system subject to a fundamental interplay between intrinsic nonlinearities and a combination of several driving forces. We have constructed a controllable and robust realization of such a system using a macroscopic doubly clamped string. We experimentally observe a hitherto unseen double hysteresis in both the amplitude and the phase of the resonator's response function and present a theoretical model that is in excellent agreement with the experiment. Our work provides a thorough understanding of the double-hysteretic response through a symmetry breaking of parametric phase states that elucidates the selection criteria governing transitions between stable solutions. Our study motivates applications ranging from ultrasensitive force detection to low-energy computing memory units.

We propose a novel method for linear detection of weak forces using parametrically driven nonlinear resonators. The method is based on a peculiar feature in the response of the resonator to a near resonant periodic external force. This feature stems from a complex interplay between the parametric drive, external force and nonlinearities. For weak parametric drive, the response exhibits the standard Duffing-like single jump hysteresis. For stronger drive amplitudes, we find a qualitatively new double jump hysteresis which arises from stable solutions generated by the cubic Duffing nonlinearity. The additional jump exists only if the external force is present and the frequency at which it occurs depends linearly on the amplitude of the external force, permitting a straightforward ultrasensitive detection of weak forces. With state-of-the-art nanomechanical resonators, our scheme should permit force detection in the atto-newton range.

Sensitive detection of weak magnetic moments is an essential capability in many areas of nanoscale science and technology, including nanomagnetism, quantum readout of spins, and nanoscale magnetic resonance imaging. Here, we show that the write head of a commercial hard drive may enable significant advances in nanoscale spin detection. By approaching a sharp diamond tip to within 5 nm from the pole and measuring the induced diamagnetic moment with a nanomechanical force transducer, we demonstrate a spin sensitivity of 0.032 Bohr magnetons per root Hz, equivalent to 21 proton magnetic moments. The high sensitivity is enabled in part by the pole's strong magnetic gradient of up to 28 million Tesla per meter and in part by the absence of non-contact friction due to the extremely flat writer surface. In addition, we demonstrate quantitative imaging of the pole field with about 10 nm spatial resolution. We foresee diverse applications for write heads in experimental condensed matter physics, especially in spintronics, ultrafast spin manipulation, and mesoscopic physics.

Carbon nanotube mechanical resonators have attracted considerable interest because of their small mass, the high quality of their surface, and the pristine electronic states they host. However, their small dimensions result in fragile vibrational states that are difficult to measure. Here we observe quality factors $Q$ as high as $5\times10^6$ in ultra-clean nanotube resonators at a cryostat temperature of 30 mK, where we define $Q$ as the ratio of the resonant frequency over the linewidth. Measuring such high quality factors requires both employing an ultra-low noise method to detect minuscule vibrations rapidly, and carefully reducing the noise of the electrostatic environment. We observe that the measured quality factors fluctuate because of fluctuations of the resonant frequency. The quality factors we measure are record high; they are comparable to the highest $Q$ reported in mechanical resonators of much larger size, a remarkable result considering that reducing the size of resonators is usually concomitant with decreasing quality factors. The combination of ultra-low size and very large $Q$ offers new opportunities for ultra-sensitive detection schemes and quantum optomechanical experiments.

We report a method for accelerated nanoscale nuclear magnetic resonance imaging by detecting several signals in parallel. Our technique relies on phase multiplexing, where the signals from different nuclear spin ensembles are encoded in the phase of an ultrasensitive magnetic detector. We demonstrate this technique by simultaneously acquiring statistically polarized spin signals from two different nuclear species (1H, 19F) and from up to six spatial locations in a nanowire test sample using a magnetic resonance force microscope. We obtain one-dimensional imaging resolution better than 5 nm, and subnanometer positional accuracy.

We studied monolayers of noble gas atoms (Xe, Kr, Ar, and Ne) deposited on individual ultra- clean suspended nanotubes. For this, we recorded the resonance frequency of the mechanical motion of the nanotube, since it provides a direct measure of the coverage. The latter is the number of adsorbed atoms divided by the number of the carbon atoms of the suspended nanotube. Monolayers formed when the temperature was lowered in a constant pressure of noble gas atoms. The coverage of Xe monolayers remained constant at 1/6 over a large temperature range. This finding reveals that Xe monolayers are solid phases with a triangular atomic arrangement, and are commensurate with the underlying carbon nanotube. By comparing our measurements to theoretical calculations, we identify the phases of Ar and Ne monolayers as fluids, and we tentatively describe Kr monolayers as solid phases. These results underscore that mechanical resonators made from single nanotubes are excellent probes for surface science.

Nanotubes behave as semi-flexible polymers in that they can bend by a sizeable amount. When integrating a nanotube in a mechanical resonator, the bending is expected to break the symmetry of the restoring potential. Here we report on a new detection method that allows us to demonstrate such symmetry breaking. The method probes the motion of the nanotube resonator at nearly zero-frequency; this motion is the low-frequency counterpart of the second overtone of resonantly excited vibrations. We find that symmetry breaking leads to the spectral broadening of mechanical resonances, and to an apparent quality factor that drops below 100 at room temperature. The low quality factor at room temperature is a striking feature of nanotube resonators whose origin has remained elusive for many years. Our results shed light on the role played by symmetry breaking in the mechanics of nanotube resonators.

Since the advent of atomic force microscopy, mechanical resonators have been used to study a wide variety of phenomena, such as the dynamics of individual electron spins, persistent currents in normal metal rings, and the Casimir force. Key to these experiments is the ability to measure weak forces. Here, we report on force sensing experiments with a sensitivity of 12 zN Hz^(-1/2) at a temperature of 1.2 K using a resonator made of a carbon nanotube. An ultra-sensitive method based on cross-correlated electrical noise measurements, in combination with parametric downconversion, is used to detect the low-amplitude vibrations of the nanotube induced by weak forces. The force sensitivity is quantified by applying a known capacitive force. This detection method also allows us to measure the Brownian vibrations of the nanotube down to cryogenic temperatures. Force sensing with nanotube resonators offers new opportunities for detecting and manipulating individual nuclear spins as well as for magnetometry measurements.

We report on the nonlinear coupling between the mechanical modes of a nanotube resonator. The coupling is revealed in a pump-probe experiment where a mode driven by a pump force is shown to modify the motion of a second mode measured with a probe force. In a second series of experiments, we actuate the resonator with only one oscillating force. Mechanical resonances feature exotic lineshapes with reproducible dips, peaks, and jumps when the measured mode is commensurate with another mode with a frequency ratio of either 2 or 3. Conventional lineshapes are recovered by detuning the frequency ratio using the voltage on a nearby gate electrode. The exotic lineshapes are attributed to strong coupling between the mechanical modes. The possibility to control the strength of the coupling with the gate voltage holds promise for various experiments, such as quantum manipulation, mechanical signal processing, and the study of the quantum-toclassical transition.

Nanoelectromechanical systems (NEMS) have generated considerable interest as inertial mass sensors. NEMS resonators have been used to weigh cells, biomolecules, and gas molecules, creating many new possibilities for biological and chemical analysis [1-4]. Recently, NEMS-based mass sensors have been employed as a new tool in surface science in order to study e.g. the phase transitions or the diffusion of adsorbed atoms on nanoscale objects [5-7]. A key point in all these experiments is the ability to resolve small masses. Here we report on mass sensing experiments with a resolution of 1.7 yg (1 yg = 10^-24 g), which corresponds to the mass of one proton, or one hydrogen atom. The resonator is made of a ~150 nm long carbon nanotube resonator vibrating at nearly 2 GHz. The unprecedented level of sensitivity allows us to detect adsorption events of naphthalene molecules (C10H8) and to measure the binding energy of a Xe atom on the nanotube surface (131 meV). These ultrasensitive nanotube resonators offer new opportunities for mass spectrometry, magnetometry, and adsorption experiments.

A hallmark of mechanical resonators made from a single nanotube is that the resonance frequency can be widely tuned. Here, we take advantage of this property to realize parametric amplification and self-oscillation. The gain of the parametric amplification can be as high as 18.2 dB and tends to saturate at high parametric pumping due to nonlinear damping. These measurements allow us to determine the coefficient of the linear damping force. The corresponding damping rate is lower than the one obtained from the lineshape of the resonance (without pumping), supporting the recently reported scenario that describes damping in nanotube resonators by a nonlinear force. The possibility to combine nanotube resonant mechanics and parametric amplification holds promise for future ultra-low force sensing experiments.

Graphene and carbon nanotubes represent the ultimate size limit of one and two-dimensional nanoelectromechanical resonators. Because of their reduced dimensionality, graphene and carbon nanotubes display unusual mechanical behavior; in particular, their dynamics is highly nonlinear. Here, we review several types of nonlinear behavior in resonators made from nanotubes and graphene. We first discuss an unprecedented scenario where damping is described by a nonlinear force. This scenario is supported by several experimental facts: (i) the quality factor varies with the amplitude of the motion as a power law whose exponent coincides with the value predicted by the nonlinear damping model, (ii) hysteretic behavior (of the motional amplitude as a function of driving frequency) is absent in some of our resonators even for large driving forces, as expected when nonlinear damping forces are large, and (iii) when we quantify the linear damping force (by performing parametric excitation measurements) we find that it is significantly smaller than the nonlinear damping force. We then review parametric excitation measurements, an alternative actuation method which is based on nonlinear dynamics. Finally, we discuss experiments where the mechanical motion is coupled to electron transport through a nanotube. The coupling can be made so strong that the associated force acting on the nanotube becomes highly nonlinear with displacement and velocity. Overall, graphene and nanotube resonators hold promise for future studies on classical and quantum nonlinear dynamics.

Carbon nanotubes and graphene allow fabricating outstanding nanomechanical resonators. They hold promise for various scientific and technological applications, including sensing of mass, force, and charge, as well as the study of quantum phenomena at the mesoscopic scale. Here, we have discovered that the dynamics of nanotube and graphene resonators is in fact highly exotic. We propose an unprecedented scenario where mechanical dissipation is entirely determined by nonlinear damping. As a striking consequence, the quality factor Q strongly depends on the amplitude of the motion. This scenario is radically different from that of other resonators, whose dissipation is dominated by a linear damping term. We believe that the difference stems from the reduced dimensionality of carbon nanotubes and graphene. Besides, we exploit the nonlinear nature of the damping to improve the figure of merit of nanotube/graphene resonators.

In this Letter we demonstrate that Permalloy (Py), a widely used Ni/Fe alloy, forms contacts to carbon nanotubes (CNTs) that meet the requirements for the injection and detection of spin-polarized currents in carbon-based spintronic devices. We establish the material quality and magnetization properties of Py strips in the shape of suitable electrical contacts and find a sharp magnetization switching tunable by geometry in the anisotropic magnetoresistance (AMR) of a single strip at cryogenic temperatures. In addition, we show that Py contacts couple strongly to CNTs, comparable to Pd contacts, thereby forming CNT quantum dots at low temperatures. These results form the basis for a Py-based CNT spin-valve exhibiting very sharp resistance switchings in the tunneling magnetoresistance, which directly correspond to the magnetization reversals in the individual contacts observed in AMR experiments.

We show a detailed investigation of the split Kondo effect in a carbon nanotube quantum dot with multiple gate electrodes. It is found that the splitting decreases for increasing magnetic field, to result in a recovered zero-bias Kondo resonance at finite magnetic field. Surprisingly, in the same charge state, but under different gate-configurations, the splitting does not disappear for any value of the magnetic field, but we observe an avoided crossing of two high-conductance lines. We think that our observations can be understood in terms of a two-impurity Kondo effect with two spins coupled antiferromagnetically. The exchange coupling between the two spins can be influenced by a local gate, and the non-recovery of the Kondo resonance for certain gate configurations is explained by the existence of a small antisymmetric contribution to the exchange interaction between the two spins.

We investigate the Josephson current in a single wall carbon nanotube connected to superconducting electrodes. We focus on the parameter regime in which transport is dominated by Kondo physics. A sizeable supercurrent is observed for odd number of electrons on the nanotube when the Kondo temperature Tk is sufficiently large compared to the superconducting gap. On the other hand when, in the center of the Kondo ridge, Tk is slightly smaller than the superconducting gap, the supercurrent is found to be extremely sensitive to the gate voltage Vbg. Whereas it is largely suppressed at the center of the ridge, it shows a sharp increase at a finite value of Vbg. This increase can be attributed to a doublet-singlet transition of the spin state of the nanotube island leading to a pi shift in the current phase relation. This transition is very sensitive to the asymmetry of the contacts and is in good agreement with theoretical predictions.

We have measured the current(I)-voltage(V) characteristics of a single-wall carbon nanotube quantum dot coupled to superconducting source and drain contacts in the intermediate coupling regime. Whereas the enhanced differential conductance dI/dV due to the Kondo resonance is observed in the normal state, this feature around zero bias voltage is absent in the superconducting state. Nonetheless, a pronounced even-odd effect appears at finite bias in the $dI/dV$ sub-gap structure caused by Andreev reflection. The first-order Andreev peak appearing around V=∆/e is markedly enhanced in gate-voltage regions, in which the charge state of the quantum dot is odd. This enhancement is explained by a `hidden' Kondo resonance, pinned to one contact only. A comparison with a single-impurity Anderson model, which is solved numerically in a slave-boson meanfield ansatz, yields good agreement with the experiment.

A lattice gas model is used to study the equilibrium properties and desorption kinetics of CO on Ru(0001). With interactions obtained from density functional theory (DFT) the phase diagram and temperature programmed desorption (TPD) spectra are calculated up to a coverage of 1/3 ML using top sites only. For coverages beyond 1/3 ML hollow sites are included. Good agreement is obtained between experiment and theory for coverages below 1/3 ML using top sites only. When including hollow sites, DFT calculations fail in predicting the correct binding energy differences between top and hollow sites giving disagreement with TPD, low energy electron diffraction (LEED) and heat of adsorption experiments.

Chemisorption of CO on the stepped Cu(211) surface is studied within ab-initio density functional theory (DFT) and scanning tunneling microscopy (STM) imaging as well as manipulation experiments. Theoretically we focus on the experimentally observed ordered (2x1) and (3x1) CO-phases at coverages 1/3, 1/2 and 2/3 monolayer (ML). To obtain also information for isolated CO molecules found randomly distributed at low coverages, we also performed calculations for a hypothetical (3x1) phase with 1/3 ML. The adsorption geometry, the stretching frequencies, the work functions and adsorption energies of the CO molecules in the different phases are presented and compared to experimental data. Initially and up to a coverage of 1/2 ML CO adsorbs upright on the on-top sites at step edge atoms. Determining the most favorable adsorption geometry for the 2/3 ML ordered phase turned out to be nontrivial both from the experimental and the theoretical point of view. Experimentally, both top-bridge and top-top configurations were reported, whereby only the top-top arrangement was firmly established. The calculated adsorption energies and the stretching frequencies favor the top-bridge configuration. The possible existence of both configurations at 2/3 ML is critically discussed on the basis of the presently accessible experimental and theoretical data. In addition, we present observations of STM manipulation experiments and corresponding theoretical results, which show that CO adsorbed on-top of a single Cu-adatom, which is manipulated to a location close to the lower step edge, is stronger bound than CO on-top of a step edge atom.

We have studied the trends in CO adsorption on close-packed metal surfaces: Co, Ni, Cu from the 3d row, Ru, Rh, Pd, Ag from the 4d row and Ir, Pt, Au from the 5d row using density functional theory. In particular, we were concerned with the trends in the adsorption energy, the geometry, the vibrational properties and other parameters derived from the electronic structure of the substrate. The influence of specific changes in our setup such as choice of the exchange correlation functional, the choice of pseudopotential and size of the basis set, substrate relaxation has been carefully evaluated. We found that while the geometrical and vibrational properties of the adsorbate-substrate complex are calculated with high accuracy, the adsorption energies calculated with the gradient-corrected Perdew-Wang exchange-correlation energies are overestimated. In addition, the calculations tend to favour adsorption sites with higher coordination, resulting in the prediction of wrong adsorption sites for the Rh, Pt and Cu surfaces (hollow instead of top). The revised Perdew-Burke-Erzernhof functional (RPBE) leads to lower (i.e. more realistic) adsorption energies for transition metals, but to wrong results for noble metals - for Ag and Au endothermic adsorption is predicted. The site preference remains the same. We discuss trends in relation to the electronic structure of the substrate across the Periodic Table, summarizing the state-of-the-art of CO adsorption on close-packed metal surfaces.

The adsorption of oxygen on the Ag(001) is investigated by means of density functional techniques. Starting from a characterization of the clean silver surfaces oxygen adsorption in several modifications (molecularly, on-surface, sub-surface, Ag$_2$O) for varying coverage was studied. Besides structural parameters and adsorption energies also work-function changes, vibrational frequencies and core level energies were calculated for a better characterization of the adsorption structures and an easier comparison to the rich experimental data.