arXiv subjects

Thomas Frederiksen

Publications and source records attributed to Thomas Frederiksen.

At least 37 records · Page 2Linked to original sources

arXiv2023

Detecting the spin-polarization of edge states in graphene nanoribbons

Low dimensional carbon-based materials are interesting because they can show intrinsic $π$-magnetism associated to p-electrons residing in specific open-shell configurations. Consequently, during the last years there have been impressive advances in the field combining indirect experimental fingerprints of localized magnetic moments with theoretical models. In spite of that, a characterization of their spatial- and energy-resolved spin-moment has so far remained elusive. To obtain this information, we present an approach based on the stabilization of the magnetization of $π$-orbitals by virtue of a supporting substrate with ferromagnetic ground state. Remarkably, we go beyond localized magnetic moments in radical or faulty carbon sites: In our study, energy-dependent spin-moment distributions have been extracted from spatially extended one-dimensional edge states of chiral graphene nanoribbons. This method can be generalized to other nanographene structures, representing an essential validation of these materials for their use in spintronics and quantum technologies.

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arXiv2022

Magnetic frustration and fractionalization in oligo(indenoindenes)

Poly(indenoindenes) are π-conjugated ladder carbon polymers with alternating hexagons and pentagons hosting one unpaired electron for each five-membered ring in the open-shell limit. Here we study the main magnetic interactions that are present in finite oligo(indenoindenes) (OInIn), classifying the six possible isomers in two different classes of three isomers each. One class can be rationalized by frustrated S = 1/2 Heisenberg chains, with ferromagnetic interactions between neighbour sites and antiferromagnetic interactions between the next neighbours. The other class is characterized by the more trivial antiferromagnetic order. Employing several levels of theory we further show that the ground state of one of the isomers is a valence-bond solid (VBS) of ferromagnetic dimers (S = 1). This is topologically similar to that of the Affleck-Kennedy-Lieb-Tasaki (AKLT) model, which is known to show fractional S = 1/2 states at the edges.

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arXiv2022

Length-independent quantum transport through topological band states of graphene nanoribbons

Atomically precise graphene nanoribbons (GNRs) have emerged as promising candidates for nanoelectronic applications due to their widely tunable energy band gaps resulting from lateral quantum confinement and edge effects. Here we report on the electronic transport characterization of an edge-modified GNR suspended between the tip of a scanning tunneling microscope (STM) and a Au(111) substrate. Differential conductance measurements on this metal-GNR-metal junction reveal loss-less transport properties (inverse decay length $β< 0.001 /\overset{\circ}{\mathrm{A}}$) with high conductance ($\sim 0.1$ G$_0$) at low voltages (50 meV) over long distances ($z > 10$ nm). The transport behavior is sensitive to the coupling between ribbon and electrodes, an effect that is rationalized using tight-binding and density functional theory simulations. From extensive modelling we infer that the length-independent transport is a manifestation of band transport through topological valence states, which originate from the zigzag segments on the GNR edges.

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arXiv2022

Spin-polarizing electron beam splitter from crossed graphene nanoribbons

Junctions composed of two crossed graphene nanoribbons (GNRs) have been theoretically proposed as electron beam splitters where incoming electron waves in one GNR can be split coherently into propagating waves in \emph{two} outgoing terminals with nearly equal amplitude and zero back-scattering. Here we scrutinize this effect for devices composed of narrow zigzag GNRs taking explicitly into account the role of Coulomb repulsion that leads to spin-polarized edge states within mean-field theory. We show that the beam-splitting effect survives the opening of the well-known correlation gap and, more strikingly, that a \emph{spin-dependent} scattering potential emerges which spin-polarizes the transmitted electrons in the two outputs. A near-perfect polarization can be achieved by joining several junctions in series. Our findings suggest that GNRs are interesting building blocks in spintronics and quantum technologies with applications for interferometry and entanglement.

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arXiv2022

Carbon-based nanostructures as a versatile platform for tunable $π$-magnetism

Emergence of $π$-magnetism in open-shell nanographenes has been theoretically predicted decades ago but their experimental characterization was elusive due to the strong chemical reactivity that makes their synthesis and stabilization difficult. In recent years, on-surface synthesis under vacuum conditions has provided unprecedented opportunities for atomically precise engineering of nanographenes, which in combination with scanning probe techniques have led to a substantial progress in our capabilities to realize localized electron spin states and to control electron spin interactions at the atomic scale. Here we review the essential concepts and the remarkable advances in the last few years, and outline the versatility of carbon-based $π$-magnetic materials as an interesting platform for applications in spintronics and quantum technologies.

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arXiv2021

Dynamic friction unraveled using an atomically defined model system

The pervasive phenomenon of friction has been studied at the nanoscale by controlled manipulation of single atoms and molecules, which permitted a precise determination of the static friction force necessary to initiate motion. However, much less is known about the atomistic dynamics during manipulation. Here we reveal the complete manipulation process of a carbon monoxide molecule on a copper surface at low temperatures using a combination of atomic force microscopy, vibrational spectroscopy for different isotope molecules and density functional theory. We measured the energy dissipation associated with manipulation and relate its origin to hysteresis involving an intermediate state, which enables an atomistic interpretation of dynamic friction. Our results show how friction forces can be controlled and optimized, facilitating new fundamental insights for tribology.

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arXiv2021

Magnetic Interactions Between Radical Pairs in Chiral Graphene Nanoribbons

Magnetic graphene nanoribbons (GNRs) have become promising candidates for future applications, including quantum technologies. Here, we characterize magnetic states hosted by chiral graphene nanoribbons (chGNRs). The substitution of a hydrogen atom at the chGNR edge by a ketone group effectively adds one p_z electron to the π-electron network, thus producing an unpaired π radical. A closely related scenario occurs for regular ketone-functionalized chGNRs in which one oxygen atom is missing. Two such radical states can interact via exchange coupling and we study those interactions as a function of their relative position, which includes a remarkable dependence on the chirality, as well as on the nature of the surrounding GNR, i.e., with or without ketone functionalization. In addition, we determine the parameters whereby this type of systems with oxygen heteroatoms can be adequately described within the widely used mean-field Hubbard model. Altogether, we provide new insights to both theoretically model and devise GNR-based nanostructures with tunable magnetic properties.

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arXiv2021

On-surface synthesis and collective spin excitations of a triangulene-based nanostar

Triangulene nanographenes are open-shell molecules with predicted high spin state due to the frustration of their conjugated network. Their long-sought synthesis became recently possible over a metal surface. Here, we present a macrocycle formed by six [3]triangulenes, which was obtained by combining the solution synthesis of a dimethylphenyl-anthracene cyclic hexamer and the on-surface cyclodehydrogenation of this precursor over a gold substrate. The resulting triangulene nanostar exhibits a collective spin state generated by the interaction of its 12 unpaired π-electrons along the conjugated lattice, corresponding to the antiferromagnetic ordering of six S = 1 sites (one per triangulene unit). Inelastic electron tunneling spectroscopy resolved three spin excitations connecting the singlet ground state with triplet states. The nanostar behaves close to predictions from the Heisenberg model of a S = 1 spin ring, representing a unique system to test collective spin modes in cyclic systems.

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arXiv2021

Topological phase transition in chiral graphene nanoribbons: from edge bands to end states

Precise control over the size and shape of graphene nanostructures allows engineering spin-polarized edge and topological states, representing a novel source of non-conventional $π$-magnetism with promising applications in quantum spintronics. A prerequisite for their emergence is the existence of robust gapped phases, which are difficult to find in extended graphene systems: only armchair graphene nanoribbons (GNRs) show a band gap that, however, closes for any other GNR orientation. Here we show that semi-metallic chiral GNRs (chGNRs) narrowed down to nanometer widths undergoes a topological phase transition, becoming first topological insulators, and transforming then into trivial band insulators for the narrowest chGNRs. We fabricated atomically precise chGNRs of different chirality and size by on surface synthesis using predesigned molecular precursors. Combining scanning tunnelling microscopy (STM) measurements and theory simulations, we follow the evolution of topological properties and bulk band gap depending on the width, length, and chirality of chGNRs. The first emerging gapped phases are topological, protected by a chiral interaction pattern between edges. For narrower ribbons, the symmetry of the interaction pattern changes, and the topological gap closes and re-opens again as a trivial band insulator. Our findings represent a new platform for producing topologically protected spin states and demonstrates the potential of connecting chiral edge and defect structure with band engineering.

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arXiv2020

Magnetism of topological boundary states induced by boron substitution in graphene nanoribbons

Graphene nanoribbons (GNRs), low-dimensional platforms for carbon-based electronics, show the promising perspective to also incorporate spin polarization in their conjugated electron system. However, magnetism in GNRs is generally associated to localized states around zigzag edges, difficult to fabricate and with high reactivity. Here we demonstrate that magnetism can also be induced away from physical GNR zigzag edges through atomically precise engineering topological defects in its interior. A pair of substitutional boron atoms inserted in the carbon backbone breaks the conjugation of their topological bands and builds two spin-polarized boundary states around. The spin state was detected in electrical transport measurements through boron-substituted GNRs suspended between tip and sample of a scanning tunneling microscope. First-principle simulations find that boron pairs induce a spin 1, which is modified by tuning the spacing between pairs. Our results demonstrate a route to embed spin chains in GNRs, turning them basic elements of spintronic devices.

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arXiv2020

Crossed graphene nanoribbons as beam splitters and mirrors for electron quantum optics

We analyze theoretically 4-terminal electronic devices composed of two crossed graphene nanoribbons (GNRs) and show that they can function as beam splitters or mirrors. These features are identified for electrons in the low-energy region where a single valence or conduction band is present. Our modeling is based on $p_z$ orbital tight-binding with Slater--Koster type matrix elements fitted to accurately reproduce the low-energy bands from density functional theory calculations. We analyze systematically all devices that can be constructed with either zigzag or armchair GNRs in AA and AB stackings. From Green's function theory the elastic electron transport properties are quantified as a function of the ribbon width. We find that devices composed of relatively narrow zigzag GNRs and AA-stacked armchair GNRs are the most interesting candidates to realize electron beam splitters with a close to 50-50 ratio in the two outgoing terminals. Structures with wider ribbons instead provide electron mirrors, where the electron wave is mostly transferred into the outgoing terminal of the other ribbon, or electron filters where the scattering depends sensitively on the wavelength of the propagating electron. We also test the robustness of these transport properties against variations in intersection angle, stacking pattern, lattice deformation (uniaxial strain), inter-GNR separation, and electrostatic potential differences between the layers. These generic features show that GNRs are interesting basic components to construct electronic quantum optical setups.

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arXiv2020

Uncovering the Triplet Ground State of Triangular Graphene Nanoflakes Engineered with Atomic Precision on a Metal Surface

Graphene can develop large magnetic moments in custom crafted open-shell nanostructures such as triangulene, a triangular piece of graphene with zigzag edges. Current methods of engineering graphene nano-systems on surfaces succeeded in producing atomically precise open-shell structures, but demonstration of their net spin remains elusive to date. Here, we fabricate triangulene-like graphene systems and demonstrate that they possess a spin $S=1$ ground state. Scanning tunnelling spectroscopy identifies the fingerprint of an underscreened $S=1$ Kondo state on \rev{these} flakes at low temperatures, signaling the dominant ferromagnetic interactions between two spins. Combined with simulations based on the meanfield Hubbard model, we show that this $S=1$ $π$-paramagnetism is robust, and can be manipulated to a $S=1/2$ state by adding additional H-atoms to the radical sites. \rev{Our results demonstrate that $π$-paramagnetism of high-spin graphene flakes can survive on surfaces, opening the door to study the quantum behaviour of interacting $π$-spins in graphene systems.

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arXiv2019

Single-photon emission mediated by single-electron tunneling in plasmonic nanojunctions

Recent scanning tunnelling microscopy (STM) experiments reported single-molecule fluorescence induced by tunneling currents in the nanoplasmonic cavity formed by the STM tip and the substrate.The electric field of the cavity mode couples with the current-induced charge fluctuations of the molecule, allowing the excitation of the mode. We investigate theoretically this system for the experimentally relevant limit of large damping rate $κ$ for the cavity mode and arbitrary coupling strength to a single-electronic level. We find that for bias voltages close to the first inelastic threshold of photon emission, the emitted light displays anti-bunching behavior with vanishing second-order photon correlation function. At the same time, the current and the intensity of emitted light display Franck--Condon steps at multiples of the cavity frequency $ω_c$ with a width controlled by $κ$ rather than the temperature $T$. For large bias voltages, we predict strong photon bunching of the order of the $κ/Γ$ where $Γ$ is the electronic tunneling rate. Our theory thus predicts that strong coupling to a single level allows current-driven non-classical light emission.

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arXiv2019

Conductance channels of a platform molecule on Au(111) probed with shot noise

The shot noise of the current $I$ through junctions to single trioxatriangulenium cations (TOTA$^+$) on Au(111) is measured with a low temperature scanning tunneling microscope using Au tips. The noise is significantly reduced compared to the Poisson noise power of $2eI$ and varies linearly with the junction conductance. The data are consistent with electron transmission through a single spin-degenerate transport channel and show that TOTA$^+$ in a Au contact does not acquire an unpaired electron. Ab initio calculations reproduce the observations and show that the current involves the lowest unoccupied orbital of the molecule and tip states close to the Fermi level.

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arXiv2018

Full-scale Simulation of Electron Transport in Nanoporous Graphene: Probing the Talbot Effect

Designing platforms to control phase-coherence and interference of electron waves is a cornerstone for future quantum electronics, computing or sensing. Nanoporous graphene (NPG) consisting of linked graphene nanoribbons has recently been fabricated using molecular precursors and bottom-up assembly [Moreno et al., Science 360, 199 (2018)] opening an avenue for controlling the electronic current in a two-dimensional material. By simulating electron transport in real-sized NPG samples we predict that electron waves injected from the tip of a scanning tunneling microscope (STM) behave similarly to photons in coupled waveguides, displaying a Talbot interference pattern. We link the origins of this effect to the band structure of the NPG and further demonstrate how this pattern may be mapped out by a second STM probe. We enable atomistic parameter-free calculations beyond the 100 nm scale by developing a new multi-scale method where first-principles density functional theory regions are seamlessly embedded into a large-scale tight-binding.

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arXiv2018

Magnetic-State Controlled Molecular Vibrational Dynamics at Buried Molecular-Metal Interfaces

Self-assembled molecular structures have been intensively used in molecular electronics and spintronics. However, detailed nature of the interfaces between molecular layers and extended metallic contacts used to bias the real devices remains unclear. Buried interfaces greatly restrict application of standard techniques such as Raman or scanning electron microscopies. Here we introduce low frequency noise spectroscopy as a tool to characterize buried molecular-metal interfaces. We take advantage of vibrational heating of the molecules with incomplete contacts to the interface. Electrons, being the main spin and charge carriers propagating through the interfaces involving self-assembled molecules, interact inelastically with charged atomic ions. Such interactions produce quantum molecular vibrations (phonons). Detailed investigation of both conductance and conductance fluctuations in magnetic tunnel junctions with few nm Perylenetetracarboxylic dianhydride (PTCDA) allows to map vibrational heating at specific biases taking place in 'hot spots' where self-assembled layers weaker contact the metallic electrodes. We follow this effect as a function of PTCDA thickness and find the best molecular-metal order for the lowest (3-5 monolayers) barriers. Moreover, we unveil interplay between spin and phonons at interface showing experimentally and by modelling spin-control over molecular vibrational heating. We find that vibrational heating related low frequency noise essentially depends on the relative alignment of the electrodes with noise changes well beyond expectations from fluctuation-dissipation theorem.

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arXiv2018

Single Spin Localization and Manipulation in Graphene Open-Shell Nanostructures

Predictions state that graphene can spontaneously develop magnetism from the Coulomb repulsion of its $π$-electrons, but its experimental verification has been a challenge. Here, we report on the observation and manipulation of individual magnetic moments localized in graphene nanostructures on a Au(111) surface. Using scanning tunneling spectroscopy, we detected the presence of single electron spins localized around certain zigzag sites of the carbon backbone via the Kondo effect. Two near-by spins were found coupled into a singlet ground state, and the strength of their exchange interaction was measured via singlet-triplet inelastic tunnel electron excitations. Theoretical simulations demonstrate that electron correlations result in spin-polarized radical states with the experimentally observed spatial distributions. Hydrogen atoms bound to these radical sites quench their magnetic moment, permitting us to switch the spin of the nanostructure using the tip of the microscope.

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arXiv2017

Submolecular resolution by variation of IETS amplitude and its relation to AFM/STM signal

Here we show scanning tunnelling microscopy (STM), non-contact atomic force microscopy (AFM) and inelastic electron tunnelling spectroscopy (IETS) measurements on organic molecule with a CO- terminated tip at 5K. The high-resolution contrast observed simultaneously in all channels unam- biguously demonstrates the common imaging mechanism in STM/AFM/IETS, related to the lateral bending of the CO-functionalized tip. The IETS spectroscopy reveals that the submolecular con- trast at 5K consists of both renormalization of vibrational frequency and variation of the amplitude of IETS signal. This finding is also corroborated by first principles simulations. We extend accord- ingly the probe-particle AFM/STM/IETS model to include these two main ingredients necessary to reproduce the high-resolution IETS contrast. We also employ the first principles simulations to get more insight into different response of frustrated translation and rotational modes of CO-tip during imaging.

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