Kondo resonances in molecular devices

Many-body Effects on Electronic Transport in Molecular Junctions: A Quantum Perspective

This concept delves into quantum particle transport at the nanoscale, with a particular focus on how electrons move through molecular circuits. The thriving field of single molecular electronics benefits from the unique electrical and other properties of nanostructures. It concentrates on single molecular junctions that serve as bridges between electrodes. In this context, the electronic correlation-induced many-body effect gives rise to resonant states. These states, along with conductance, depend on electron spin. Thus, the field acts as a bridge between quantum and macroscopic worlds, unveiling unique behaviors of electrons. Additionally, external factors, such as magnetic fields and voltages, offer means to control the electron correlation in these junctions.

From Solution to Surface: Persistence of the Diradical Character of a Diindenoanthracene Derivative on a Metallic Substrate

Organic diradicals are envisioned as elementary building blocks for designing a new generation of spintronic devices and have been used in constructing prototypical field effect transistors and nonlinear optical devices. Open-shell systems, however, are also reactive, thus requiring design strategies to "protect" their radical character from the environment, especially when they are embedded in solid-state devices. Here, we report the persistence on a metallic surface of the diradical character of a diindeno[b,i]anthracene (DIAn) core protected by bulky end-groups. Our scanning tunneling spectroscopy measurements on single-molecules detected singlet-triplet excitations that were absent for DIAn species packed in assembled structures. Density functional theory simulations unravel that the molecular geometry on the metal substrate can crucially modify the value of the singlet-triplet gap via the delocalization of the radical sites. The persistence of the diradical character over metallic substrates is a promising finding for integrating radical-based materials into functional devices.

Electrically Controlled Bimetallic Junctions for Atomic-Scale Electronics

Forming atomic-scale contacts with attractive geometries and material compositions is a long-term goal of nanotechnology. Here, we show that a rich family of bimetallic atomic-contacts can be fabricated in break-junction setups. The structure and material composition of these contacts can be controlled by atomically precise electromigration, where the metal types of the electron-injecting and sink electrodes determine the type of atoms added to, or subtracted from, the contact structure. The formed bimetallic structures include, for example, platinum and aluminum electrodes bridged by an atomic chain composed of platinum and aluminum atoms as well as iron-nickel single-atom contacts that act as a spin-valve break junction without the need for sophisticated spin-valve geometries. The versatile nature of atomic contacts in bimetallic junctions and the ability to control their structure by electromigration can be used to expand the structural variety of atomic and molecular junctions and their span of properties.

Radical Single-Molecule Junctions

Radicals are unique molecular systems for applications in electronic devices due to their open-shell electronic structures. Radicals can function as good electrical conductors and switches in molecular circuits while also holding great promise in the field of molecular spintronics. However, it is both challenging to create stable, persistent radicals and to understand their properties in molecular junctions. The goal of this Perspective is to address this dual challenge by providing design principles for the synthesis of stable radicals relevant to molecular junctions, as well as offering current insight into the electronic properties of radicals in single-molecule devices. By exploring both the chemical and physical properties of established radical systems, we will facilitate increased exploration and development of radical-based molecular systems.

Structural Regulation of Mechanical Gating in Molecular Junctions

In contrast to silicon-based transistors, single-molecule junctions can be gated by simple mechanical means. Specifically, charge can be transferred between the junction's electrodes and its molecular bridge when the interelectrode distance is modified, leading to variations in the electronic transport properties of the junction. While this effect has been studied extensively, the influence of the molecular orientation on mechanical gating has not been addressed, despite its potential influence on the gating effectiveness. Here, we show that the same molecular junction can experience either clear mechanical gating or none, depending on the molecular orientation in the junctions. The effect is found in silver-ferrocene-silver break junctions and analyzed in view of ab initio and transport calculations, where the influence of the molecular orbital geometry on charge transfer to or from the molecule is revealed. The molecular orientation is thus a new degree of freedom that can be used to optimize mechanically gated molecular junctions.

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.

Magnetic Fingerprints in an All-Organic Radical Molecular Break Junction

Polycyclic aromatic hydrocarbons radicals are organic molecules with a nonzero total magnetic moment. Here, we report on charge-transport experiments with bianthracene-based radicals using a mechanically controlled break junction technique at low temperatures (6 K). The conductance spectra demonstrate that the magnetism of the diradical is preserved in solid-state devices and that it manifests itself either in the form of a Kondo resonance or inelastic electron tunneling spectroscopy signature caused by spin-flip processes. The magnetic fingerprints depend on the exact configuration of the molecule in the junction; this picture is supported by reference measurements on a radical molecule with the same backbone but with one free spin, in which only Kondo anomalies are observed. The results show that the open-shell structures based on the bianthracene core are interesting systems to study spin-spin interactions in solid-state devices, and this may open the way to control them either electrically or by mechanical strain.

Unravelling the robustness of magnetic anisotropy of a nickelocene molecule in different environments: a first-principles-based study

Recent scanning tunneling spectroscopy with single metallocene molecule-functionalized tips have proved to be a powerful tool to probe and control individual spins and spin-spin exchange interactions due to the robustness of the magnetic properties of the metallocene molecule in different surroundings. However, accurate prediction of such robustness at a first-principles-based level by the conventional density functional theory (DFT) has remained challenging. In this paper, we have performed a detailed investigation of the evolution of electronic and magnetic properties of a nickelocene molecule (NiCp₂) in different environments, i.e., free-standing, adsorbed on Cu(100) and as a functionalized tip apex. Using an embedding method, which combines DFT and the complete active space self-consistent field (CASSCF) method recently developed, we demonstrate that the nickelocene molecule almost preserves its spin and magnetic anisotropy upon adsorption on Cu(100), and also in the position of the tip apex. In particular, the cyclic π* orbital of the Cp rings could hybridize with the singly occupied d_π orbitals of the Ni center of the molecule, protecting these orbitals from external states. Hence the molecular spin maintains S = 1, the same as in the free-standing case, and its magnetic anisotropy is also robust with energies of 3.56, 3.34, and 3.51 meV in free-standing, adsorbed on Cu(100), and functionalized tip apex states, respectively, in good agreement with previous theoretical and experimental results. This work thus provides a first-principles-based understanding of the relevant experiments. Such agreement between theoretical simulations and experimental measurements highlights the potential usefulness of the method for investigating the local electronic and spin states of organometallic molecule-surface composite systems.

Interplay between Magnetoresistance and Kondo Resonance in Radical Single-Molecule Junctions

We report transport measurements on tunable single-molecule junctions of the organic perchlorotrityl radical molecule, contacted with gold electrodes at low temperature. The current-voltage characteristics of a subset of junctions shows zero-bias anomalies due to the Kondo effect and in addition elevated magnetoresistance (MR). Junctions without Kondo resonance reveal a much stronger MR. Furthermore, we show that the amplitude of the MR can be tuned by mechanically stretching the junction. On the basis of these findings, we attribute the high MR to an interference effect involving spin-dependent scattering at the metal-molecule interface and assign the Kondo effect to the unpaired spin located in the center of the molecule in asymmetric junctions.

Correlation anisotropy driven Kosterlitz-Thouless-type quantum phase transition in a Kondo simulator

The precise manipulation of the quantum states of individual atoms/molecules adsorbed on metal surfaces is one of the most exciting frontiers in nanophysics, enabling us to realize novel single molecular logic devices and quantum information processing. Herein, by modeling an iron phthalocyanine molecule adsorbed on the Au(111) surface with a two-impurity Anderson model, we demonstrate that the quantum states of such a system could be adjusted by the uniaxial magnetic anisotropy D_z. For negative D_z, the ground state is dominated by a parallel configuration of the z component of local spins, whereas it turns to be an antiparallel one when D_z becomes positive. Interestingly, we found that these two phases are separated by a Kosterlitz-Thouless-type quantum phase transition, which is confirmed by the critical behaviors of the transmission coefficient and the local magnetic moment. Both phases are associated with spin correlation anisotropy, thus move against the Kondo effect. When the external magnetic field is applied, it first plays a role in compensating for the effect of D_z, and then it contributes significantly to the Zeeman effect for positive D_z, accompanied by the reappearance and the splitting of the Kondo peak, respectively. For fixed negative D_z, only the Zeeman behavior is revealed. Our results provide deep insights into the manipulation of the quantum phase within a single molecular junction.

Single-molecule nano-optoelectronics: insights from physics

Single-molecule optoelectronic devices promise a potential solution for miniaturization and functionalization of silicon-based microelectronic circuits in the future. For decades of its fast development, this field has made significant progress in the synthesis of optoelectronic materials, the fabrication of single-molecule devices and the realization of optoelectronic functions. On the other hand, single-molecule optoelectronic devices offer a reliable platform to investigate the intrinsic physical phenomena and regulation rules of matters at the single-molecule level. To further realize and regulate the optoelectronic functions toward practical applications, it is necessary to clarify the intrinsic physical mechanisms of single-molecule optoelectronic nanodevices. Here, we provide a timely review to survey the physical phenomena and laws involved in single-molecule optoelectronic materials and devices, including charge effects, spin effects, exciton effects, vibronic effects, structural and orbital effects. In particular, we will systematically summarize the basics of molecular optoelectronic materials, and the physical effects and manipulations of single-molecule optoelectronic nanodevices. In addition, fundamentals of single-molecule electronics, which are basic of single-molecule optoelectronics, can also be found in this review. At last, we tend to focus the discussion on the opportunities and challenges arising in the field of single-molecule optoelectronics, and propose further potential breakthroughs.

Construction and physical properties of low-dimensional structures for nanoscale electronic devices

Over the past decades, construction of nanoscale electronic devices with novel functionalities based on low-dimensional structures, such as single molecules and two-dimensional (2D) materials, has been rapidly developed. To investigate their intrinsic properties for versatile functionalities of nanoscale electronic devices, it is crucial to precisely control the structures and understand the physical properties of low-dimensional structures at the single atomic level. In this review, we provide a comprehensive overview of the construction of nanoelectronic devices based on single molecules and 2D materials and the investigation of their physical properties. For single molecules, we focus on the construction of single-molecule devices, such as molecular motors and molecular switches, by precisely controlling their self-assembled structures on metal substrates and charge transport properties. For 2D materials, we emphasize their spin-related electrical transport properties for spintronic device applications and the role that interfaces among 2D semiconductors, contact electrodes, and dielectric substrates play in the electrical performance of electronic, optoelectronic, and memory devices. Finally, we discuss the future research direction in this field, where we can expect a scientific breakthrough.

Single-Molecule Junction: A Reliable Platform for Monitoring Molecular Physical and Chemical Processes

Monitoring and manipulating the physical and chemical behavior of single molecules is an important development direction of molecular electronics that aids in understanding the molecular world at the single-molecule level. The electrical detection platform based on single-molecule junctions can monitor physical and chemical processes at the single-molecule level with a high temporal resolution, stability, and signal-to-noise ratio. Recently, the combination of single-molecule junctions with different multimodal control systems has been widely used to explore significant physical and chemical phenomena because of its powerful monitoring and control capabilities. In this review, we focus on the applications of single-molecule junctions in monitoring molecular physical and chemical processes. The methods developed for characterizing single-molecule charge transfer and spin characteristics as well as revealing the corresponding intrinsic mechanisms are introduced. Dynamic detection and regulation of single-molecule conformational isomerization, intermolecular interactions, and chemical reactions are also discussed in detail. In addition to these dynamic investigations, this review discusses the open challenges of single-molecule detection in the fields of physics and chemistry and proposes some potential applications in this field.

Trapping integrated molecular devices via a local transport circulation

Interactions between quantum systems and their environments may always result in inevitable decoherence. Isolation of the quantum system from the undesired environment noise brings us a great challenge for an...

Phase transitions induced by exchange coupling, magnetic field, and temperature in a strongly correlated molecular trimer with triangular topology

Regulating the physical properties such as the quantum phase and the Kondo effect of molecular electronic devices near critical points may play a key role in increasing the robustness of...

Quantum Circuit Rules for Molecular Electronic Systems: Where Are We Headed Based on the Current Understanding of Quantum Interference, Thermoelectric, and Molecular Spintronics Phenomena?

In this minireview, we discuss important aspects of the various quantum phenomena (such as quantum interference, spin-dependent charge transport, and thermoelectric effects) relevant in single-molecule charge transport and list some of the basic circuit rules devised for different molecular systems. These quantum phenomena, in conjunction with the existing empirical circuit rules, can help in predicting some of the structure-property relationships in molecular circuits. However, a universal circuit law that predicts the charge transport properties of a molecular circuit has not been derived yet. Having such law(s) will help to design and build a complex molecular device leading to exciting unique applications that are not possible with the traditional silicon-based technologies. Based on the existing knowledge in the literature, here we open the discussion on the possible future research directions for deriving unified circuit law(s) to predict the charge transport in complex single-molecule circuits.

A review of oligo(arylene ethynylene) derivatives in molecular junctions

Oligo(arylene ethynylene) (OAE) derivatives are the "workhorse" molecules of molecular electronics. Their ease of synthesis and flexibility of functionalisation mean that a diverse array of OAE molecular wires have been designed, synthesised and studied theoretically and experimentally in molecular junctions using both single-molecule and ensemble methods. This review summarises the breadth of molecular designs that have been investigated with emphasis on structure-property relationships with respect to the electronic conductance of OAEs. The factors considered include molecular length, connectivity, conjugation, (anti)aromaticity, heteroatom effects and quantum interference (QI). Growing interest in the thermoelectric properties of OAE derivatives, which are expected to be at the forefront of research into organic thermoelectric devices, is also explored.

Local decomposition of hybridization functions: Chemical insight into correlated molecular adsorbates

Hybridization functions are an established tool for investigating the coupling between a correlated subsystem (often a single transition metal atom) and its uncorrelated environment (the substrate and any ligands present). The hybridization function can provide valuable insight into why and how strong correlation features such as the Kondo effect can be chemically controlled in certain molecular adsorbates. To deepen this insight, we introduce a local decomposition of the hybridization function, based on a truncated cluster approach, enabling us to study individual effects on this function coming from specific parts of the systems (e.g., the surface, ligands, or parts of larger ligands). It is shown that a truncated-cluster approach can reproduce the Co 3d and Mn 3d hybridization functions from periodic boundary conditions in Co(CO)₄/Cu(001) and MnPc/Ag(001) qualitatively well. By locally decomposing the hybridization functions, it is demonstrated at which energies the transition metal atoms are mainly hybridized with the substrate or with the ligand. For the Kondo-active 3d_x²-y² orbital in Co(CO)₄/Cu(001), the hybridization function at the Fermi energy is substrate-dominated, so we can assign its enhancement compared with ligand-free Co to an indirect effect of ligand-substrate interactions. In MnPc/Ag(001), the same is true for the Kondo-active orbital, but for two other orbitals, there are both direct and indirect effects of the ligand, together resulting in such strong screening that their potential Kondo activity is suppressed. A local decomposition of hybridization functions could also be useful in other areas, such as analyzing the electrode self-energies in molecular junctions.

Kondo effect and RKKY interaction assisted by magnetic anisotropy in a frustrated magnetic molecular device at zero and finite temperature

Molecular magnetic compounds, which combine the advantages of nanoscale behaviors with the properties of bulk magnetic materials, are particularly attractive in the fields of high-density information storage and quantum computing. Before molecular electronic devices can be fabricated, a crucial task is the measurement and understanding of the transport behaviors. Herein, we consider a magnetic molecular trimer sandwiched between two metal electrodes, and, with the aid of the sophisticated full density matrix numerical renormalization group (FDM-NRG) technique, we study the effect of magnetic anisotropy on the charge transport properties, illustrated by the local density of states (LDOS, which is proportional to the differential conductance), the Kondo effect, and the temperature and inter-monomer hopping robustness. Three kinds of energy peaks are clarified in the LDOS: the Coulomb, the Kondo and the Ruderman-Kittel-Kasuya-Yosida (RKKY) peaks. The local magnetic moment and entropy go through four different regimes as the temperature decreases. The Kondo temperature TK could be described by a generalized Haldane's formula, revealing in detail the process where the local moment is partially screened by the itinerant electrons. A relationship between the width of the Kondo resonant peak WK and TK is built, ensuring the extraction of TK from WK in an efficient way. As the inter-monomer hopping integral varies, the ground state of the trimer changes from a spin quadruplet to a magnetically frustrated phase, then to an orbital spin singlet through two first order quantum phase transitions. In the first two phases, the Kondo peak in the transmission coefficient reaches its unitary limit, while in the orbital spin singlet, it is totally suppressed. We demonstrate that magnetic anisotropy may also induce the Kondo effect, even without Coulomb repulsion, hence it is replaceable in the many-body behaviours at low temperature.

Remote Mesoscopic Signatures of Induced Magnetic Texture in Graphene

Mesoscopic conductance fluctuations are a ubiquitous signature of phase-coherent transport in small conductors, exhibiting universal character independent of system details. In this Letter, however, we demonstrate a pronounced breakdown of this universality, due to the interplay of local and remote phenomena in transport. Our experiments are performed in a graphene-based interaction-detection geometry, in which an artificial magnetic texture is induced in the graphene layer by covering a portion of it with a micromagnet. When probing conduction at some distance from this region, the strong influence of remote factors is manifested through the appearance of giant conductance fluctuations, with amplitude much larger than e^{2}/h. This violation of one of the fundamental tenets of mesoscopic physics dramatically demonstrates how local considerations can be overwhelmed by remote signatures in phase-coherent conductors.

The Kondo Effect of a Molecular Tip As a Magnetic Sensor

A single molecule offers to tailor and control the probing capability of a scanning tunneling microscope when placed on the tip. With the help of first-principles calculations, we show that on-tip spin sensitivity is possible through the Kondo ground state of a spin S = 1/2 cobaltocene molecule. When attached to the tip apex, we observe a reproducible Kondo resonance, which splits apart upon tuning the exchange coupling of cobaltocene to an iron atom on the surface. The spin-split Kondo resonance provides quantitative information on the exchange field and on the spin polarization of the iron atom. We also demonstrate that molecular vibrations cause the emergence of Kondo side peaks, which, unlike the Kondo resonance, are sensitive to cobaltocene adsorption.

Synchronously voltage-manipulable spin reversing and selecting assisted by exchange coupling in a monomeric dimer with magnetic interface

The use of the molecular spin state as a quantum of next-generation information technology is receiving impressive research attention, within which the fundamental issues include manipulating the phase transition between the spin-up and -down states and generating spin polarized current. The spinterface between ferromagnetic electrodes and a molecular bridge represents one of the most intriguing elements in this context. Herein, by means of the celebrated numerical renormalization group technique, we present an original way to realize spin reversal in a monomeric dimer. Our scheme is based on the exchange interactions between electronic spins on one monomer and those on the other one or on the electrodes, which could be easily controlled through purely electronic technology. Through a careful engineering of the interfacial parameters, one of the monomers is devoted to the spin reversing, whereas the other one contributes to the spin selecting. The charge numbers of spin-up and -down electrons swap their respective occupancies at some particular points, indicating charge sensing between different spins. The competition between the spinterface and the molecular energy level results in charge oscillating in a single spin channel, which is unfavorable to the spin selecting. The observation may provide a prospective example for a multifunctional magnetoelectronics molecular device, which works without any external magnetic field.

Tunable giant magnetoresistance in a single-molecule junction

Controlling electronic transport through a single-molecule junction is crucial for molecular electronics or spintronics. In magnetic molecular devices, the spin degree-of-freedom can be used to this end since the magnetic properties of the magnetic ion centers fundamentally impact the transport through the molecules. Here we demonstrate that the electron pathway in a single-molecule device can be selected between two molecular orbitals by varying a magnetic field, giving rise to a tunable anisotropic magnetoresistance up to 93%. The unique tunability of the electron pathways is due to the magnetic reorientation of the transition metal center, resulting in a re-hybridization of molecular orbitals. We obtain the tunneling electron pathways by Kondo effect, which manifests either as a peak or a dip line shape. The energy changes of these spin-reorientations are remarkably low and less than one millielectronvolt. The large tunable anisotropic magnetoresistance could be used to control electronic transport in molecular spintronics.

Molecular electronics or spintronics relies on manipulating the electronic transport through microscopic molecule structures. Here the authors demonstrate the selective electron pathway in single-molecule device by magnetic field which enables a tunable anisotropic magnetoresistance up to 93%.

Exchange-dependent spin polarized transport and phase transition in a triple monomer molecule

Molecular junctions contribute significantly to the fundamental understanding of the quantum information technologies in molecular spintronics. In this paper, with the aid of the state of the art numerical renormalization group method, we find a triple monomer molecule structure with strong electron-electron interactions could be a potential candidate for a multifunctional spin polarizer when an external magnetic field along the z axis is applied. It is demonstrated that the polarizing scenarios depend closely on the inter-orbital exchange couplings, and results in several kinds of spin polarizers, e.g., the unidirectional, the bidirectional, the dual, and the ternary spin polarizers. We show in detail the related phase diagram, and conclude the Zeeman effect and the charge switching for the bonding, anti-bonding and non-bonding orbitals are responsible for the spin polarizing transport. We stress even when the energy levels are chosen beyond the Kondo regime, the structure still shows a promising platform for molecular spintronics components.

The Environment-Dependent Behavior of the Blatter Radical at the Metal-Molecule Interface

Stable organic radicals have potential applications for building organic spintronic devices. To fulfill this potential, the interface between organic radicals and metal electrodes must be well characterized. Here, through a combined effort that includes synthesis, scanning tunneling microscopy, X-ray spectroscopy, and single-molecule conductance measurements, we comprehensively probe the electronic interaction between gold metal electrodes and a benchtop stable radical-the Blatter radical. We find that despite its open-shell character and having a half-filled orbital close to the Fermi level, the radical is stable on a gold substrate under ultrahigh vacuum. We observe a Kondo resonance arising from the radical and spectroscopic signatures of its half-filled orbitals. By contrast, in solution-based single-molecule conductance measurements, the radical character is lost through oxidation with charge transfer occurring from the molecule to metal. Our experiments show that the stability of radical states can be very sensitive to the environment around the molecule.

Sub-5 nm Metal Nanogaps: Physical Properties, Fabrication Methods, and Device Applications

Sub-5 nm metal nanogaps have attracted widespread attention in physics, chemistry, material sciences, and biology due to their physical properties, including great plasmon-enhanced effects in light-matter interactions and charge tunneling, Coulomb blockade, and the Kondo effect under an electrical stimulus. These properties especially meet the needs of many cutting-edge devices, such as sensing, optical, molecular, and electronic devices. However, fabricating sub-5 nm nanogaps is still challenging at the present, and scaled and reliable fabrication, improved addressability, and multifunction integration are desired for further applications in commercial devices. The aim of this work is to provide a comprehensive overview of sub-5 nm nanogaps and to present recent advancements in metal nanogaps, including their physical properties, fabrication methods, and device applications, with the ultimate aim to further inspire scientists and engineers in their research.

Influence of Quantum Interference on the Thermoelectric Properties of Molecular Junctions

Molecular junctions offer unique opportunities for controlling charge transport on the atomic scale and for studying energy conversion. For example, quantum interference effects in molecular junctions have been proposed as an avenue for highly efficient thermoelectric power conversion at room temperature. Toward this goal, we investigated the effect of quantum interference on the thermoelectric properties of molecular junctions. Specifically, we employed oligo(phenylene ethynylene) (OPE) derivatives with a para-connected central phenyl ring ( para-OPE3) and meta-connected central ring ( meta-OPE3), which both covalently bind to gold via sulfur anchoring atoms located at their ends. In agreement with predictions from ab initio modeling, our experiments on both single molecules and monolayers show that meta-OPE3 junctions, which are expected to exhibit destructive interference effects, yield a higher thermopower (with ∼20 μV/K) compared with para-OPE3 (with ∼10 μV/K). Our results show that quantum interference effects can indeed be employed to enhance the thermoelectric properties of molecular junctions.

Electrostatic Gate Control in Molecular Transistors

Molecular transistors, in which single molecules serve as active channel components in a three-terminal device geometry, constitute the building blocks of molecular scale electronic circuits. To demonstrate such devices, a gate electrode has been incorporated in several test beds of molecular electronics. The frontier orbitals' alignments of a molecular transistor can be delicately tuned by modifying the molecular orbital energy with the gate electrode. In this review, we described electrostatic gate control of solid-state molecular transistors. In particular, we focus on recent experimental accomplishments in fabrication and characterization of molecular transistors.

Tuning the Kondo resonance in two-dimensional lattices of cerium molecular complexes

Cerium intermetallics have raised a lot of interest for the past forty years thanks to their very unusual and interesting electronic and magnetic properties. This can be explained by the peculiar electronic configuration of Ce (4f1) that allows different oxidation states leading to singular behavior such as quantum phase transitions, heavy-fermion behavior and the Kondo effect. In this work, we used a mixed-valence molecular analogue to study the Kondo effect down to the atomic scale by means of scanning tunneling microscopy/spectroscopy (STM/STS) for which new many-body effects are expected to emerge due to reduced dimensionality and specific chemical environment of the 4f-ion. For that purpose, double-decker molecular complexes hosting a Ce ion were synthesized and adsorbed onto Ag and Cu (111) surfaces forming two-dimensional lattices. As a result, we observed a zero-bias conductance resonance on Ag only indicative of a Kondo effect arising from the coupling between a molecular spin and the conducting electrons of the metallic surface. The emergence of the Kondo effect is discussed in terms of intermolecular and molecule/substrate interactions. This work expands the little knowledge to date on the structural and related electronic properties of Ce-based molecular systems on surfaces. In particular, it shows that Ce-based double deckers are good platforms to obtain insight into 4f-induced many-body effects down to the nanometer scale and in two-dimensional lattices. Moreover, this outcome has a strong impact for future applications of molecular devices in which both metals are commonly used as electrical contacts.

Abrupt Switching of Crystal Fields during Formation of Molecular Contacts

Magnetic molecules have the potential to be used as building blocks for bits in quantum computers. The spin states of the magnetic ion in the molecule can be represented by the effective spin Hamiltonian describing the zero field splitting (ZFS) of the magnetic states. We determined the ZFS of mechanically flexible metal-chelate molecules (Co, Ni, and Cu as metal ions) adsorbed on Cu₂N/Cu(100) by inelastic tunneling spectroscopy at temperatures down to 30 mK. When moving the tip toward the molecule, the tunneling current abruptly jumps to higher values, indicating the sudden deformation of the molecule bridging the tunneling junction. Hand in hand with the formation of the contact, an abrupt change of the ZFS occurs. This work also implies that ZFS expected in mechanical break junctions can drastically deviate from that of adsorbed molecules probed by other techniques.

Spin Control Induced by Molecular Charging in a Transport Junction

The ability of molecules to maintain magnetic multistability in nanoscale-junctions will determine their role in downsizing spintronic devices. While spin-injection from ferromagnetic leads gives rise to magnetoresistance in metallic nanocontacts, nonmagnetic leads probing the magnetic states of the junction itself have been considered as an alternative. Extending this experimental approach to molecular junctions, which are sensitive to chemical parameters, we demonstrate that the electron affinity of a molecule decisively influences its spin transport. We use a scanning tunneling microscope to trap a meso-substituted iron porphyrin, putting the iron center in an environment that provides control of its charge and spin states. A large electron affinity of peripheral ligands is shown to enable switching of the molecular S = 1 ground state found at low electron density to S = ¹/₂ at high density, while lower affinity keeps the molecule inactive to spin-state transition. These results pave the way for spin control using chemical design and electrical means.

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.

Enhanced Cooperativity in Supported Spin-Crossover Metal-Organic Frameworks

The impact of surface deposition on cooperativity is explored in Au(111)-supported self-assembled metal-organic frameworks (MOFs) based on Fe(II) ions. Using a thermodynamic model, we first demonstrate that dimensionality reduction combined with deposition on a metal surface is likely to deeply enhance the spin-crossover cooperativity, going from γ_3D = 16 K for the bulk material to γ_2D^supp = 386 K for its 2D supported derivative. On the basis of density functional theory, we then elucidate the electronic structure of a promising Fe-based MOF. A chemical strategy is proposed to turn a weakly interacting magnetic system into a strongly cooperative spin-crossover monolayer with γ_MOF^Au(111) = 83 K. These results open a promising route to the fabrication of cooperative materials based on SCO Fe(II) platforms.

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.

Controlling electronic access to the spin excitations of a single molecule in a tunnel junction

Spintronic phenomena underpin new device paradigms for data storage and sensing. Scaling these down to the single molecule level requires controlling the properties of current-carrying molecular orbitals to enable access to spin states through phenomena such as inelastic electron tunnelling. Here we show that the spintronic properties of a tunnel junction containing a single molecule can be controlled using the local environment as a pseudo-gate. For tunnelling through iron phthalocyanine (FePc) on an insulating copper nitride (Cu₂N) monolayer above Cu(001), we find that spin transitions may be strongly excited depending on the binding site of the central Fe atom. Different interactions between the Fe and the underlying Cu or N atoms shift the Fe d orbitals with respect to the Fermi energy and control the relative strength of the spin excitations; this effect is captured in a simple co-tunnelling model. This work demonstrates the importance of the atomic-scale environment for the development of single molecule spintronic devices.

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.

Large Magnetoresistance at Room Temperature in Organic Molecular Tunnel Junctions with Nonmagnetic Electrodes

We report room-temperature resistance changes of up to 30% under weak magnetic fields (0.1 T) for molecular tunnel junctions composed of oligophenylene thiol molecules, 1-2 nm in length, sandwiched between gold contacts. The magnetoresistance (MR) is independent of field orientation and the length of the molecule; it appears to be an interface effect. Theoretical analysis suggests that the source of the MR is a two-carrier (two-hole) interaction at the interface, resulting in spin coupling between the tunneling hole and a localized hole at the Au/molecule contact. Such coupling leads to significantly different singlet and triplet transmission barriers at the interface. Even weak magnetic fields impede spin relaxation processes and thus modify the ratio of holes tunneling via the singlet state versus the triplet state, which leads to the large MR. Overall, the experiments and analysis suggest significant opportunities to explore large MR effects in molecular tunnel junctions based on widely available molecules.

Sub-molecular modulation of a 4f driven Kondo resonance by surface-induced asymmetry

Coupling between a magnetic impurity and an external bath can give rise to many-body quantum phenomena, including Kondo and Hund's impurity states in metals, and Yu-Shiba-Rusinov states in superconductors. While advances have been made in probing the magnetic properties of d-shell impurities on surfaces, the confinement of f orbitals makes them difficult to access directly. Here we show that a 4f driven Kondo resonance can be modulated spatially by asymmetric coupling between a metallic surface and a molecule containing a 4f-like moment. Strong hybridization of dysprosium double-decker phthalocyanine with Cu(001) induces Kondo screening of the central magnetic moment. Misalignment between the symmetry axes of the molecule and the surface induces asymmetry in the molecule's electronic structure, spatially mediating electronic access to the magnetic moment through the Kondo resonance. This work demonstrates the important role that molecular ligands have in mediating electronic and magnetic coupling and in accessing many-body quantum states.

In the Kondo effect, a bath of conduction electrons screens a localized magnetic moment. Here, the authors demonstrate Kondo screening of a normally isolated 4f-like moment in a magnetic molecule on a Cu(001) surface that is modulated by strong ligand-mediated coupling.

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.

Universality and Scaling in a Charge Two-Channel Kondo Device

We study a charge two-channel Kondo model, demonstrating that recent experiments [Z. Iftikhar et al, Nature (London) 526, 233 (2015)] realize an essentially perfect quantum simulation-not just of its universal physics, but also nonuniversal effects away from the scaling limit. Numerical renormalization group (RG) calculations yield conductance line shapes encoding RG flow to a critical point involving a free Majorana fermion. By mimicking the experimental protocol, the experimental curve is reproduced quantitatively over 9 orders of magnitude, although we show that far greater bandwidth/temperature separation is required to obtain the universal result. Fermi liquid instabilities are also studied: In particular, our exact analytic results for nonlinear conductance provide predictions away from thermal equilibrium, in the regime of existing experiments.