One of the manifestations of chirality-induced spin selectivity (CISS) is the appearance of a magnetocurrent. Magnetocurrent is the observation that the charge currents at finite bias in a two terminal device for opposite magnetizations of one of the leads differ. Magnetocurrents can only occur in the presence of interactions of the electrons either with vibrational modes or among themselves through the Coulomb interaction. In experiments on chiral molecules assembled in monolayers, the magnetocurrent seems to be dominantly cubic (odd) in bias voltage while theory finds a dominantly even bias voltage dependence. Thus far, theoretical work has predicted a magnetocurrent which is even bias. Here we analyze the bias voltage dependence of the magnetocurrent numerically and analytically involving the spin-orbit and Coulomb interactions (through the Hartree-Fock and Hubbard One approximations). For both approximations it is found that for strong Coulomb interactions the magnetocurrent is dominantly odd in bias voltage, confirming the symmetry observed in experiment.

One of the manifestations of chirality-induced spin selectivity is the appearance of a magnetocurrent. Magnetocurrent is defined as the difference between the charge currents at finite bias in a two terminal device for opposite magnetizations of one of the leads. In experiments on chiral molecules assembled in monolayers the magnetocurrent is dominantly odd in bias voltage, while theory often yields an even one. From theory it is known that the spin-orbit coupling and chirality of the molecule can only generate a finite magnetocurrent in the presence of interactions, either of the electrons with vibrational modes or among themselves, through the Coulomb interaction. Here we analytically show that the magnetocurrent in bipartite-chiral structures mediated through Coulomb interactions is exactly even in the wide band limit and exactly odd for semi-infinite leads due to the bipartite lattice symmetry of the Green’s function. Our numerical results confirm these analytical findings.

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.

One of the manifestations of chirality-induced spin selectivity is the magnetoresistance (MR) in two-terminal transport measurements on molecular junctions. This paper investigates the effect of spin-orbit coupling in the leads on the polarization of the transmission. A helicene molecule between two gold contacts is studied using a tight binding model. To study the occurrence of MR, which is prohibited in coherent transport, as a consequence of the Büttiker reciprocity, we add Büttiker probes to the system in order to incorporate inelastic scattering effects. We show that for a strict two-terminal system without inelastic scattering, the MR is strictly zero in the linear and nonlinear regimes. We show that for a two-terminal system with inelastic scattering, a nonzero MR does appear in the nonlinear regime, reaching values of the order of 0.1%. Our calculations show that for a two-terminal system respecting time-reversal symmetry and charge conservation, a nonzero MR can only be obtained through inelastic scattering. However, spin-orbit coupling in the leads in combination with inelastic scattering modeled with the Büttiker probe method cannot explain the magnitude of the MR measured in experiments.

Interest in building dedicated quantum information science and engineering (QISE) education programs has greatly expanded in recent years. These programs are inherently convergent, complex, often resource intensive and likely require collaboration with a broad variety of stakeholders. In order to address this combination of challenges, we have captured ideas from many members in the community. This manuscript not only addresses policy makers and funding agencies (both public and private and from the regional to the international level) but also contains needs identified by industry leaders and discusses the difficulties inherent in creating an inclusive QISE curriculum. We report on the status of eighteen post-secondary education programs in QISE and provide guidance for building new programs. Lastly, we encourage the development of a comprehensive strategic plan for quantum education and workforce development as a means to make the most of the ongoing substantial investments being made in QISE.

In recent years, a wide range of single-molecule devices has been realized, enabled by technological advances combined with the versatility offered by synthetic chemistry. In particular, single-molecule diodes have attracted significant attention with an ongoing effort to increase the rectification ratio between the forward and reverse current. Various mechanisms have been investigated to improve rectification, either based on molecule-intrinsic properties or by engineering the coupling of the molecule to the electrodes. In this perspective, we first provide an overview of the current experimental approaches reported in literature to achieve rectification at the single-molecule level. We then proceed with our recent efforts in this direction, exploiting the internal structure of multi-site molecules, yielding the highest rectification ratio based on a molecule-intrinsic mechanism. We introduce the theoretical framework for multi-site molecules and infer general design guidelines from this. Based on these guidelines, a series of two-site molecules have been developed and integrated into devices. Using two- and three-terminal mechanically controllable break junction measurements, we show that depending on the on-site energies, which are tunable by chemical design, the devices either exhibit pronounced negative differential conductance, or behave as highly-efficient rectifiers. Finally, we propose a design of a single-molecule diode with a theoretical rectification ratio exceeding a million.

Single-molecule junctions — devices in which a single molecule is electrically connected by two electrodes — enable the study of a broad range of quantum-transport phenomena even at room temperature. These quantum features are related to molecular orbital and spin degrees of freedom and are characterized by various energy scales that can be chemically and physically tuned: level spacings, charging energies, tunnel couplings, exchange energies, vibrational energies and Kondo correlation energies. The competition between these different energy scales leads to a rich variety of processes, which researchers are now starting to be able to control and tune experimentally. In this Technical Review, we present the status of the molecular electronics field from this quantum-transport perspective with a focus on recent experimental results obtained using break-junction devices, including scanning probe and mechanically controlled break junctions, as well as electromigrated gold and graphene break junctions.

Although molecular rectifiers were proposed over four decades ago^1,2, until recently reported rectification ratios (RR) were rather moderate^2–11 (RR ~ 10¹). This ceiling was convincingly broken using a eutectic GaIn top contact¹² to probe molecular monolayers of coupled ferrocene groups (RR ~ 10⁵), as well as using scanning tunnelling microscopy-break junctions^13–16 and mechanically controlled break junctions¹⁷ to probe single molecules (RR ~ 10²–10³). Here, we demonstrate a device based on a molecular monolayer in which the RR can be switched by more than three orders of magnitude (between RR ~ 10⁰ and RR ≥ 10³) in response to humidity. As the relative humidity is toggled between 5% and 60%, the current–voltage (I–V) characteristics of a monolayer of di-nuclear Ru-complex molecules reversibly change from symmetric to strongly asymmetric (diode-like). Key to this behaviour is the presence of two localized molecular orbitals in series, which are nearly degenerate in dry circumstances but become misaligned under high humidity conditions, due to the displacement of counter ions (PF₆ ^–). This asymmetric gating of the two relevant localized molecular orbital levels results in humidity-controlled diode-like behaviour.

A method is presented for predicting one-particle energies for a molecule in a junction with one metal electrode, using density functional theory methods. In contrast to previous studies, in which restricted spin configurations were analyzed, we take spin polarization into account. Furthermore, in addition to junctions in which the molecule is weakly coupled, our method is also capable of describing junctions in which the molecule is chemisorbed to the metal contact. We implemented a fully self-consistent scissor operator to correct the highest occupied molecular orbital-lowest unoccupied molecular orbital gap in transport calculations for single molecule junctions. We present results for various systems and compare our results with those obtained by other groups.

The use of graphene in electronic devices requires a band gap, which can be achieved by creating nanostructures such as graphene nanoribbons. A wide variety of atomically precise graphene nanoribbons can be prepared through on-surface synthesis, bringing the concept of graphene nanoribbon electronics closer to reality. For future applications it is beneficial to integrate contacts and more functionality directly into single ribbons by using heterostructures. Here, we use the on-surface synthesis approach to fabricate a metal-semiconductor junction and a tunnel barrier in a single graphene nanoribbon consisting of 5- and 7-atom wide segments. We characterize the atomic scale geometry and electronic structure by combined atomic force microscopy, scanning tunneling microscopy, and conductance measurements complemented by density functional theory and transport calculations. These junctions are relevant for developing contacts in all-graphene nanoribbon devices and creating diodes and transistors, and act as a first step toward complete electronic devices built into a single graphene nanoribbon.

We investigate transport through mechanically triggered single-molecule switches that are based on the coordination sphere-dependent spin state of Fe^II-species. In these molecules, in certain junction configurations the relative arrangement of two terpyridine ligands within homoleptic Fe^II-complexes can be mechanically controlled. Mechanical pulling may thus distort the Fe^II coordination sphere and eventually modify their spin state. Using the movable nanoelectrodes in a mechanically controlled break-junction at low temperature, current-voltage measurements at cryogenic temperatures support the hypothesized switching mechanism based on the spin-crossover behavior. A large fraction of molecular junctions formed with the spin-crossover-active Fe^II-complex displays a conductance increase for increasing electrode separation and this increase can reach 1-2 orders of magnitude. Theoretical calculations predict a stretching-induced spin transition in the Fe^II-complex and a larger transmission for the high-spin configuration.

Rectification has been at the foundation of molecular electronics. Most single-molecule diodes realized experimentally so far are based on asymmetries in the coupling with the electrodes or using the donor-acceptor principle. In general, however, their rectification ratios are usually small (<10). Here, we propose a single-molecule diode based on an orbital resonance while using the highest occupied molecular orbital (HOMO) and HOMO-1 as transport channels. Our proposed diode design is based on an asymmetric two-site model and analyzed with DFT + NEGF calculations. We find high rectification ratios, even in the case of symmetric coupling to the electrodes. In addition, we show that diode parameters such as the operating voltage and rectification ratio can be tuned by chemical design.