The Theory of Scanning Quantum Dot Microscopy

Electrostatic forces are among the most common interactions in nature and omnipresent at the nanoscale. Scanning probe methods represent a formidable approach to study these interactions locally. The lateral resolution of such images is, however, often limited as they are based on measuring the force (gradient) due to the entire tip interacting with the entire surface. Recently, we developed scanning quantum dot microscopy (SQDM), a new technique for the imaging and quantification of surface potentials which is based on the gating of a nanometer-size tip-attached quantum dot by the local surface potential and the detection of charge state changes via non-contact atomic force microscopy. Here, we present a rigorous formalism in the framework of which SQDM can be understood and interpreted quantitatively. In particular, we present a general theory of SQDM based on the classical boundary value problem of electrostatics, which is applicable to the full range of sample properties (conductive vs insulating, nanostructured vs homogeneously covered). We elaborate the general theory into a formalism suited for the quantitative analysis of images of nanostructured but predominantly flat and conductive samples

The origin of high-resolution IETS-STM images of organic molecules with functionalized tips

Recently, the family of high-resolution scanning probe imaging techniques using decorated tips has been complimented by a method based on inelastic electron tunneling spectroscopy (IETS). The new technique resolves the inner structure of organic molecules by mapping the vibrational energy of a single carbonmonoxide (CO) molecule positioned at the apex of a scanning tunnelling microscope (STM) tip. Here, we explain high-resolution IETS imaging by extending the model developed earlier for STM and atomic force microscopy (AFM) imaging with decorated tips. In particular, we show that the tip decorated with CO acts as a nanoscale sensor that changes the energy of the CO frustrated translation in response to the change of the local curvature of the surface potential. In addition, we show that high resolution AFM, STM and IETS-STM images can deliver information about intramolecular charge transfer for molecules deposited on a~surface. To demonstrate this, we extended our numerical model by taking into the account the electrostatic force acting between the decorated tip and surface Hartree potential.Comment: 5 pages, 4 figure

The mechanism of high-resolution STM/AFM imaging with functionalized tips

High resolution Atomic Force Microscopy (AFM) and Scanning Tunnelling Microscopy (STM) imaging with functionalized tips is well established, but a detailed understanding of the imaging mechanism is still missing. We present a numerical STM/AFM model, which takes into account the relaxation of the probe due to the tip-sample interaction. We demonstrate that the model is able to reproduce very well not only the experimental intra- and intermolecular contrasts, but also their evolution upon tip approach. At close distances, the simulations unveil a significant probe particle relaxation towards local minima of the interaction potential. This effect is responsible for the sharp sub-molecular resolution observed in AFM/STM experiments. In addition, we demonstrate that sharp apparent intermolecular bonds should not be interpreted as true hydrogen bonds, in the sense of representing areas of increased electron density. Instead they represent the ridge between two minima of the potential energy landscape due to neighbouring atoms

Scanning Quantum Dot Microscopy

Interactions between atomic and molecular objects are to a large extent defined by the nanoscale electrostatic potentials which these objects produce. We introduce a scanning probe technique that enables three-dimensional imaging of local electrostatic potential fields with sub-nanometer resolution. Registering single electron charging events of a molecular quantum dot attached to the tip of a (qPlus tuning fork) atomic force microscope operated at 5 K, we quantitatively measure the quadrupole field of a single molecule and the dipole field of a single metal adatom, both adsorbed on a clean metal surface. Because of its high sensitivity, the technique can record electrostatic potentials at large distances from their sources, which above all will help to image complex samples with increased surface roughness.Comment: main text: 5 pages, 4 figures, supplementary information file: 4 pages, 2 figure

Electron energy loss spectroscopy with parallel readout of energy and momentum

We introduce a high energy resolution electron source that matches the requirements for parallel readout of energy and momentum of modern hemispherical electron energy analyzers. The system is designed as an add-on device to typical photoemission chambers. Due to the multiplex gain, a complete phonon dispersion of a Cu(111) surface was measured in seven minutes with 4 meV energy resolution

kMap.py: A Python program for simulation and data analysis in photoemission tomography

For organic molecules adsorbed as well-oriented ultra-thin films on metallic surfaces, angle-resolved photoemission spectroscopy has evolved into a technique called photoemission tomography (PT). By approximating the final state of the photoemitted electron as a free electron, PT uses the angular dependence of the photocurrent, a so-called momentum map or k-map, and interprets it as the Fourier transform of the initial state's molecular orbital, thereby gains insights into the geometric and electronic structure of organic/metal interfaces. In this contribution, we present kMap.py which is a Python program that enables the user, via a PyQt-based graphical user interface, to simulate photoemission momentum maps of molecular orbitals and to perform a one-to-one comparison between simulation and experiment. Based on the plane wave approximation for the final state, simulated momentum maps are computed numerically from a fast Fourier transform of real space molecular orbital distributions, which are used as program input and taken from density functional calculations. The program allows the user to vary a number of simulation parameters such as the final state kinetic energy, the molecular orientation or the polarization state of the incident light field. Moreover, also experimental photoemission data can be loaded into the program enabling a direct visual comparison as well as an automatic optimization procedure to determine structural parameters of the molecules or weights of molecular orbitals contributions. With an increasing number of experimental groups employing photoemission tomography to study adsorbate layers, we expect kMap.py to serve as an ideal analysis software to further extend the applicability of PT

How cold is the junction of a millikelvin scanning tunnelling microscope?

We employ a scanning tunnelling microscope (STM) cooled to millikelvin temperatures by an adiabatic demagnetization refrigerator (ADR) to perform scanning tunnelling spectroscopy (STS) on an atomically clean surface of Al(100) in a superconducting state using normal-metal and superconducting STM tips. Varying the ADR temperatures between 30 mK and 1.2 K, we show that the temperature of the STM junction $T$ is decoupled from the temperature of the surrounding environment $T_{\mathrm{env}}$. Simulating the STS data with the $P(E)$ theory, we determine that $T_{\mathrm{env}} \approx 1.5$ K, while the fitting of the superconducting gap spectrum yields the lowest $T=77$ mK.Comment: 12 pages, 10 figure

Induced Superconductivity in Hybrid Au/YBa2Cu3O7-x Electrodes on Vicinal Substrates

Superconducting electrodes are an integral part of hybrid Josephson junctions used in many applications including quantum technologies. We report on the fabrication and characterization of superconducting hybrid Au/YBa2Cu3O7-x (YBCO) electrodes on vicinal substrates. In these structures, superconducting CuO2-planes face the gold film, resulting in a higher value and smaller variation of the induced energy gap compared to the conventional Au/YBCO electrodes based on films with the c-axis normal to the substrate surface. Using scanning tunneling microscopy, we observe an energy gap of about 10-17 meV at the surface of the 15- nm-thick gold layer deposited in situ atop the YBCO film. To study the origin of this gap, we fabricate nanoconstrictions from the Au/YBCO heterostructure and measure their electrical transport characteristics. The conductance of the nanoconstrictions shows a series of dips due to multiple Andreev reflections in YBCO and gold providing clear evidence of the superconducting nature of the gap in gold. We consider the Au/YBCO electrodes to be a versatile platform for hybrid Josephson devices with a high operating temperature