Spin conductances and magnetization production in chiral molecular junctions.

Motivated by experimental reports on chirality induced spin selectivity, we investigate a minimal model that allows us to calculate the charge and spin conductances through helical molecules analytically. The spin-orbit interaction is assumed to be non-vanishing on the molecule and negligible in the reservoirs (leads). The band structure of the molecule features four helical modes with spin-momentum locking that are analogous of edge-currents in the quantum spin Hall effect. While charge is conserved and therefore the charge current is independent of where it is measured-reservoirs or molecule-our detailed calculations reveal that the spin currents in the left and right leads are equal in magnitudes but with opposite signs (in linear response). We predict that transport currents flowing through helical molecules are accompanied by a spin accumulation in the contact region with the same magnetization direction for source and drain. Furthermore, we predict that the spin-conductance can be extracted directly from measuring the (quasi-static) spin accumulation-rather than the spin current itself, which is very challenging to obtain experimentally.

Chirality-controlled spin scattering through quantum interference.

Chirality-induced spin selectivity has been reported in many experiments, but a generally accepted theoretical explanation has not yet been proposed. Here, we introduce a simple model system of a straight cylindrical free-electron wire containing a helical string of atomic scattering centers with spin-orbit interaction. The advantage of this simple model is that it allows deriving analytical expressions for the spin scattering rates, such that the origin of the effect can be easily followed. We find that spin-selective scattering can be viewed as resulting from the constructive interference of partial waves scattered by the spin-orbit terms. We demonstrate that forward scattering rates are independent of spin, while back scattering is spin dependent over wide windows of energy. Although the model does not represent the full details of electron transmission through chiral molecules, it clearly reveals a mechanism that could operate in chiral systems.

Solitonics with Polyacetylenes.

Polyacetylene molecular wires have attracted a long-standing interest for the past 40 years. From a fundamental perspective, there are two main reasons for the interest. First, polyacetylenes are a prime realization of a one-dimensional topological insulator. Second, long molecules support freely propagating topological domain-wall states, so-called "solitons," which provide an early paradigm for spin-charge separation. Because of recent experimental developments, individual polyacetylene chains can now be synthesized on substrates. Motivated by this breakthrough, we here propose a novel way for chemically supported soliton design in these systems. We demonstrate how to control the soliton position and how to read it out via external means. Also, we show how extra soliton-antisoliton pairs arise when applying a moderate static electric field. We thus make a step toward functionality of electronic devices based on soliton manipulation, that is, "solitonics".

Mechanically Tunable Quantum Interference in Ferrocene-Based Single-Molecule Junctions.

Ferrocenes are ubiquitous organometallic building blocks that comprise a Fe atom sandwiched between two cyclopentadienyl (Cp) rings that rotate freely at room temperature. Of widespread interest in fundamental studies and real-world applications, they have also attracted some interest as functional elements of molecular-scale devices. Here we investigate the impact of the configurational degrees of freedom of a ferrocene derivative on its single-molecule junction conductance. Measurements indicate that the conductance of the ferrocene derivative, which is suppressed by 2 orders of magnitude as compared to a fully conjugated analogue, can be modulated by altering the junction configuration. Ab initio transport calculations show that the low conductance is a consequence of destructive quantum interference effects of the Fano type that arise from the hybridization of localized metal-based d-orbitals and the delocalized ligand-based π-system. By rotation of the Cp rings, the hybridization, and thus the quantum interference, can be mechanically controlled, resulting in a conductance modulation that is seen experimentally.

Near Length-Independent Conductance in Polymethine Molecular Wires.

Polymethine dyes are linear π-conjugated compounds with an odd number of carbons that display a much greater delocalization in comparison to polyenes that have an even number of carbon atoms in their main chain. Herein, we perform scanning tunneling microscope based break-junction measurements on a series of three cyanine dyes of increasing length. We demonstrate, at the single molecule level, that these short chain polymethine systems exhibit a substantially smaller decay in conductance with length (attenuation factor ß = 0.04 Å-1) compared to traditional polyenes (ß ≈ 0.2 Å-1). Furthermore, we show that by changing solvent we are able to shift the ß value, demonstrating a remarkable negative ß value, with conductance increasing with molecular length. First principle calculations provide support for the experimentally observed near-uniform length dependent conductance and further suggest that the variations in ß with solvent are due to solvent-induced changes in the alignment of the frontier molecular orbitals relative to the Fermi energy of the leads. A simplified Hückel model suggests that the smaller decay in conductance correlates with the smaller degree of bond order alternation present in polymethine compounds compared to polyenes. These findings may enable the design of molecular wires without a length-dependent decay for efficient electron transport at the nanoscale.

Perspective: Theory of quantum transport in molecular junctions.

Molecular junctions, where single molecules are bound to metal or semiconductor electrodes, represent a unique architecture to investigate molecules in a distinct nonequilibrium situation and, in a broader context, to study basic mechanisms of charge and energy transport in a many-body quantum system at the nanoscale. Experimental studies of molecular junctions have revealed a wealth of interesting transport phenomena, the understanding of which necessitates theoretical modeling. The accurate theoretical description of quantum transport in molecular junctions is challenging because it requires methods that are capable to describe the electronic structure and dynamics of molecules in a condensed phase environment out of equilibrium, in some cases with strong electron-electron and/or electronic-vibrational interaction. This perspective discusses recent progress in the theory and simulation of quantum transport in molecular junctions. Furthermore, challenges are identified, which appear crucial to achieve a comprehensive and quantitative understanding of transport in these systems.

Density Propagator for Many-Body Localization: Finite-Size Effects, Transient Subdiffusion, and Exponential Decay.

We investigate charge relaxation in quantum wires of spinless disordered fermions (t-V model). Our observable is the time-dependent density propagator Π_{ϵ}(x,t), calculated in windows of different energy density ϵ of the many-body Hamiltonian and at different disorder strengths W, not exceeding the critical value W_{c}. The width Δx_{ϵ}(t) of Π_{ϵ}(x,t) exhibits a behavior dlnΔx_{ϵ}(t)/dlnt=ß_{ϵ}(t), where the exponent function ß_{ϵ}(t)≲1/2 is seen to depend strongly on L at all investigated parameter combinations. (i) We confirm the existence of a region in phase space that exhibits subdiffusive dynamics in the sense that ß_{ϵ}(t)<1/2 in a large window of times. However, subdiffusion might possibly be transient, only, finally giving way to a conventional diffusive behavior with ß_{ϵ}=1/2. (ii) We cannot confirm the existence of many-body mobility edges even in regions of the phase diagram that have been reported to be deep in the delocalized phase. (iii) (Transient) subdiffusion 0<ß_{ϵ}(t)≲1/2 coexists with an enhanced probability for returning to the origin Π_{ϵ}(0,t), decaying much slower than 1/Δx_{ϵ}(t). Correspondingly, the spatial decay of Π_{ϵ}(x,t) is far from Gaussian, being exponential or even slower. On a phenomenological level, our findings are broadly consistent with the effects of strong disorder and (fractal) Griffiths regions.

Silver Makes Better Electrical Contacts to Thiol-Terminated Silanes than Gold.

We report that the single-molecule junction conductance of thiol-terminated silanes with Ag electrodes are higher than the conductance of those formed with Au electrodes. These results are in contrast to the trends in the metal work function Φ(Ag)<Φ(Au). As such, a better alignment of the Au Fermi level to the molecular orbital of silane that mediates charge transport would be expected. This conductance trend is reversed when we replace the thiols with amines, highlighting the impact of metal-S covalent and metal-NH2 dative bonds in controlling the molecular conductance. Density functional theory calculations elucidate the crucial role of the chemical linkers in determining the level alignment when molecules are attached to different metal contacts. We also demonstrate that conductance of thiol-terminated silanes with Pt electrodes is lower than the ones formed with Au and Ag electrodes, again in contrast to the trends in the metal work-functions.

Impact of Electrode Density of States on Transport through Pyridine-Linked Single Molecule Junctions.

We study the impact of electrode band structure on transport through single-molecule junctions by measuring the conductance of pyridine-based molecules using Ag and Au electrodes. Our experiments are carried out using the scanning tunneling microscope based break-junction technique and are supported by density functional theory based calculations. We find from both experiments and calculations that the coupling of the dominant transport orbital to the metal is stronger for Au-based junctions when compared with Ag-based junctions. We attribute this difference to relativistic effects, which result in an enhanced density of d-states at the Fermi energy for Au compared with Ag. We further show that the alignment of the conducting orbital relative to the Fermi level does not follow the work function difference between two metals and is different for conjugated and saturated systems. We thus demonstrate that the details of the molecular level alignment and electronic coupling in metal-organic interfaces do not follow simple rules but are rather the consequence of subtle local interactions.

Current patterns and orbital magnetism in mesoscopic dc transport.

We present ab initio calculations of the local current density j(r) as it arises in dc-transport measurements. We discover pronounced patterns in the local current density, ring currents ("eddies"), that go along with orbital magnetism. Importantly, the magnitude of the ring currents can exceed the (average) transport current by orders of magnitude. We find associated magnetic fields that exhibit drastic fluctuations with field gradients reaching 1 T nm⁻¹ V⁻¹. The relevance of our observations for spin relaxation in systems with very weak spin-orbit interaction, such as organic semiconductors, is discussed. In such systems, spin relaxation induced by bias driven orbital magnetism competes with relaxation induced by the hyperfine interaction and appears to be of similar strength. We propose a NMR-type experiment in the presence of dc-current flow to observe the spatial fluctuations of the induced magnetic fields.

Atomically wired molecular junctions: connecting a single organic molecule by chains of metal atoms.

Using a break junction technique, we find a clear signature for the formation of conducting hybrid junctions composed of a single organic molecule (benzene, naphthalene, or anthracene) connected to chains of platinum atoms. The hybrid junctions exhibit metallic-like conductance (~0.1-1G0), which is rather insensitive to further elongation by additional atoms. At low bias voltage the hybrid junctions can be elongated significantly beyond the length of the bare atomic chains. Ab initio calculations reveal that benzene based hybrid junctions have a significant binding energy and high structural flexibility that may contribute to the survival of the hybrid junction during the elongation process. The fabrication of hybrid junctions opens the way for combining the different properties of atomic chains and organic molecules to realize a new class of atomic scale interfaces.

Spin-Orbit Torque in Single-Molecule Junctions from ab Initio.

The use of electric fields applied across magnetic heterojunctions that lack spatial inversion symmetry has been previously proposed as a nonmagnetic means of controlling localized magnetic moments through spin-orbit torques (SOT). The implementation of this concept at the single-molecule level has remained a challenge, however. Here, we present first-principles calculations of SOT in a single-molecule junction under bias and beyond linear response. Employing a self-consistency scheme invoking density functional theory and nonequilibrium Green's function theory including spin-orbit interaction, we compute the change of the magnetization with the bias voltage and the associated current-induced SOT. Within the linear regime our quantitative estimates for the SOT in single-molecule junctions yield values similar to those known for magnetic interfaces. Our findings contribute to an improved microscopic understanding of SOT in single molecules.

Photooxidation driven formation of Fe-Au linked ferrocene-based single-molecule junctions.

Metal-metal contacts, though not yet widely realized, may provide exciting opportunities to serve as tunable and functional interfaces in single-molecule devices. One of the simplest components which might facilitate such binding interactions is the ferrocene group. Notably, direct bonds between the ferrocene iron center and metals such as Pd or Co have been demonstrated in molecular complexes comprising coordinating ligands attached to the cyclopentadienyl rings. Here, we demonstrate that ferrocene-based single-molecule devices with Fe-Au interfacial contact geometries form at room temperature in the absence of supporting coordinating ligands. Applying a photoredox reaction, we propose that ferrocene only functions effectively as a contact group when oxidized, binding to gold through a formal Fe3+ center. This observation is further supported by a series of control measurements and density functional theory calculations. Our findings extend the scope of junction contact chemistries beyond those involving main group elements, lay the foundation for light switchable ferrocene-based single-molecule devices, and highlight new potential mechanistic function(s) of unsubstituted ferrocenium groups in synthetic processes.

Ab initio simulations of scanning-tunneling-microscope images with embedding techniques and application to C58-dimers on Au(111).

We present a modification of the standard electron transport methodology based on the (non-equilibrium) Green's function formalism to efficiently simulate STM-images. The novel feature of this method is that it employs an effective embedding technique that allows us to extrapolate properties of metal substrates with adsorbed molecules from quantum-chemical cluster calculations. To illustrate the potential of this approach, we present an application to STM-images of C58-dimers immobilized on Au(111)-surfaces that is motivated by recent experiments.

C58 on Au(111): a scanning tunneling microscopy study.

C58 fullerenes were adsorbed onto room temperature Au(111) surface by low-energy (~6 eV) cluster ion beam deposition under ultrahigh vacuum conditions. The topographic and electronic properties of the deposits were monitored by means of scanning tunnelling microscopy (STM at 4.2 K). Topographic images reveal that at low coverages fullerene cages are pinned by point dislocation defects on the herringbone reconstructed gold terraces (as well as by step edges). At intermediate coverages, pinned monomers act as nucleation centres for the formation of oligomeric C58 chains and 2D islands. At the largest coverages studied, the surface becomes covered by 3D interlinked C58 cages. STM topographic images of pinned single adsorbates are essentially featureless. The corresponding local densities of states are consistent with strong cage-substrate interactions. Topographic images of [C58]n oligomers show a stripe-like intensity pattern oriented perpendicular to the axis connecting the cage centers. This striped pattern becomes even more pronounced in maps of the local density of states. As supported by density functional theory, DFT calculations, and also by analogous STM images previously obtained for C60 polymers [M. Nakaya, Y. Kuwahara, M. Aono, and T. Nakayama, J. Nanosci. Nanotechnol. 11, 2829 (2011)], we conclude that these striped orbital patterns are a fingerprint of covalent intercage bonds. For thick C58 films we have derived a bandgap of 1.2 eV from scanning tunnelling spectroscopy data confirming that the outermost C58 layer behaves as a wide band semiconductor.

Single molecule magnetoresistance with combined antiferromagnetic and ferromagnetic electrodes.

The magnetoresistance of a hydrogen-phthalocyanine molecule placed on an antiferromagnetic Mn(001) surface and contacted by a ferromagnetic Fe electrode is investigated using density functional theory based transport calculations and low-temperature scanning tunneling microscopy. A large and negative magnetoresistance ratio of ~50% is observed in combination with a high conductance. The effect originates from a lowest unoccupied molecular orbital (LUMO) doublet placed almost in resonance with the Fermi energy. As a consequence, irrespective of the mutual alignment of magnetizations, electron transport is always dominated by resonant transmission of Mn-majority charge carries going through LUMO levels.

Current-induced mechanical torque in chiral molecular rotors.

There has been great endeavor to engineer molecular rotors operated by an electrical current. A frequently met operation principle is the transfer of angular momentum taken from the incident flux. In this paper, we present an alternative driving agent that works also in situations where angular momentum of the incoming flux is conserved. This situation arises typically with molecular rotors that exhibit an easy axis of rotation. For quantitative analysis we investigate here a classical model where molecule and wires are represented by a rigid curved path. We demonstrate that in the presence of chirality, the rotor generically undergoes a directed motion, provided that the incident current exceeds a threshold value. Above this threshold, the corresponding rotation frequency (per incoming particle current) for helical geometries turns out to be 2πm/M1, where m/M1 is the ratio of the mass of an incident charge carrier and the mass of the helix per winding number.

Finite-size effects and irrelevant corrections to scaling near the integer quantum Hall transition.

We present a numerical finite-size scaling study of the localization length in long cylinders near the integer quantum Hall transition employing the Chalker-Coddington network model. Corrections to scaling that decay slowly with increasing system size make this analysis a very challenging numerical problem. In this work we develop a novel method of stability analysis that allows for a better estimate of error bars. Applying the new method we find consistent results when keeping second (or higher) order terms of the leading irrelevant scaling field. The knowledge of the associated (negative) irrelevant exponent y is crucial for a precise determination of other critical exponents, including multifractal spectra of wave functions. We estimate |y|>/~0.4, which is considerably larger than most recently reported values. Within this approach we obtain the localization length exponent 2.62±0.06 confirming recent results. Our stability analysis has broad applicability to other observables at integer quantum Hall transition, as well as other critical points where corrections to scaling are present.

Highly conducting single-molecule topological insulators based on mono- and di-radical cations.

Single-molecule topological insulators are promising candidates as conducting wires over nanometre length scales. A key advantage is their ability to exhibit quasi-metallic transport, in contrast to conjugated molecular wires which typically exhibit a low conductance that decays as the wire length increases. Here, we study a family of oligophenylene-bridged bis(triarylamines) with tunable and stable mono- or di-radicaloid character. These wires can undergo one- and two-electron chemical oxidations to the corresponding mono-cation and di-cation, respectively. We show that the oxidized wires exhibit reversed conductance decay with increasing length, consistent with the expectation for Su-Schrieffer-Heeger-type one-dimensional topological insulators. The 2.6-nm-long di-cation reported here displays a conductance greater than 0.1G0, where G0 is the conductance quantum, a factor of 5,400 greater than the neutral form. The observed conductance-length relationship is similar between the mono-cation and di-cation series. Density functional theory calculations elucidate how the frontier orbitals and delocalization of radicals facilitate the observed non-classical quasi-metallic behaviour.

Theory of Chirality Induced Spin Selectivity: Progress and Challenges.

A critical overview of the theory of the chirality-induced spin selectivity (CISS) effect, that is, phenomena in which the chirality of molecular species imparts significant spin selectivity to various electron processes, is provided. Based on discussions in a recently held workshop, and further work published since, the status of CISS effects-in electron transmission, electron transport, and chemical reactions-is reviewed. For each, a detailed discussion of the state-of-the-art in theoretical understanding is provided and remaining challenges and research opportunities are identified.