Differential Conductance Mapping Research Articles

Importance of accurately measuring LDOS maps using scanning tunneling spectroscopy in materials presenting atom-dependent charge order: The case of the correlated Pb/Si(111) single atomic layer

We address here general issues and show how to properly extract the local charge order in two-dimensional systems from scanning tunneling microscopy/spectroscopy (STM/STS) measurements. When the charge order presents spatial variations at the atomic scale inside the unit cell and is energy dependent, particular care should be taken. We show that the widely used lock-in technique performed while acquiring an STM topography in a closed feedback loop cannot be used to extract this local charge order from STS $dI/dV$ differential conductance maps. In such situations, the use of the lock-in technique leads to systematically incorrect $dI/dV$ measurements, giving a false local charge order. We show that a correct method is either to perform a constant height measurement or to perform a full grid of $dI/dV(V)$ spectroscopies, using a set point for the bias voltage outside the bandwidth of the correlated material where the local density of states (LDOS) is expected to be spatially homogeneous. We take as a paradigmatic example of two-dimensional material the 1/3 single-layer Pb/Si(111) phase. As large areas of this phase cannot be grown, charge ordering in this system is not accessible to angular resolved photoemission or grazing x-ray diffraction. Two previous investigations by STM/STS supplemented by ab initio density functional theory (DFT) calculations concluded that this material undergoes a phase transition to a low-temperature $3\ifmmode\times\else\texttimes\fi{}3$ reconstruction where one Pb atom moves up, the two remaining Pb atoms shifting down. A third STM/STS study by Adler et al. [F. Adler, S. Rachel, M. Laubach, J. Maklar, A. Fleszar, J. Sch\"afer, and R. Claessen, Phys. Rev. Lett. 123, 086401 (2019)] came to the opposite conclusion, i.e., that two Pb atoms move up, while one Pb atom shifts down. We show that this latter erroneous conclusion comes from an artifact induced by the lock-in technique. In contrast, using a full grid of $dI/dV$($V$) spectroscopy measurements, our results show that the energy-dependent LDOS maps agree very well with state-of-the-art DFT calculations, confirming the one-up two-down charge ordering. We show that this structural and charge reordering inside the $3\ifmmode\times\else\texttimes\fi{}3$ unit cell is equally driven by electron-electron interactions and the coupling to the substrate.

Rotation symmetry breaking in the normal state of a kagome superconductor KV3Sb5

Recently discovered kagome superconductors AV3Sb5 (A=K, Rb, Cs) provide a fresh opportunity to realize and study correlation-driven electronic phenomena on a kagome lattice. The observation of a 2a0 by 2a0 charge density wave (CDW) in the normal state of all members of AV3Sb5 kagome family has generated an enormous amount of interest, in an effort to uncover the nature of this CDW state, and identify any "hidden" broken symmetries. We use spectroscopic-imaging scanning tunneling microscopy to reveal a pronounced intensity anisotropy between different 2a0 CDW directions in KV3Sb5. In particular, by examining the strength of ordering wave vectors as a function of energy in Fourier transforms of differential conductance maps, we find that one of the CDW directions is distinctly different compared to the other two. This observation points towards an intrinsic rotation symmetry broken electronic ground state, where the symmetry is reduced from C6 to C2. Furthermore, in contrast to previous reports, we find that the CDW phase is insensitive to magnetic field direction, regardless of the presence or absence of atomic defects. Our experiments, combined with earlier observations of a stripe 4a0 charge ordering in CsV3Sb5, establish correlation-driven rotation symmetry breaking as a unifying feature of AV3Sb5 kagome superconductors.

Cascade of correlated electron states in the kagome superconductor CsV3Sb5.

The kagome lattice of transition metal atoms provides an exciting platform to study electronic correlations in the presence of geometric frustration and nontrivial band topology1-18, which continues to bear surprises. Here, using spectroscopic imaging scanning tunnelling microscopy, we discover a temperature-dependentcascade of different symmetry-broken electronic states in a new kagome superconductor, CsV3Sb5. We reveal, at a temperature far above the superconducting transition temperature Tc ~ 2.5 K, a tri-directional charge order with a 2a0 period that breaks the translation symmetry of the lattice. As the system is cooled down towards Tc, we observe a prominent V-shaped spectral gap opening at the Fermi level and an additional breaking of the six-fold rotational symmetry, which persists through the superconducting transition. This rotational symmetry breaking is observed as the emergence of an additional 4a0 unidirectional charge order and strongly anisotropic scattering in differential conductance maps. The latter can be directly attributed to the orbital-selective renormalization of the vanadium kagome bands. Our experiments reveal a complex landscape of electronic states that can coexist on a kagome lattice, and highlight intriguing parallels to high-Tc superconductors and twisted bilayer graphene.

Investigating the effect of electric fields on lead halide perovskites by scanning tunneling microscopy

Lead halide perovskites have emerged as promising absorber materials over the last decade to increase the efficiency of photovoltaics beyond its current limits. However, to further optimize the performance of perovskites more detailed studies need to be performed, which allow for the correlation of film morphology and local electronic properties at the nanoscale. Here, we present a scanning tunneling microscopy (STM) approach to probe the effect of an applied electric field of a methylammonium formamidinium lead triiodide perovskite thin film on the film response by current–voltage spectroscopy, current imaging tunneling spectroscopy, differential conductance mapping, and x-ray absorption spectroscopy by means of synchrotron x-ray STM. We find a strong correlation between the measurement conditions and the obtained current–voltage characteristics when imaging under opposite bias polarities. In particular, we find similarities to already observed poling effects for lead halide perovskites, which result in either a positively or negatively charged interface due to ion and vacancy migration. Our results provide insight into the influence of measurement conditions such as bias polarity on the performance assessment of perovskite thin films by STM.

Visualization of localized perturbations on a (001) surface of the ferromagnetic semimetal EuB6

We performed scanning tunneling microscopy (STM) and spectroscopy on a (001) surface of the ferromagnetic semimetal ${\mathrm{EuB}}_{6}$. Large-amplitude oscillations emanating from the elastic scattering of electrons by the surface impurities are observed in topography and in differential conductance maps. Fourier transform of the conductance maps embracing these regions indicate a holelike dispersion centered around the $\overline{\mathrm{\ensuremath{\Gamma}}}$ point of the two-dimensional Brillouin zone. Using density functional theory slab calculations, we identify a spin-split surface state, which stems from the dangling ${p}_{z}$ orbitals of the apical boron atom. Hybridization with bulk electronic states leads to a resonance enhancement in certain regions around the $\overline{\mathrm{\ensuremath{\Gamma}}}$ point, contributing to the remarkably strong real-space response around static point defects, which are observed in STM measurements.

√3 × 2 and √3 × √7 Charge Density Wave Driven by Lattice Distortion in Monolayer VSe2

A charge density wave (CDW), an ordered modulation of electron distribution and lattice distortion, is one of the intriguing phenomena observed in transition metal dichalcogenides. Recent STM studies reported a new CDW phase with √3 × 2 and √3 × √7 periodicities in monolayer (ML) VSe2 grown on graphene, which is totally different from the 4 x 4 x 3 CDW periodicity in bulk. Although the emergence of new CDW phase is of great research interest, the origin of the new modulation in ML VSe2 has not been clearly investigated. In this report, we conduct a systematic study to understand the nature of the √3 × 2 and √3 × √7 CDW in ML VSe2 using scanning tunneling microscopy (STM). Bias dependent topography and differential conductance (dI/dV) mapping indicate that the √3 × 2 and √3 × √7 modulations are mostly driven by strong lattice distortions of the Se atoms rather than by charge orderings. In addition, STM topography reveals that the v3 × 2 modulation corresponds to a gap feature, and the v3 × v7 modulation corresponds to an isolated Se atom in the distorted lattice structures. Our work provides prerequisite information to understand the emergence of √3, × 2 and √3, × √7 CDW in ML VSe2.

MathemaTB: A Mathematica package for tight-binding calculations

MathemaTB is a package developed to enable tight-binding calculations within Mathematica. The package presents 62 functions dedicated to facilitating these quantum mechanical computations. MathemaTB offers functionalities to carry out matrix manipulation, data analysis and visualizations on molecules, wave functions, Hamiltonians, coefficient matrices, and energy spectra, providing a unique insight into the interplay between geometric and electronic structure. Crystal orbitals, projected dispersions and densities of states can be obtained with only a few lines of code. The effect of different structures, heteroatoms and tight-binding parameters can easily be explored. Calculations can be carried out on molecules (Hückel-type calculations) or on systems with periodicities in one, two or three dimensions. Particularly powerful features are the possibility to plot band structures both along paths (one-dimensional) and over planes (two-dimensional) in reciprocal space, where in each case the localization of the wave function onto different sites, symmetries or basis functions can be visualized with color coding. Further features involve crystal orbital plotting with color coding of the complex phase, mean field Hubbard tight-binding and manipulation of the Hamiltonian matrix with numerical and symbolic elements. The conjunction of tight-binding functions, matrix algebra functions for symmetry, overlap and change of basis, wave function- and dispersion functions and a high degree of interactivity and flexibility makes MathemaTB a useful package for electronic structure calculations. Program summaryProgram Title: MathemaTBProgram Files doi:http://dx.doi.org/10.17632/52bykkbr9n.1Licensing provisions: LGPLProgramming language: Wolfram Mathematica v. 11.0Supplementary material: MathemaTB manualNature of problem: The tight-binding method is a useful method for determining the electronic structure in molecules and condensed matter systems. The MathemaTB package provides an implementation of the tight-binding machinery that allows such calculations to be performed in Mathematica.Solution method: A package containing functions to aid in setting up, performing and analyzing tight-binding calculations within Mathematica. The package allows insightful and interactive electronic structure calculations with a high degree of flexibility.Additional comments including restrictions and unusual features: MathemaTB supports molecular and crystal orbitals with color-coding of the complex phase. Supports projected dispersions and local density of states. Allows overlap and change of basis of the Hamiltonian. Supports Hubbard mean field tight-binding. Supports numerical and analytical diagonalization of the Hamiltonian and Hamiltonians with symbolic quantities. Allows plotting the (projected) dispersion in two dimensions. Facilitates simulating differential conductance maps.

Observation of the Magnetization Reorientation in Self-Assembled Metallic Fe-Silicide Nanowires at Room Temperature by Spin-Polarized Scanning Tunneling Spectromicroscopy

The quasi-periodic magnetic domains in metallic Fe-silicide nanowires self-assembled on the Si(110)-16 × 2 surface have been observed at room temperature by direct imaging of both the topographic and magnetic structures using spin-polarized scanning tunneling microscopy/spectroscopy. The spin-polarized differential conductance (dI/dV) map of the rectangular-sectional Fe-silicide nanowire with a width and height larger than 36 and 4 nm, respectively, clearly shows an array of almost parallel streak domains that alternate an enhanced (reduced) density of states over in-plane (out-of-plane) magnetized domains with a magnetic period of 5.0 ± 1.0 nm. This heterostructure of magnetic Fe-silicide nanowires epitaxially integrated with the Si(110)-16 × 2 surface will have a significant impact on the development of Si-based spintronic nanodevices.

Long starphene single molecule NOR Boolean logic gate

Using a low temperature scanning tunneling microscope (LT-UHV-STM), local electronic tunneling spectroscopy and differential conductance mapping are performed to investigate how by extending one phenyl more each branch of the conjugated board of a trinaphthylene starphene molecule, the corresponding longer trianthracene starphene new molecule is functioning like a NOR Boolean logic gate according to a Quantum Hamiltonian Computing (QHC) design. Here the STM tip is used to manipulate single Au atoms one at a time for contacting a trianthracene molecule. Each Au atom is acting like a classical digital input on the molecule encoding for a logical “0'' when the atom is not interacting with the trianthracene input branch and for a logical “1'' when interacting. The inputs are converted in quantum information inside the trianthracene molecule and the logical output status available on the output branch. QHC is demonstrated to be robust since quantum information transfer can be used on the long range along the trianthracene for the NOR logic gate to function properly as compared to the shorter trinaphthylene molecule.

Chevron-based graphene nanoribbon heterojunctions: Localized effects of lateral extension and structural defects on electronic properties

Graphene nanoribbon (GNR) heterojunctions have been synthesized by a bottom-up approach on an Au (111) substrate from a mixture of two structurally similar but visually distinct chevron-type molecular precursors. The resulting heterojunctions were composed of the units of chevron GNRs (cGNRs) and new laterally extended chevron GNRs (eGNRs), which contained an additional benzene ring. Because of their intentional visual difference, cGNR and eGNR units could be conveniently distinguished in scanning tunneling microscopy images. Differential conductance (dI/dV) mapping of GNR heterojunctions revealed differences in electronic structures of cGNRs and eGNRs. Interestingly, the characteristic conduction band states of cGNRs in the dI/dV maps were shown to be sensitive to the effects of both lateral extension of ribbons and the edge defects, emphasizing the importance of synthesizing GNRs and GNR heterojunctions with atomic precision. The dI/dV maps further showed that both effects could be localized within the corresponding GNR units even if they are bonded to structurally and electronically different neighbors, which suggests a possibility of engineering complex GNR-based electronic nanostructures with nanoscale modulation of properties. The new eGNR units could be potentially combined with other chevron-type GNRs, such as nitrogen-doped cGNRs, into a variety of new GNR heterojunctions.

Evaluating the Sources of Graphene\u2019s Resistivity Using Differential Conductance

We explore the contributions to the electrical resistance of monolayer and bilayer graphene, revealing transitions between different regimes of charge carrier scattering. In monolayer graphene at low densities, a nonmonotonic variation of the resistance is observed as a function of temperature. Such behaviour is consistent with the influence of scattering from screened Coulomb impurities. At higher densities, the resistance instead varies in a manner consistent with the influence of scattering from acoustic and optical phonons. The crossover from phonon-, to charged-impurity, limited conduction occurs once the concentration of gate-induced carriers is reduced below that of the residual carriers. In bilayer graphene, the resistance exhibits a monotonic decrease with increasing temperature for all densities, with the importance of short-range impurity scattering resulting in a “universal” density-independent (scaled) conductivity at high densities. At lower densities, the conductivity deviates from this universal curve, pointing to the importance of thermal activation of carriers out of charge puddles. These various assignments, in both systems, are made possible by an approach of “differential-conductance mapping”, which allows us to suppress quantum corrections to reveal the underlying mechanisms governing the resistivity.

Direct observation of subsurface charge ordering in Fe3O4(001) by scanning tunneling microscopy/spectroscopy

In this study, we characterized Fe3O4(001) films using scanning tunneling microscopy/spectroscopy (STM/STS). On the film surfaces, individual iron atoms and ()R45° reconstructed structures were observed by STM. The STS results showed that the local density of states just below the Fermi level was higher in narrow sections than in wide sections of the surface reconstruction perpendicular to the iron rows. Periodic density of states modulations reproducing this electronic structure were clearly observed in the differential tunneling conductance map. These experimental results revealed the presence of subsurface charge ordering of Fe2+–Fe2+ and Fe3+–Fe3+ dimers, as proposed in previous density functional theory studies.

Energetic and Spatial Mapping of Resonant Electronic Excitations

In this article, we present a detailed study of the rotational movement of transition metal phthalocyanine molecules ((TM)Pc) on topological insulators by means of scanning tunneling microscopy and spectroscopy. Our data taken on two different systems, namely FePc on Bi2Te3 and MnPc on Sb2Te3, reveal that the energetic onset of the rotational motion coincides with the energetic position of the lowest unoccupied molecular orbital (LUMO). The strong correlation between molecular motion and tunneling into molecular orbitals is corroborated by a very good agreement between the spatial distribution of the switching frequency and the differential conductance map of the LUMO. These results lead to the conclusion that the driving mechanism of the rotational motion is resonant electronic excitation, which we were able to resolve energetically and spatially.

In-Plane Intermolecular Interaction Assisted Assembly and Modified Electronic States of Metallofullerene Gd@C₈₂.

Orientational configuration and electronic states of Gd@C82 bonding to Cu(111) have been thoroughly investigated by low-temperature scanning tunneling microscopy/spectroscopy (LT-STM/S) and differential conductance mapping complemented by first-principles calculations. We clarify that individual Gd@C82 energetically adopts tilting adsorption configuration with the scanning tunneling spectroscopy (STS) states readily assigned to the C82 cage/Cu(111) hybrid states and the Gd/cage hybrid states, respectively. Moreover, upon assembling and sufficient thermal activation, Gd@C82 fullerenes are inclined to restore the energetically favored tilting orientational configuration similar to an individual one. This suggests the feasibility of high-level integration of single-Gd@C82 based moletronic device with the performances almost unchanged by two-dimensional arrangement. Furthermore, by rationalizing the inter-Gd@C82 interaction induced slight energy offset of the electronic states, we qualitatively confirm the shown electronic hybrid states as Cu(111)-, C82 cage- and Gd-dominant hybrid states, respectively.

Interfacial Coupling and Electronic Structure of Two-Dimensional Silicon Grown on the Ag(111) Surface at High Temperature.

Freestanding silicene, a monolayer of Si arranged in a honeycomb structure, has been predicted to give rise to massless Dirac fermions, akin to graphene. However, Si structures grown on a supporting substrate can show properties that strongly deviate from the freestanding case. Here, combining scanning tunneling microscopy/spectroscopy and differential conductance mapping, we show that the electrical properties of the phase of few-layer Si grown on Ag(111) strongly depend on film thickness, where the electron phase coherence length decreases and the free-electron-like surface state gradually diminishes when approaching the interface. These features are presumably attributable to the inelastic inter-band electron-electron scattering originating from the overlap between the surface state, interface state and the bulk state of the substrate. We further demonstrate that the intrinsic electronic structure of the as grown phase is identical to that of the R30° reconstructed Ag on Si(111), both of which exhibit the parabolic energy-momentum dispersion relation with comparable electron effective masses. These findings highlight the essential role of interfacial coupling on the properties of two-dimensional Si structures grown on supporting substrates, which should be thoroughly scrutinized in pursuit of silicene.

Layer-dependent properties and noncollinear spin structure of epitaxial antiferromagnetic Mn films onCo/Cu(001)

The surface of expanded face-centered tetragonal antiferromagnetic Mn films of a few atomic monolayers thickness grown epitaxially on $\mathrm{Co}/\mathrm{Cu}(001)$ was investigated at room temperature by scanning tunneling microscopy and scanning tunneling spectroscopy using a ferromagnetic ring-shaped bulk iron probe. We show that the main contribution to the contrast modulation observed as a function of Mn thickness in differential conductance maps is not due to spin-polarized tunneling from a layerwise antiferromagnetic spin alignment. Instead, it is mainly of electronic origin resulting from layer-dependent electronic properties of the Mn film, probably related to different levels of intermixing with Co atoms. On the atomic scale, the Mn surface demonstrates a geometrical reconstruction with a $(12\ifmmode\times\else\texttimes\fi{}2)$ periodicity in two orthogonal domains on the fourfold symmetric substrate with an apparent surface corrugation of up to 0.3 \AA{}. Simultaneously recorded differential conductance maps show different textures in the two orthogonal domains, providing evidence for noncollinearity in the Mn surface spin structure.

Investigation of scanning tunneling spectra on iron-based superconductor FeSe0.5Te0.5

FeSe0.5Te0.5 single crystals with superconducting critical temperature of 13.5 K are investigated by scanning tunneling microscopy/spectroscopy (STM/STS) measureflents in detail. STM image on the top surface shows an atomically resolved square lattice consisted by white and dark spots with a constant of about 3.73 0.03 which is consistent with the lattice constant 3.78 . The Se and Te atoms with a height difference of about 0.35 are successfully identified since the sizes of the two kinds of atoms are different. The tunneling spectra show very large zero-bias conductance value and asymmetric coherent peaks in the superconducting state. According to the positions of coherence peaks, we determine the superconducting gap 2 = 5.5 meV, and the reduced gap 2/kBTc = 4.9 is larger than the value predicted by the weak-coupling BCS theory. The zero-bias conductance at 1.7 K only have a decrease of about 40% compared with the normal state conductance, which may originate from some scattering and broadening mechanism in the material. This broadening effect will also make the superconducting gap determined by the distance between the coherence peaks larger than the exact gap value. The asymmetric structure of the tunneling spectra near the superconducting gap is induced by the hump on the background. This hump appears at temperature more than twice the superconducting critical temperature. This kind of hump has also been observed in other iron pnictides and needs further investigation. A possible bosonic mode outside the coherence peak with a mode energy of about 5.5 meV is observed in some tunneling spectra, and the ratio between the mode energy and superconducting transition temperature /kBTc 4.7 is roughly consistent with the universal ratio 4.3 in iron-based superconductors. The high-energy background of the spectra beyond the superconducting gaps shows a V-shape feature. The slopes of the differential conductance spectra at high energy are very different in the areas of Te-atom cluster and Se-atom cluster, and the difference extends to the energy of more than 300 meV. The differential conductance mapping has very little information about the quasi-particle interference of the superconducting state, which may result from the other strong scattering mechanism in the sample.

Manipulation of a single molecule ground state by means of gold atom contacts

Single gold adatoms were manipulated on a Au(111) surface with the tip of a scanning tunnelling microscope to contact selected peripheral π bonds of a single Coronene molecule. Tunnelling electron spectroscopy and differential conductance mapping of the Au–Coronene complexes show how Coronene’s electronic ground state is shifted down in energy as the function of the number of interacting Au atoms, demonstrating that a Coronene molecule can function like a single molecule counter. The number of interacting atoms can be counted by simply following the linear energy downshift of Coronene’s ground state.

Mapping the first electronic resonances of a Cu phthalocyanine STM tunnel junction

Using a low temperature, ultrahigh vacuum scanning tunneling microscope (STM), dI/dV differential conductance maps were recorded at the tunneling resonance energies for a single Cu phthalocyanine molecule adsorbed on an Au(111) surface. We demonstrated that, contrary to the common assumption, such maps are not representative of the molecular orbital spatial expansion, but rather result from their complex superposition captured by the STM tip apex with a superposition weight which generally does not correspond to the native weight used in the standard Slater determinant basis set. Changes in the molecule conformation on the Au(111) surface further obscure the identification between dI/dV conductance maps and the native molecular orbital electronic probability distribution in space.

Simulation of spin-polarized scanning tunneling spectroscopy on complex magnetic surfaces: Case of a Cr monolayer on Ag(111)

We propose a computationally efficient atom-superposition-based method for simulating spin-polarized scanning tunneling spectroscopy (SP-STS) on complex magnetic surfaces based on the sample and tip electronic structures obtained from first principles. We go beyond the commonly used local density of states (LDOS) approximation for the differential conductance, dI/dV. The capabilities of our approach are illustrated for a Cr monolayer on a Ag(111) surface in a noncollinear magnetic state. We find evidence that the simulated tunneling spectra and magnetic asymmetries are sensitive to the tip electronic structure, and we analyze the contributing terms. Related to SP-STS experiments, we show a way to simulate two-dimensional differential conductance maps and qualitatively correct effective spin polarization maps on a constant current contour above a magnetic surface.