Theory of the fano resonance in the STM tunneling density of states due to a single kondo impurity

Tunable Magnetic Coupling in Graphene Nanoribbon Quantum Dots

Carbon-based quantum dots (QDs) enable flexible manipulation of electronic behavior at the nanoscale, but controlling their magnetic properties requires atomically precise structural control. While magnetism is observed in organic molecules and graphene nanoribbons (GNRs), GNR precursors enabling bottom-up fabrication of QDs with various spin ground states have not yet been reported. Here the development of a new GNR precursor that results in magnetic QD structures embedded in semiconducting GNRs is reported. Inserting one such molecule into the GNR backbone and graphitizing it results in a QD region hosting one unpaired electron. QDs composed of two precursor molecules exhibit nonmagnetic, antiferromagnetic, or antiferromagnetic ground states, depending on the structural details that determine the coupling behavior of the spins originating from each molecule. The synthesis of these QDs and the emergence of localized states are demonstrated through high-resolution atomic force microscopy (HR-AFM), scanning tunneling microscopy (STM) imaging, and spectroscopy, and the relationship between QD atomic structure and magnetic properties is uncovered. GNR QDs provide a useful platform for controlling the spin-degree of freedom in carbon-based nanostructures.

Unraveling the Nature of Spin Coupling in a Metal-Free Diradical: Theoretical Distinction of Ferromagnetic and Antiferromagnetic Interactions

Metal-free diradicals based on polycyclic aromatic hydrocarbons are promising candidates for organic spintronics due to their stable magnetism and tunable spin coupling. However, distinguishing and elucidating the origins of ferromagnetic and antiferromagnetic interactions in these systems remain challenging. Here, we investigate the 2-OS diradical molecule sandwiched between gold electrodes using a combined density functional theory and hierarchical equations of motion approach. We find that the dihedral angle between the radical moieties controls the nature and strength of the intramolecular spin coupling, transitioning smoothly from antiferromagnetic to ferromagnetic as the angle increases. Distinct features in the inelastic electron tunneling spectra are identified that can discern the two coupling regimes, including spin excitation steps whose energies directly reveal the exchange coupling constant. Mechanical stretching of the junction is predicted to modulate the spectral line shapes by adjusting the hybridization of the molecular radicals with the electrodes. Our work elucidates the electronic origin of tunable spin interactions in 2-OS and provides spectroscopic fingerprints for characterizing magnetism in metal-free diradicals.

Kondo Effect of Co-Porphyrin: Remarkable Sensitivity to Adsorption Sites and Orientations

We investigated the Kondo effect of cobalt(II)-5-15-bis(4'-bromophenyl)-10,20-bis(4'-iodophenyl)porphyrin (CoTPPBr2I2) molecules on Au(111) with low-temperature scanning tunneling microscopy under ultrahigh vacuum conditions. The molecules exhibit four adsorption configurations at the top and bridge sites of the surface with different molecular orientations. The Kondo resonance shows extraordinary sensitivity to the adsorption configuration. By switching the molecule between different configurations, the Kondo temperature is varied over a wide range from ≈8 up to ≈250 K. Density functional theory calculations reveal that changes of the adsorption configuration lead to distinct variations of the hybridization between the molecule and the surface. Furthermore, we show that surface reconstruction plays a significant role for the molecular Kondo effect.

Shaping Electronic Flows with Strongly Correlated Physics

Nonequilibrium quantum transport is of central importance in nanotechnology. Its description requires the understanding of strong electronic correlations that couple atomic-scale phenomena to the nanoscale. So far, research in correlated transport has focused predominantly on few-channel transport, precluding the investigation of cross-scale effects. Recent theoretical advances enable the solution of models that capture the interplay between quantum correlations and confinement beyond a few channels. This problem is the focus of this study. We consider an atomic impurity embedded in a metallic nanosheet spanning two leads, showing that transport is significantly altered by tuning only the phase of a single local hopping parameter. Furthermore─depending on this phase─correlations reshape the electronic flow throughout the sheet, either funneling it through the impurity or scattering it away from a much larger region. This demonstrates the potential for quantum correlations to bridge length scales in the design of nanoelectronic devices and sensors.

Tweezer-like magnetic tip control of the local spin state in the FeOEP/Pb(111) adsorption system: a preliminary exploration based on first-principles calculations

The magnetic interactions between the spin-polarized scanning tunnelling microscopy (SP-STM) tip and the localized spin impurities lead to various forms of the Kondo effect. Although these intriguing phenomena enrich Kondo physics, detailed theoretical simulations and explanations are still lacking due to the rather complex formation mechanisms. Here, by combining density functional theory (DFT), complete active space self-consistent field (CASSCF) theory, and hierarchical equations of motion (HEOM) methods, we perform first-principles-based simulation to elaborate the regulation process of the magnetic Co-tip on the spin state and transport behaviour of FeOEP/Pb(111) system. Compared with the non-magnetic tip, the stronger interaction between the magnetic tip and FeOEP molecule results in a more drastic deformation of the molecular structure with more electron transfer from the local environment to Fe-3d orbitals. The magnetic anisotropy of FeOEP changes very drastically from positive values in the tunnelling region to negative values in the contact region. The ferromagnetic electron correlation between the magnetic tip and the molecule induces an asymmetric Kondo line-shape near the Fermi level. This work highlights that the DFT + CASSCF + HEOM approach can not only predict complex quantum phenomena and explain underlying physical mechanisms, but also facilitate the design of more fascinating quantum control experiments.

Unveiling the Decisive Factor for the Sharp Transition in the Scanning Tunneling Spectroscopy of a Single Nickelocene Molecule

Scanning tunneling microscopy (STM) has been utilized to realize the precise measurement and control of local spin states. Experiments have demonstrated that when a nickelocene (Nc) molecule is attached to the apex of an STM tip, the dI/dV spectra exhibit a sharp or a smooth transition when the tip is displaced toward the substrate. However, what leads to the two distinct types of transitions remains unclear, and more intriguingly, the physical origin of the abrupt change in the line shape of dI/dV spectra remains unclear. To clarify these intriguing issues, we perform first-principles-based simulations on the STM tip control process for the Cu tip/Nc/Cu(100) junction. In particular, we find that the suddenly enhanced hybridization between the d orbitals on the Ni ion and the metallic bands in the substrate leads to Kondo correlation overwhelming spin excitation, which is the main cause of the sharp transition in the dI/dV spectra observed experimentally.

Origin of Asymmetric Splitting of Kondo Peak in Spin-Polarized Scanning Tunneling Spectroscopy: Insights from First-Principles-Based Simulations

The spin-polarized scanning tunneling microscope (SP-STM) has served as a versatile tool for probing and manipulating the spintronic properties of atomic and molecular devices with high precision. The interplay between the local spin state and its surrounding magnetic environment significantly affects the transport behavior of the device. Particularly, in the contact regime, the strong hybridization between the SP-STM tip and the magnetic atom or molecule could give rise to unconventional Kondo resonance signatures in the differential conductance (dI/dV) spectra. This poses challenges for the simulation of a realistic tip control process. By combining the density functional theory and the hierarchical equations of motion methods, we achieve first-principles-based simulation of the control of a Ni-tip/Co/Cu(100) junction in both the tunneling and contact regimes. The calculated dI/dV spectra reproduce faithfully the experimental data. A cotunneling mechanism is proposed to elucidate the physical origin of the observed unconventional Kondo signatures.

Moiré Tuning of Spin Excitations: Individual Fe Atoms on MoS_{2}/Au(111)

Magnetic adatoms on properly designed surfaces constitute exquisite systems for addressing, controlling, and manipulating single quantum spins. Here, we show that monolayers of MoS_{2} on a Au(111) surface provide a versatile platform for controllably tuning the coupling between adatom spins and substrate electrons. Even for equivalent adsorption sites with respect to the atomic MoS_{2} lattice, we observe that Fe adatoms exhibit behaviors ranging from pure spin excitations, characteristic of negligible exchange and dominant single-ion anisotropy, to a fully developed Kondo resonance, indicating strong exchange and negligible single-ion anisotropy. This tunability emerges from a moiré structure of MoS_{2} on Au(111) in conjunction with pronounced many-body renormalizations. We also find striking spectral variations in the immediate vicinity of the Fe atoms, which we explain by quantum interference reflecting the formation of Fe-S hybrid states despite the nominally inert nature of the substrate. Our work establishes monolayer MoS_{2} as a tuning layer for adjusting the quantum spin properties over an extraordinarily broad parameter range. The considerable variability can be exploited for quantum spin manipulations.

Iron phthalocyanine on Au(111) is a "non-Landau" Fermi liquid

The paradigm of Landau’s Fermi liquid theory has been challenged with the finding of a strongly interacting Fermi liquid that cannot be adiabatically connected to a non-interacting system. A spin-1 two-channel Kondo impurity with anisotropy D has a quantum phase transition between two topologically different Fermi liquids with a peak (dip) in the Fermi level for D < D_c (D > D_c). Extending this theory to general multi-orbital problems with finite magnetic field, we reinterpret in a unified and consistent fashion several experimental studies of iron phthalocyanine molecules on Au(111) that were previously described in disconnected and conflicting ways. The differential conductance shows a zero-bias dip that widens when the molecule is lifted from the surface (reducing the Kondo couplings) and is transformed continuously into a peak under an applied magnetic field. We reproduce all features and propose an experiment to induce the topological transition.

Single molecules on metal surfaces are paradigmatic systems for the study of many-body phenomena. Here, the authors show that several spectroscopic experiments on iron phthalocyanine on Au(111) surface can be described in a unified way in terms of a strongly interacting topologically non-trivial (non-Landau) Fermi liquid.

Local Kondo scattering in 4d-electron RuOx nanoclusters on atomically-resolved ultrathin SrRuO3 films

Perovskite SrRuO₃ is a unique 4d transition metal oxide with coexisting spin-orbit coupling (SOC) and electron-electron correlation. However, the intrinsic, non-reconstructed surface structure of SrRuO₃ has not been reported so far. Here we report an atomic imaging of the non-reconstructed, SrO-terminated SrRuO₃ surface by scanning tunneling microscopy/spectroscopy. Moreover, a Kondo resonant behavior is revealed in RuO_x clusters located on top of the nonmagnetic SrO surface layer. The density functional theory calculations confirm that RuO_x clusters possess localized 4d-electron-involved spin moments and hybridize with the conduction electrons in the metal host, resulting in the appearance of the Kondo resonance features around the Fermi level. Our work demonstrates that artificially-engineered transition metal oxides provide new opportunities to explore the Kondo physics in 4d multi-orbital systems.

Ligand Non-innocence and Single Molecular Spintronic Properties of AgII Dibenzocorrole Radical on Ag(111)

A facile method for the quantitative preparation of silver dibenzo-fused corrole Ag-1 is described. In contrast to the saddle conformation resolved by single-crystal X-ray analysis for Ag-1, it adopts an unprecedented domed geometry, with up and down orientations, when adsorbed on an Ag(111) surface. Sharp Kondo resonances near Fermi level, both at the corrole ligand and the silver center were observed by cryogenic STM, with relatively high Kondo temperature (172 K), providing evidence for a non-innocent Ag^II -corrole^.2- species. Further investigation validates that benzene ring fusion and molecule-substrate interactions play pivotal roles in enhancing Ag(4d(x² -y² ))-corrole (π) orbital interactions, thereby stabilizing the open-shell singlet Ag^II -corrole^.2- on Ag(111) surface. Moreover, this strategy used for constructing metal-free benzene-ring fused corrole ligand gives rise to inspiration of designing novel metal-corrole compound for multichannel molecular spintronics devices.

Theory of Differential Conductance of Co on Cu(111) Including Co s and d Orbitals, and Surface and Bulk Cu States

We revisit the theory of the Kondo effect observed by a scanning-tunneling microscope (STM) for transition-metal atoms (TMAs) on noble-metal surfaces, including d and s orbitals of the TMA, surface and bulk conduction states of the metal, and their hopping to the tip of the STM. Fitting the experimentally observed STM differential conductance for Co on Cu(111) including both the Kondo feature near the Fermi energy and the resonance below the surface band, we conclude that the STM senses mainly the Co s orbital and that the Kondo antiresonance is due to interference between states with electrons in the s orbital and a localized d orbital mediated by the conduction states.

Interfering Tunneling Paths through Magnetic Molecules on Superconductors: Asymmetries of Kondo and Yu-Shiba-Rusinov Resonances

Magnetic adsorbates on superconductors induce a Kondo resonance outside and Yu-Shiba-Rusinov (YSR) bound states inside the superconducting energy gap. When probed by scanning tunneling spectroscopy, the associated differential-conductance spectra frequently exhibit characteristic bias-voltage asymmetries. Here, we observe correlated variations of Kondo and YSR asymmetries across an Fe-porphyrin molecule adsorbed on Pb(111). We show that both asymmetries originate in interfering tunneling paths via a spin-carrying orbital and the highest occupied molecular orbital (HOMO). Strong evidence for this model comes from nodal planes of the HOMO, where tunneling reveals symmetric Kondo and YSR resonances. Our results establish an important mechanism for the asymmetries of Kondo and YSR line shapes.

A new view on the origin of zero-bias anomalies of Co atoms atop noble metal surfaces

Many-body phenomena are paramount in physics. In condensed matter, their hallmark is considerable on a wide range of material characteristics spanning electronic, magnetic, thermodynamic and transport properties. They potentially imprint non-trivial signatures in spectroscopic measurements, such as those assigned to Kondo, excitonic and polaronic features, whose emergence depends on the involved degrees of freedom. Here, we address systematically zero-bias anomalies detected by scanning tunneling spectroscopy on Co atoms deposited on Cu, Ag and Au(111) substrates, which remarkably are almost identical to those obtained from first-principles. These features originate from gaped spin-excitations induced by a finite magnetic anisotropy energy, in contrast to the usual widespread interpretation relating them to Kondo resonances. Resting on relativistic time-dependent density functional and many-body perturbation theories, we furthermore unveil a new many-body feature, the spinaron, resulting from the interaction of electrons and spin-excitations localizing electronic states in a well defined energy.

Real-Space Imaging of a Single-Molecule Monoradical Reaction

Organic radicals consisting of light elements exhibit a low spin-orbit coupling and weak hyperfine interactions with a long spin coherence length, which are crucial for future applications in molecular spintronics. However, the synthesis and characterization of these organic radicals have been a formidable challenge due to their chemical instability arising from unpaired electrons. Here, we report a direct imaging of the surface chemical transformation of an organic monoradical synthesized via the monodehydrogenation of a chemically designed precursor. Bond-resolved scanning tunneling microscopy unambiguously resolves various products formed through a complex structural dissociation and rearrangement of organic monoradicals. Density functional theory calculations reveal detailed reaction pathways from the monoradical to different cyclized products. Our study provides unprecedented insights into complex surface reaction mechanisms of organic radical reactions at the single molecule level, which may guide the design of stable organic radicals for future quantum technology applications.

Molecular molds for regularizing Kondo states at atom/metal interfaces

Adsorption of magnetic transition metal atoms on a metal surface leads to the formation of Kondo states at the atom/metal interfaces. However, the significant influence of surrounding environment presents challenges for potential applications. In this work, we realize a novel strategy to regularize the Kondo states by moving a CoPc molecular mold on an Au(111) surface to capture the dispersed Co adatoms. The symmetric and ordered structures of the atom-mold complexes, as well as the strong dπ-π bonding between the Co adatoms and conjugated isoindole units, result in highly robust and uniform Kondo states at the Co/Au(111) interfaces. Even more remarkably, the CoPc further enables a fine tuning of Kondo states through the molecular-mold-mediated superexchange interactions between Co adatoms separated by more than 12 Å. Being highly precise, efficient and reproducible, the proposed molecular mold strategy may open a new horizon for the construction and control of nano-sized quantum devices.

Sensing the Spin of an Individual Ce Adatom

The magnetic moment of rare earth elements originates from electrons in the partially filled 4f orbitals. Accessing this moment electrically by scanning tunneling spectroscopy is hampered by shielding of outerlying orbitals. Here, we show that we can detect the magnetic moment of an individual Ce atom adsorbed on a Cu_{2}N ultrathin film on Cu(100) by using a sensor tip that has its apex functionalized with a Kondo screened spin system. We calibrate the sensor tip by deliberately coupling it to a well characterized Fe atom. Subsequently, we use the splitting of the tip's Kondo resonance when approaching a spectroscopically dark Ce atom to sense its magnetic moment.

Real space manifestations of coherent screening in atomic scale Kondo lattices

The interaction among magnetic moments screened by conduction electrons drives quantum phase transitions between magnetically ordered and heavy-fermion ground states. Here, starting from isolated magnetic impurities in the Kondo regime, we investigate the formation of the finite size analogue of a heavy Fermi liquid. We build regularly-spaced chains of Co adatoms on a metallic surface by atomic manipulation. Scanning tunneling spectroscopy is used to obtain maps of the Kondo resonance intensity with sub-atomic resolution. For sufficiently small interatomic separation, the spatial distribution of Kondo screening does not coincide with the position of the adatoms. It also develops enhancements at both edges of the chains. Since we can rule out any other interaction between Kondo impurities, this is explained in terms of the indirect hybridization of the Kondo orbitals mediated by a coherent electron gas, the mechanism that causes the emergence of heavy quasiparticles in the thermodynamic limit.

Topological Fano Resonances

The Fano resonance is a widespread wave scattering phenomenon associated with a peculiar asymmetric and ultrasharp line shape, which has found applications in a large variety of prominent optical devices. While its substantial sensitivity to geometrical and environmental changes makes it the cornerstone of efficient sensors, it also renders the practical realization of Fano-based systems extremely challenging. Here, we introduce the concept of topological Fano resonance, whose ultrasharp asymmetric line shape is guaranteed by design and protected against geometrical imperfections, yet remaining sensitive to external parameters. We report the experimental observation of such resonances in an acoustic system, and demonstrate their inherent robustness to geometrical disorder. Such topologically protected Fano resonances, which can also be found in microwave, optical, and plasmonic systems, open up exciting frontiers for the generation of various reliable wave-based devices including low-threshold lasers, perfect absorbers, ultrafast switches or modulators, and highly accurate interferometers, by circumventing the performance degradations caused by inadvertent fabrication flaws.

Simulation of inelastic spin flip excitations and Kondo effect in STM spectroscopy of magnetic molecules on metal substrates

Single-ion magnetic anisotropy in molecular magnets leads to spin flip excitations that can be measured by inelastic scanning tunneling microscope (STM) spectroscopy. Here I present a semi ab initio scheme to compute the spectral features associated with inelastic spin flip excitations and Kondo effect of single molecular magnets. To this end density functional theory calculations of the molecule on the substrate are combined with more sophisticated many-body techniques for solving the Anderson impurity problem of the spin-carrying orbitals of the magnetic molecule coupled to the rest of the system, containing a phenomenological magnetic anisotropy term. For calculating the STM spectra an exact expression for the [Formula: see text] in the ideal STM limit, when the coupling to the STM tip becomes negligibly small, is derived. In this limit the [Formula: see text] is simply related to the spectral function of the molecule-substrate system. For the case of an Fe porphyrin molecule on the Au(1 1 1) substrate, the calculated STM spectra are in good agreement with recently measured STM spectra, showing the typical step features at finite bias associated with spin flip excitation of a spin-1 quantum magnet. For the case of Kondo effect in Mn porphyrin on Au(1 1 1), the agreement with the experimental spectra is not as good due to the neglect of quantum interference in the tunneling.

On-surface structural and electronic properties of spontaneously formed Tb2Pc3 single molecule magnets

The single molecule magnet (SMM) bis(phthalocyaninato)terbium(iii) (TbPc2) has received significant and increasing attention as an exemplar system for realizing molecule-based spin electronics. Attaining higher nuclearity via multi-decker TbPc systems has remained an outstanding challenge, as known examples of Tb2Pc3 systems are only those containing Pc rings with substituents (e.g. alkyl, alkoxyl). Here we report on the spontaneous formation of Tb2Pc3 species from TbPc2 precursors via sublimation in ultrahigh vacuum (UHV) onto an Ag(111) surface. The presence of Tb2Pc3 molecules on the surface are inspected using scanning probe microscopy with submolecular resolution supported by density functional theory (DFT) calculations and additional chemical analysis. We observe the selective presence of a Kondo resonance (30 K) in the Tb2Pc3 species, that we attribute to differences in the orientation of the internal molecular ligands. Formation of triple-decker complexes offers new possibilities to study and control magnetic interactions not accessible with standard TbPc2 molecules.

Precise Control of Local Spin States in an Adsorbed Magnetic Molecule with an STM Tip: Theoretical Insights from First-Principles-Based Simulation

The precise tuning of local spin states in adsorbed organometallic molecules by a mechanically controlled scanning tunneling microscope (STM) tip has become a focus of recent experiments. However, the underlying mechanisms remain somewhat unclear. We investigate theoretically the STM tip control of local spin states in a single iron(II) porphyrin molecule adsorbed on the Pb(111) substrate. A combined density functional theory and hierarchical equations of motion approach is employed to simulate the tip tuning process in conjunction with the complete active space self-consistent field method for accurate computation of magnetic anisotropy. Our first-principles-based simulation accurately reproduces the tuning of magnetic anisotropy realized in experiment. Moreover, we elucidate the evolution of geometric and electronic structures of the composite junction and disclose the delicate competition between the Kondo resonance and local spin excitation. The understanding and insight provided by the first-principles-based simulation may help to realize more fascinating quantum state manipulations.

Ligand-Induced Energy Shift and Localization of Kondo Resonances in Cobalt-Based Complexes on Cu(111)

Magnetic sandwich complexes are of particular interest for molecular spintronics. Using scanning tunneling microscopy, we evidence the successful deposition of 1,3,5-tris(η⁶-borabenzene-η⁵-cyclopentadienylcobalt) benzene, a molecule composed of three connected magnetic sandwich units, on Cu(111). Scanning tunneling spectra reveal two distinct spatial-dependent narrow resonances close to the Fermi level for the trimer molecules as well as for molecular fragments composed of one and two magnetic units. With the help of density functional theory, these resonances are interpreted as two Kondo resonances originating from two distinct nondegenerate d-like orbitals. These Kondo resonances are found to have defined spatial extents dictated by the hybridization of the involved orbitals with that of the ligands. These results opens promising perspectives for investigating complex Kondo systems composed of several "Kondo" orbitals.

Anomalous Kondo resonance mediated by semiconducting graphene nanoribbons in a molecular heterostructure

Kondo resonances in heterostructures formed by magnetic molecules on a metal require free host electrons to interact with the molecular spin and create delicate many-body states. Unlike graphene, semiconducting graphene nanoribbons do not have free electrons due to their large bandgaps, and thus they should electronically decouple molecules from the metal substrate. Here, we observe unusually well-defined Kondo resonances in magnetic molecules separated from a gold surface by graphene nanoribbons in vertically stacked heterostructures. Surprisingly, the strengths of Kondo resonances for the molecules on graphene nanoribbons appear nearly identical to those directly adsorbed on the top, bridge and threefold hollow sites of Au(111). This unexpectedly strong spin-coupling effect is further confirmed by density functional calculations that reveal no spin–electron interactions at this molecule-gold substrate separation if the graphene nanoribbons are absent. Our findings suggest graphene nanoribbons mediate effective spin coupling, opening a way for potential applications in spintronics.

Semiconducting graphene nanoribbon provides a platform for band-gap engineering desired for electronic and optoelectronic applications. Here, Li et al. show that graphene nanoribbon can effectively mediate the interaction of molecular magnetic moment and electronic spin in underlying metallic substrates.

A gateway towards non-collinear spin processing using three-atom magnets with strong substrate coupling

A cluster of a few magnetic atoms on the surface of a nonmagnetic substrate is one suitable realization of a bit for spin-based information technology. The prevalent approach to achieve magnetic stability is decoupling the cluster spin from substrate conduction electrons in order to suppress destabilizing spin-flips. However, this route entails less flexibility in tailoring the coupling between the bits needed for spin-processing. Here, we use a spin-resolved scanning tunneling microscope to write, read, and store spin information for hours in clusters of three atoms strongly coupled to a substrate featuring a cloud of non-collinearly polarized host atoms, a so-called non-collinear giant moment cluster. The giant moment cluster can be driven into a Kondo screened state by simply moving one of its atoms to a different site. Using the exceptional atomic tunability of the non-collinear substrate mediated Dzyaloshinskii–Moriya interaction, we propose a logical scheme for a four-state memory.

Information technology based on few atom magnets requires both long spin-energy relaxation times and flexible inter-bit coupling. Here, the authors show routes to manipulate information in three-atom clusters strongly coupled to substrate electrons by exploiting Dzyaloshinskii–Moriya interactions.

Kondo blockade due to quantum interference in single-molecule junctions

Molecular electronics offers unique scientific and technological possibilities, resulting from both the nanometre scale of the devices and their reproducible chemical complexity. Two fundamental yet different effects, with no classical analogue, have been demonstrated experimentally in single-molecule junctions: quantum interference due to competing electron transport pathways, and the Kondo effect due to entanglement from strong electronic interactions. Here we unify these phenomena, showing that transport through a spin-degenerate molecule can be either enhanced or blocked by Kondo correlations, depending on molecular structure, contacting geometry and applied gate voltages. An exact framework is developed, in terms of which the quantum interference properties of interacting molecular junctions can be systematically studied and understood. We prove that an exact Kondo-mediated conductance node results from destructive interference in exchange-cotunneling. Nonstandard temperature dependences and gate-tunable conductance peaks/nodes are demonstrated for prototypical molecular junctions, illustrating the intricate interplay of quantum effects beyond the single-orbital paradigm.

Ensemble Control of Kondo Screening in Molecular Adsorbates

Switching the magnetic properties of organic semiconductors on a metal surface has thus far largely been limited to molecule-by-molecule tip-induced transformations in scanned probe experiments. Here we demonstrate with molecular resolution that collective control of activated Kondo screening can be achieved in thin-films of the organic semiconductor titanyl phthalocyanine on Cu(110) to obtain tunable concentrations of Kondo impurities. Using low-temperature scanning tunneling microscopy and spectroscopy, we show that a thermally activated molecular distortion dramatically shifts surface-molecule coupling and enables ensemble-level control of Kondo screening in the interfacial spin system. This is accompanied by the formation of a temperature-dependent Abrikosov-Suhl-Kondo resonance in the local density of states of the activated molecules. This enables coverage-dependent control over activation to the Kondo screening state. Our study thus advances the versatility of molecular switching for Kondo physics and opens new avenues for scalable bottom-up tailoring of the electronic structure and magnetic texture of organic semiconductor interfaces at the nanoscale.

Two-Orbital Kondo Screening in a Self-Assembled Metal-Organic Complex

Iron atoms adsorbed on a Cu(111) surface and buried under polyphenyl dicarbonitrile molecules exhibit strongly spatial anisotropic Kondo features with directionally dependent Kondo temperatures and line shapes, as evidenced by scanning tunneling spectroscopy. First-principles calculations find nearly full polarization for the half-filled Fe 3d_xz and 3d_yz orbitals, which therefore can give rise to Kondo screening with the experimentally observed directional dependence and distinct Kondo temperatures. X-ray absorption spectroscopy and X-ray magnetic circular dichroism measurements confirm that the spin in both channels is effectively Kondo-screened. At ideal Fe coverage, these two-orbital Kondo impurities are arranged in a self-assembled honeycomb superlattice.

Theory of scanning tunneling spectroscopy: from Kondo impurities to heavy fermion materials

Kondo systems ranging from the single Kondo impurity to heavy fermion materials present us with a plethora of unconventional properties whose theoretical understanding is still one of the major open problems in condensed matter physics. Over the last few years, groundbreaking scanning tunneling spectroscopy (STS) experiments have provided unprecedented new insight into the electronic structure of Kondo systems. Interpreting the results of these experiments-the differential conductance and the quasi-particle interference spectrum-however, has been complicated by the fact that electrons tunneling from the STS tip into the system can tunnel either into the heavy magnetic moment or the light conduction band states. In this article, we briefly review the theoretical progress made in understanding how quantum interference between these two tunneling paths affects the experimental STS results. We show how this theoretical insight has allowed us to interpret the results of STS experiments on a series of heavy fermion materials providing detailed knowledge of their complex electronic structure. It is this knowledge that is a conditio sine qua non for developing a deeper understanding of the fascinating properties exhibited by heavy fermion materials, ranging from unconventional superconductivity to non-Fermi-liquid behavior in the vicinity of quantum critical points.

The Kondo tip decorated by the Co atom

The Kondo effect of single Co adatoms on Ru(0001) is detected with two different kinds of co-decorated tip (Kondo tip) by using low temperature scanning tunneling microscopy and scanning tunneling spectroscopy. We call the relatively separated two magnetic impurities in the tunneling region 'two Kondo system' to distinguish it from the 'two-impurity Kondo system'. We find that the artificially constructed Kondo tips can be generally categorized into two types of Kondo resonances, which have distinct Fano line shapes with quantum interference factor |q| ≫ 1 and |q| ∼ 1, respectively. The tunneling spectra of six constructed two Kondo systems can be well fitted by summing the two Fano resonances of the two subsystems and a linear background. More interestingly, by extracting the amplitudes of the two Fano resonances in the spectra, we find that the electron transmission of such a two Kondo system in the tunneling region is dominated by the quantum interference of the Kondo tip, which is directly related to the geometric configuration of the adsorbed Kondo atom on the tip.

Kondo Resonance of a Co Atom Exchange Coupled to a Ferromagnetic Tip

The Kondo effect of a Co atom on Cu(100) was investigated with a low-temperature scanning tunneling microscope using a monoatomically sharp nickel tip. Upon a tip-Co contact, the differential conductance spectra exhibit a spin-split asymmetric Kondo resonance. The computed ab initio value of the exchange coupling is too small to suppress the Kondo effect, but sufficiently large to produce the splitting observed. A quantitative analysis of the line shape using the numerical renormalization group technique indicates that the junction spin polarization is weak.

Asymmetry parameter of peaked Fano line shapes

The spectroscopic line shape of electronic and vibrational excitations is ubiquitously described by a Fano profile. In the case of nearly symmetric and peaked Fano line shapes, the fit of the conventional Fano function to experimental data leads to difficulties in unambiguously extracting the asymmetry parameter, which may vary over orders of magnitude without degrading the quality of the fit. Moreover, the extracted asymmetry parameter depends on initially guessed values. Using the spectroscopic signature of the single-Co Kondo effect on Au(110) the ambiguity of the extracted asymmetry parameter is traced to the highly symmetric resonance profile combined with the inevitable scattering of experimental data. An improved parameterization of the conventional Fano function is suggested that enables the nonlinear optimization in a reduced parameter space. In addition, the presence of a global minimum in the sum of squared residuals and thus the independence of start parameters may conveniently be identified in a two-dimensional plot. An angular representation of the asymmetry parameter is suggested in order to reliably determine uncertainty margins via linear error propagation.

Metallic, magnetic and molecular nanocontacts

Scanning tunnelling microscopy and break-junction experiments realize metallic and molecular nanocontacts that act as ideal one-dimensional channels between macroscopic electrodes. Emergent nanoscale phenomena typical of these systems encompass structural, mechanical, electronic, transport, and magnetic properties. This Review focuses on the theoretical explanation of some of these properties obtained with the help of first-principles methods. By tracing parallel theoretical and experimental developments from the discovery of nanowire formation and conductance quantization in gold nanowires to recent observations of emergent magnetism and Kondo correlations, we exemplify the main concepts and ingredients needed to bring together ab initio calculations and physical observations. It can be anticipated that diode, sensor, spin-valve and spin-filter functionalities relevant for spintronics and molecular electronics applications will benefit from the physical understanding thus obtained.

Electron–phonon coupling in engineered magnetic molecules

We probe electron–phonon coupling in CoTPyP and CrTPyP synthesized magnetic molecules. Low temperatures STS reveals pronounced Kondo resonances at zero bias in both molecules and additional Kondo resonance replicas observed at higher voltages in vibrating CoTPyP molecules.

Switching Molecular Kondo Effect via Supramolecular Interaction

We apply supramolecular assembly to control the adsorption configuration of Co-porphyrin molecules on Au(111) and Cu(111) surfaces. By means of cryogenic scanning tunneling microscopy, we reveal that the Kondo effect associated with the Co center is absent or present in different supramolecular systems. We perform first-principles calculations to obtain spin-polarized electronic structures and compute the Kondo temperatures using the Anderson impurity model. The switching behavior is traced to varied molecular adsorption heights in different supramolecular structures. These findings unravel that a competition between intermolecular interactions and molecule-substrate interactions subtly regulates the molecular Kondo effect in supramolecular systems.

Modulation of the molecular spintronic properties of adsorbed copper corroles

The ability to modulate the spin states of adsorbed molecules is in high demand for molecular spintronics applications. Here, we demonstrate that the spin state of a corrole complex can be tuned by expanding its fused ring as a result of the modification to the d-π interaction between the metal and ligand. A bicyclo[2.2.2]octadiene-fused copper corrole can readily be converted into a tetrabenzocorrole radical on an Au(111) substrate during the sublimation process. In the scanning tunnelling spectroscopy spectrum, a sharp Kondo resonance appears near the Fermi level on the corrole ligand of the tetrabenzocorrole molecule. In contrast, a non-fused-ring-expanded copper corrole molecule, copper 5,10,15-triphenylcorrole, shows no such Kondo feature. Mapping of the Kondo resonance demonstrates that the spin distribution of the tetrabenzocorrole molecule can be further modified by the rotation of the meso-aryl groups, in a manner that could lead to applications in molecular spintronics.

Theory for STM images of resonances in the near-field regime: application to adsorbates and local defects on graphene

We analyze the STM current through electronic resonances on a substrate as a function of tip-surface distance. We show that when the tip approaches the surface a maximum of the density of states of the electronic resonance at some energy can lead to a dip of the STM signal dI/dV. This phenomenon is a Fano effect resulting from the coupling of the electronic states of the STM tip with the resonance. In graphene such resonances can be produced by local defects or adsorbates and we analyze the cases of top and hollow configurations of adsorbates.

Revealing the atomic site-dependent g factor within a single magnetic molecule via the extended Kondo effect

The site-dependent g factor of a single magnetic molecule, with intramolecular resolution, is demonstrated for the first time by low-temperature, high-magnetic-field scanning tunneling microscopy of dehydrogenated Mn-phthalocyanine molecules on Au(111). This is achieved by exploring the magnetic-field dependence of the extended Kondo effect at different atomic sites of the molecule. Importantly, an inhomogeneous distribution of the g factor inside a single molecule is revealed. Our results open up a new route to access local spin properties within a single molecule.

Interplay between the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida interaction

The interplay between the Ruderman-Kittel-Kasuya-Yosida interaction and the Kondo effect is expected to provide the driving force for the emergence of many phenomena in strongly correlated electron materials. Two magnetic impurities in a metal are the smallest possible system containing all these ingredients and define a bottom-up approach towards a long-term understanding of concentrated/dense systems. Here we report on the experimental and theoretical investigation of iron dimers buried below a Cu(100) surface by means of low-temperature scanning tunnelling spectroscopy combined with density functional theory and numerical renormalization group calculations. The Kondo effect, in particular the width of the Abrikosov-Suhl resonance, is strongly altered or even suppressed due to magnetic coupling between the impurities. It oscillates as a function of dimer separation revealing that it is related to indirect exchange interactions mediated by the conduction electrons.

Inducing magnetism in pure organic molecules by single magnetic atom doping

We report on in situ chemical reactions between an organic trimesic acid (TMA) ligand and a Co atom center. By varying the substrate temperature, we are able to explore the Co-TMA interactions and create novel magnetic complexes that preserve the chemical structure of the ligands. Using scanning tunneling microscopy and spectroscopy combined with density functional theory calculations, we elucidate the structure and the properties of the newly synthesized complex at atomic or molecular size level. Hybridization between the atomic orbitals of the Co and the π orbitals of the ligand results in a delocalized spin distribution onto the TMA. The here demonstrated possibility to conveniently magnetize such versatile molecules opens up new potential applications for TMAs in molecular spintronics.

Relevance of hybridization and filling of 3d orbitals for the Kondo effect in transition metal phthalocyanines

Magnetic organic molecules, such as 3d transition metal phthalocyanines (TMPc), exhibit properties which make them promising candidates for future applications in magnetic data storage or spin-based data processing. Due to their small size, however, TMPc molecules are prone to quantum effects. For example, the interaction of uncompensated molecular spins with conduction electrons of the substrate may lead to the formation of a many-body singlet state, which gives rise to the so-called Kondo effect. Although the Kondo effect of TMPc molecules has been the object of several investigations, a consistent picture to describe under which conditions a Kondo state is formed is still missing. Here, we study the Kondo properties of MnPc on Ag(001) by means of the low-temperature scanning tunneling spectroscopy (LT-STS) measurements. Differential conductance dI/dU spectra reveal a zero-bias peak that is localized on the Mn ion site. Ab initio calculations combined with a many-body treatment of the multiorbital interaction show that the local Hund coupling favors the high-spin configuration on the 3d shell of the central TM atom. Therefore, each orbital gets close to its individual half-filling creating the necessary condition for many of the 3d orbitals to contribute to the observed Kondo resonance. This, however, happens only for the 3dz(2) orbital, whose hybridization to the substrate is much stronger than for the other orbitals thanks to its shape and its orientation.

Temperature and magnetic field dependence of a Kondo system in the weak coupling regime

The Kondo effect arises due to the interaction between a localized spin and the electrons of a surrounding host. Studies of individual magnetic impurities by scanning tunneling spectroscopy have renewed interest in Kondo physics; however, a quantitative comparison with theoretical predictions remained challenging. Here we show that the zero-bias anomaly detected on an organic radical weakly coupled to a Au (111) surface can be described with astonishing agreement by perturbation theory as originally developed by Kondo 60 years ago. Our results demonstrate that Kondo physics can only be fully conceived by studying both temperature and magnetic field dependence of the resonance. The identification of a spin 1/2 Kondo system is of relevance not only as a benchmark for predictions for Kondo physics but also for correlated electron materials in general.

Kondo conductance across the smallest spin 1/2 radical molecule

Molecular contacts are generally poorly conducting because their energy levels tend to lie far from the Fermi energy of the metal contact, necessitating undesirably large gate and bias voltages in molecular electronics applications. Molecular radicals are an exception because their partly filled orbitals undergo Kondo screening, opening the way to electron passage even at zero bias. Whereas that phenomenon has been experimentally demonstrated for several complex organic radicals, quantitative theoretical predictions have not been attempted so far. It is therefore an open question whether and to what extent an ab initio-based theory is able to make accurate predictions for Kondo temperatures and conductance lineshapes. Choosing nitric oxide (NO) as a simple and exemplary spin 1/2 molecular radical, we present calculations based on a combination of density functional theory and numerical renormalization group (DFT+NRG), predicting a zero bias spectral anomaly with a Kondo temperature of 15 K for NO/Au(111). A scanning tunneling spectroscopy study is subsequently carried out to verify the prediction, and a striking zero bias Kondo anomaly is confirmed, still quite visible at liquid nitrogen temperatures. Comparison shows that the experimental Kondo temperature of about 43 K is larger than the theoretical one, whereas the inverted Fano lineshape implies a strong source of interference not included in the model. These discrepancies are not a surprise, providing in fact an instructive measure of the approximations used in the modeling, which supports and qualifies the viability of the density functional theory and numerical renormalization group approach to the prediction of conductance anomalies in larger molecular radicals.

Excitation spectra of transition-metal atoms on the Ag (100) surface controlled by Hund's exchange

We report photoemission experiments revealing the valence electron spectral function of Mn, Fe, Co, and Ni atoms on the Ag (100) surface. The series of spectra shows splittings of higher energy features which decrease with the filling of the 3d shell and a highly nonmonotonic evolution of spectral weight near the Fermi edge. First principles calculations demonstrate that two manifestations of Hund's exchange J are responsible for this evolution. First, there is a monotonic reduction of the effective exchange splittings with increasing filling of the 3d shell. Second, the amount of charge fluctuations and, thus, the weight of quasiparticle peaks at the Fermi level varies nonmonotonically through this 3d series due to a distinct occupancy dependence of effective charging energies U(eff).

Surface-Supported Hydrocarbon π Radicals Show Kondo Behavior

Stable hydrocarbon radicals are utilized as spin standards and prototype metal-free molecular magnets able to withstand ambient conditions. Our study presents experimental results obtained with submolecular resolution by scanning tunneling microscopy and spectroscopy from monomers and dimers of stable hydrocarbon π radicals adsorbed on the Au(111) surface at 7-50 K. We provide conclusive evidence of the preservation of the radical spin-1/2 state, aiming to establish α,γ-bisdiphenylene-β-phenylallyl (BDPA) on Au(111) as a novel Kondo system, where the impurity spin is localized in a metal-free π molecular orbital of a neutral radical state in gas phase preserved on a metal support.

Easy-axis ferromagnetic chain on a metallic surface

The phases and excitation spectrum of an easy-axis ferromagnetic chain of S = 1/2 magnetic impurities built on the top of a clean metallic surface are studied. As a function of the (Kondo) coupling to the metallic surface and at low temperatures, the spin chain exhibits a quantum phase transition from an Ising ferromagnetic phase with long-range order to a paramagnetic phase where quantum fluctuations destroy the magnetic order. In the paramagnetic phase, the system consists of a chain of Kondo singlets where the impurities are completely screened by the metallic host. In the ferromagnetic phase, the excitations above the Ising gap are damped magnons, with a finite lifetime arising due to the coupling to the substrate. We discuss the experimental consequences of our results to spin-polarized electron energy loss spectroscopy, and we finally analyze possible extensions to spin chains with S > 1/2.