The quest for quantum ground states beyond the conventional Fermi-liquid paradigm remains a central challenge in many-body physics. The ferromagnetic Kondo effect represents a particularly intriguing case: an exotic variant of the Kondo effect in which an asymptotically free spin gives rise to singular Fermi-liquid behavior. Despite its theoretical importance, this regime has long eluded experimental observation owing to its subtle spectroscopic signatures, vanishingly small energy scales, and strict symmetry constraints in conventional nanostructures. Here, we demonstrate the coexistence of the ferromagnetic and overscreened Kondo effects within a single molecular spin systemx2014a triangulene dimer comprising spin-1 and spin-1/2 units adsorbed on a metal surface. Low-temperature scanning tunneling spectroscopy reveals characteristic signatures of singular Fermi-liquid behavior, which are fully supported by many-body calculations. The unique molecular design provides intrinsic control over spin configuration and coupling asymmetry, allowing distinct many-body regimes to be accessed within the same platform. Our results establish a robust strategy for realizing non-Fermi-liquid physics at the atomic scale and demonstrate that ferromagnetic Kondo behavior can not only be observed but also deliberately engineered in molecular systems.

The doping-driven Mott transition in the Hubbard model is described within the frame- work of steady-state density functional theory, or i-DFT. In order to access the many-body spectral function in i-DFT, an approximation for the exchange-correlation (xc) bias at arbitrary density and current is required. By using Fermi-liquid theory, a connection between the xc bias of i-DFT and the quasiparticle weight of many-body theory is derived and the results are employed to guide the construction of the approximation. Numerical results obtained with this functional demonstrate that the doping-driven Mott transition can indeed be captured with i-DFT.

A recently proposed analytical solution for the equations of motion of the one-body Green's function of the double quantum dot is extended to the out-of-equilibrium situation. By solving a linear system for the density correlators, not only the local occupations but also charge and heat currents as well as transport coefficients and the figure of merit are analytically derived in terms of system parameters and external driving forces. The emerging regions of stable occupation and finite currents are explained in terms of addition and removal energies, corresponding to the poles of the Green's function. The analytical results are validated against the hierarchical equations of motion method, showing excellent agreement.

A fully analytical approach based on the equation of motion technique to investigate the spectral properties and orbital occupations in an interacting double quantum dot in equilibrium is presented. By solving a linear system for the density correlators analytically, an explicit expression for the one-body Green's function in terms of local occupations, intra- and interdot Coulomb interactions, and the model parameters is derived. In the uncontacted limit, the results coincide with those obtained from the grand canonical ensemble. The analytical results compare favorably with numerical results obtained with the noncrossing approximation and the hierarchical equation of motion methods accurately reproducing peak positions and spectral weight distributions in the Coulomb blockade regime.

The Kondo effect describes the scattering of conduction electrons by magnetic impurities, manifesting as an electronic resonance at the Fermi energy with a distinctive temperature evolution. In this Letter, we present a critical evaluation of the current methodology employed to demonstrate Kondo behavior in transport measurements, underscoring the limitations of established theoretical frameworks and the influence of extrinsic broadening. We introduce an approach for analyzing spectroscopic indicators of the Kondo effect, employing the Hurwitz-Fano lineshape as a model for the Kondo resonance in the presence of extrinsic broadening. Through precise scanning tunneling spectroscopy measurements on an exemplary spin-1/2 Kondo system, phenalenyl on Au(111), we demonstrate the efficacy of our proposed protocol in extracting accurate intrinsic Kondo linewidths from finite-temperature measurements. The extracted linewidths exhibit a robust fit with a recently derived expression for the temperature-dependent intrinsic Kondo linewidth, providing compelling evidence for the validity of the underlying theory. Published by the American Physical Society 2024

The study of open-shell nanographenes has relied on a paradigm where spins are the only low-energy degrees of freedom. Here we show that some nanographenes can host low-energy excitations that include strongly coupled spin and orbital degrees of freedom. The key ingredient is the existence of orbital degeneracy, as a consequence of leaving the benzenoid/half-filling scenario. We analyze the case of nitrogen-doped triangulenes, using both density-functional theory and Hubbard model multiconfigurational and random-phase approximation calculations. We find a rich interplay between orbital and spin degrees of freedom that confirms the need to go beyond the spin-only paradigm, opening a new avenue in this field of research.

At low temperatures, the interaction of a nanoscale magnet with a Fermi gas can give rise to the Kondo effect. This is signaled by a zero-bias resonance with a characteristic temperature evolution of its linewidth. In order to prove the Kondo nature of the zero-bias peak and to determine the Kondo temperature in scanning tunneling spectroscopy (STS), the extrinsic contributions to the measured linewidth have to be properly taken into account. In this paper, by combination of precise STS measurements of an ideal spin-1/2 Kondo system, phenalenyl on Au(111), and by theoretical considerations, we show how to efficiently extract accurate intrinsic Kondo linewidths from finite-temperature STS measurements. The extracted linewidths fit very well with a recently derived expression for the intrinsic Kondo linewidth as a function of temperature, thus proving the validity of the theory. Finally, we show that the developed methodology allows to reliably extract the intrinsic Kondo width from a single spectrum measured at finite temperature, thus considerably reducing the experimental effort.

The limitation of Fermi liquid theory to very low energies and temperatures poses a fundamental problem for describing the temperature evolution of the Kondo peak. Here Fermi liquid theory for the single impurity Anderson model is extended beyond the low-energy and low-temperature regime by means of an ansatz for the impurity self-energy based on the accurate description of the Kondo peak by the Frota function, the similarity between energy and temperature in the second-order self-energy, and by exploiting Fermi liquid conditions. Analytic expressions for the temperature dependence of the Kondo peak height and width derived from this ansatz are in excellent agreement with numerical renormalization group data for temperatures beyond the Kondo temperature. The derived expression thus allows to unambiguously determine the intrinsic Kondo peak width and Kondo temperature from finite temperature measurements of the Kondo resonance.

In this paper we establish a connection between density functional theory (DFT) for lattice models and common real-space DFT. We consider the lattice DFT description of a two-level model subject to generic interactions in Mermin's DFT formulation in the grand canonical ensemble at finite temperature. The case of only density-density and Hund's rule interaction studied in earlier work is shown to be equivalent to an exact-exchange description of DFT in the real-space picture. In addition, we also include the so-called pair-hopping interaction which can be treated analytically and, crucially, leads to non-integer occupations of the Kohn-Sham (KS) levels even in the limit of zero temperature. Treating the hydrogen molecule in a minimal basis is shown to be equivalent to our two-level lattice DFT model. By means of the fractional occupations of the KS orbitals (which, in this case, are identical to the many-body ones) we reproduce the results of full configuration interaction, even in the dissociation limit and without breaking the spin symmetry. Beyond the minimal basis, we embed our HOMO-LUMO model into a standard DFT calculation and, again, obtain results in overall good agreement with exact ones without the need of breaking the spin symmetry.

Phenalenyl is a radical nanographene with a triangular shape hosting an unpaired electron with spin S = 1/2. The open-shell nature of the phenalenyl is expected to be retained in covalently bonded networks. As a first step, we report synthesis of the phenalenyl dimer by combining in-solution synthesis and on-surface activation and its characterization on Au(111) and on a NaCl decoupling layer by means of inelastic electron tunneling spectroscopy (IETS). IETS shows inelastic steps that are identified as singlet-triplet excitation arising from interphenalenyl exchange. Spin excitation energies with and without the NaCl decoupling layer are 48 and 41 meV, respectively, indicating significant renormalization due to exchange with Au(111) electrons. Furthermore, third-neighbor hopping-induced interphenalenyl hybridization is fundamental to explaining the position-dependent bias asymmetry of the inelastic steps and activation of kinetic interphenalenyl exchange. Our results pave the way for bottom-up synthesis of S = 1/2 spin-lattices with large exchange interactions.

Open-shell nanographenes can be covalently bonded and still preserve their local moments, forming interacting spin lattices. In the case of benzenoid nanographenes, the Ovchinnikov-Lieb rules anticipate the spin of the ground state of the superstructure and thereby the sign of the intermolecular exchange. Here we address the underlying microscopic mechanisms for intermolecular exchange in this type of system. We find that, in general, three different mechanisms contribute. First, Hund's ferromagnetic exchange that promotes ferromagnetic interactions of electrons in overlapping orbitals. Second, superexchange driven by intermolecular hybridization, identical to Anderson kinetic exchange, which is a decreasing function of the Hubbard-$U$ energy scale and is always antiferromagnetic. Third, a Coulomb-driven superexchange, that increases as a function of $U$ and involves virtual excitation of excited molecular orbitals that are extended over the entire structure. We find that Coulomb-driven superexchange can be either ferro- or antiferromagnetic, accounting for Ovchinnikov-Lieb rules. We compute these exchange energies for the case of coupled $S=1/2$ phenalenyl triangulenes, using multiconfigurational methods both with Hubbard and extended Hubbard models, thereby addressing the influence of long-range Coulomb interactions on the exchange interactions.

The charge transport properties of zero-temperature multi-orbital quantum dot systems with one dot coupled to leads and the other dots coupled only capacitatively are studied within density functional theory. It is shown that the setup is equivalent to an effective single impurity Anderson model. This allows to understand the level occupation switching effect as transitions between ground states of different integer occupations in the uncoupled dots. Level occupation switching is very sensitive to small energy differences and therefore also to the details of the parametrized exchange-correlation functionals. An existing functional already captures the effect on a qualitative level but we also provide an improved parametrization which is very accurate when compared to reference numerical renormalization group results.

Open-shell nanographenes can be covalently bonded and still preserve their local moments, forming interacting spins lattices. In the case of benzenoid nanographenes, the Ovchinnikov-Lieb rules anticipate the spin of the ground state of the superstructure, and thereby the sign of the intermolecular exchange. Here we address the underlying microscopic mechanisms for intermolecular exchange in this type of system. We find that, in general, three different mechanisms contribute. First, Hund's ferromagnetic exchange that promotes ferromagnetic interactions of electrons in overlapping orbitals. Second, superexchange driven by intermolecular hybridization, identical to Anderson kinetic exchange, which is a decreasing function of the Hubbard-$U$ energy scale, and is always antiferromagnetic. Third, a Coulomb-driven superexchange, that increases as a function of $U$, and involves virtual excitation of excited molecular orbitals that are extended over the entire structure. We find that Coulomb-driven superexchange can be either ferro or antiferromagnetic, accounting for Ovchinnikov-Lieb rules. We compute these exchange energies for the case of coupled $S=1/2$ phenalenyl triangulenes, using multi-configurational methods both with Hubbard and extended Hubbard models, thereby addressing the influence of long-range Coulomb interactions on the exchange interactions.

Open-shell nanographenes can be covalently bonded and still preserve their local moments, forming in-teracting spin lattices. In the case of benzenoid nanographenes, the Ovchinnikov-Lieb rules anticipate the spin of the ground state of the superstructure and thereby the sign of the intermolecular exchange. Here we address the underlying microscopic mechanisms for intermolecular exchange in this type of system. We find that, in general, three different mechanisms contribute. First, Hund's ferromagnetic exchange that promotes ferromagnetic interactions of electrons in overlapping orbitals. Second, superexchange driven by intermolecular hybridization, identical to Anderson kinetic exchange, which is a decreasing function of the Hubbard -U energy scale and is always antiferromagnetic. Third, a Coulomb-driven superexchange, that increases as a function of U and involves virtual excitation of excited molecular orbitals that are extended over the entire structure. We find that Coulomb-driven superexchange can be either ferro-or antiferromagnetic, accounting for Ovchinnikov-Lieb rules. We compute these exchange energies for the case of coupled S = 1/2 phenalenyl triangulenes, using multiconfigurational methods both with Hubbard and extended Hubbard models, thereby addressing the influence of long-range Coulomb interactions on the exchange interactions.

Fractionalization is a phenomenon in which strong interactions in a quantum system drive the emergence of excitations with quantum numbers that are absent in the building blocks. Outstanding examples are excitations with charge e/3 in the fractional quantum Hall effect, solitons in one-dimensional conducting polymers and Majorana states in topological superconductors. Fractionalization is also predicted to manifest itself in low-dimensional quantum magnets, such as one-dimensional antiferromagnetic S = 1 chains. The fundamental features of this system are gapped excitations in the bulk and, remarkably, S = 1/2 edge states at the chain termini, leading to a four-fold degenerate ground state that reflects the underlying symmetry-protected topological order. Here, we use on-surface synthesis to fabricate one-dimensional spin chains that contain the S = 1 polycyclic aromatic hydrocarbon triangulene as the building block. Using scanning tunneling microscopy and spectroscopy at 4.5 K, we probe length-dependent magnetic excitations at the atomic scale in both open-ended and cyclic spin chains, and directly observe gapped spin excitations and fractional edge states therein. Exact diagonalization calculations provide conclusive evidence that the spin chains are described by the S = 1 bilinear-biquadratic Hamiltonian in the Haldane symmetry-protected topological phase. Our results open a bottom-up approach to study strongly correlated quantum spin liquid phases in purely organic materials, with the potential for the realization of measurement-based quantum computation.

We study spin excitations and Kondo effect in open-shell nanographenes, motivated by recent scanning tunneling inelastic spectroscopy experiments. Specifically, we consider three systems, the triangulene, the extended triangulene with rocket shape, both with an $S=1$ ground state, and a triangulene dimer with $S=0$ on account of intermolecular exchange. We focus on the consequences of hybridization of the nanographene zero-modes with a conducting substrate on the $dI/dV$ lineshapes associated with spin excitations. The partially filled nanographene zero-modes coupled to the conduction electrons in the substrate constitute multi-orbital Anderson impurity models that we solve in the one-crossing approximation which treats the coupling to the substrate to infinite order. We find that the coupling to the substrate leads to (i) renormalization of the spin flip excitation energies of the bare molecule, (ii) broadening of the spectral features and (iii) the emergence of zero bias Kondo peaks for the $S=1$ ground states. The calculated substrate induced shift of the spin excitation energies is found to be significantly larger than their broadening, which implies that this effect has to be considered when comparing experimental results and theory.

We present a computationally efficient method to obtain the spectral function of bulk systems in the framework of steady-state density functional theory (i-DFT) using an idealized scanning tunneling microscope (STM) setup. We calculate the current through the STM tip and then extract the spectral function from the finite-bias differential conductance. The fictitious noninteracting system of i-DFT features an exchange-correlation (XC) contribution to the bias which guarantees the same current as in the true interacting system. Exact properties of the XC bias are established using Fermi-liquid theory and subsequently implemented to construct approximations for the Hubbard model. We show for two different lattice structures that the Mott metal-insulator transition is captured by i-DFT.

By reverse engineering from exact solutions, we obtain Hartree-exchange-correlation (Hxc) potentials for a double quantum dot subject to generic density-density interactions and Hund's rule coupling. We find ubiquitous step structures of the Hxc potentials that can be understood and derived from an analysis of stability diagrams. We further show that a generic Hxc potential can be decomposed into four basic potentials which allows for a straightforward parametrization and paves the road for the construction of Hxc potentials for interacting multiorbital systems. Finally, we employ our parametrization of the Hxc potential in density functional theory calculations of multiorbital quantum dots and find excellent agreement with exact many-body calculations.