Blowing the fuse: Berry's phase and runaway vibrations in molecular conductors

Nonadiabatic dynamics of molecules interacting with metal surfaces: Extending the hierarchical equations of motion and Langevin dynamics approach to position-dependent metal-molecule couplings

Electronic friction and Langevin dynamics is a popular mixed quantum-classical method for simulating the nonadiabatic dynamics of molecules interacting with metal surfaces, as it can be computationally more efficient than fully quantum approaches. In this work, we extend the theory of electronic friction within the hierarchical equations of motion formalism to models with a position-dependent metal-molecule coupling. We show that the addition of a position-dependent metal-molecule coupling adds new contributions to the electronic friction and other forces, which are highly relevant for many physical processes. Our expressions for the electronic forces within the Langevin equation are valid both in and out of equilibrium and for molecular models containing strong interactions. We demonstrate the approach by applying it to different models of interest.

Enabling Ab Initio Molecular Dynamics under Bias: The CP2K+SMEAGOL Interface for Integrating Density Functional Theory and Non-Equilibrium Green Functions

Density functional theory (DFT) combined with non-equilibrium Green's functions (NEGF) is a powerful approach to model quantum transport under external bias potentials at reasonable computational cost. In this work, we present a new interface between the popular mixed Gaussian/plane waves electronic structure package, CP2K, and the NEGF, code SMEAGOL, the most feature-rich implementation of DFT-NEGF available for CP2K to date. The CP2K+SMEAGOL interface includes the implementation of current induced forces. We verify this implementation for a variety of systems: an infinite 1D Au wire, a parallel-plate capacitor, and a Au-H2-Au junction. We find good agreement with SMEAGOL calculations performed with SIESTA for the same systems and with the example of a solvated Au wire demonstrating for the first time that DFT-NEGF can be used to perform molecular dynamics simulations under bias of large-scale condensed phase systems under realistic operating conditions.

Protein charge transfer far from equilibrium: a theoretical perspective

Potential differences for protein-assisted electron transfer across lipid bilayers or in bio-nano setups can amount to several 100 mV; they lie far outside the range of linear response theory. We describe these situations by Pauli-master equations that are based on Marcus theory of charge transfer between self-trapped electrons and that obey Kirchhoff's current law. In addition, we take on-site blockade effects and a full non-linear response of the local potentials into account. We present analytical and numerical current-potential curves and electron populations for multi-site model systems and biological electron transfer chains. Based on these, we provide empirical rules for electron populations and chemical potentials along the chain. The Pauli-master mean-field results are validated by kinetic Monte Carlo simulations. We briefly discuss the biochemical and evolutionary aspects of our findings.

Phonon and Magnon Jets above the Critical Current in Nanowires with Planar Domain Walls

We show through nonequilibrium nonadiabatic electron-spin-lattice simulations that above a critical current in magnetic atomic wires with a narrow domain wall (DW), a couple of atomic spaces in width, the electron flow triggers violent stimulated emission of phonons and magnons with an almost complete conversion of the incident electron momentum flux into a phonon and magnon flux. Just below the critical levels of the current flow, the DW achieves maximal velocity of about 3×10^{4}  m/s, entering a strongly nonadiabatic regime of DW propagation, followed by a breakdown at higher biases. Above this threshold, a further increase of the current with the applied bias is impossible-the electronic current suffers a heavy suppression and the DW stops. This poses a fundamental limit to the current densities attainable in atomic wires. At the same time it opens up an exciting way of generating the alternative quasiparticle currents, described above, once the requisite electronic-structure properties are met.

Spin dynamics and chirality induced spin selectivity

By now, it is well known that chiral molecules can affect the spin of electrons passing through. In addition, the magnetization of, e.g., nanomagnets covered by chiral molecules can be affected by the presence of molecules. We are studying the mechanisms that explain various observations involving combinations of magnets and chiral molecules. We find that there exists a molecule induced contribution to the magnetic anisotropy of the magnets. Out of equilibrium, when electrons are actually being transported through a nano-magnet covered with chiral molecules, a molecule induced torque acting on the magnetization is emerging. It is of the spin-transfer-torque kind, already discussed in other parts of spintronics. This current induced torque can help explain the observed breaking of the Onsager reciprocity principle in experiments involving magnets and chiral molecules.

Energy dynamics, heat production and heat-work conversion with qubits: toward the development of quantum machines

We present an overview of recent advances in the study of energy dynamics and mechanisms for energy conversion in qubit systems with special focus on realizations in superconducting quantum circuits. We briefly introduce the relevant theoretical framework to analyze heat generation, energy transport and energy conversion in these systems with and without time-dependent driving considering the effect of equilibrium and non-equilibrium environments. We analyze specific problems and mechanisms under current investigation in the context of qubit systems. These include the problem of energy dissipation and possible routes for its control, energy pumping between driving sources and heat pumping between reservoirs, implementation of thermal machines and mechanisms for energy storage. We highlight the underlying fundamental phenomena related to geometrical and topological properties, as well as many-body correlations. We also present an overview of recent experimental activity in this field.

On the meaning of Berry force for unrestricted systems treated with mean-field electronic structure

We show that the Berry force as computed by an approximate, mean-field electronic structure can be meaningful if properly interpreted. In particular, for a model Hamiltonian representing a molecular system with an even number of electrons interacting via a two-body (Hubbard) interaction and a spin-orbit coupling, we show that a meaningful nonzero Berry force emerges whenever there is spin unrestriction-even though the Hamiltonian is real-valued and formally the on-diagonal single-surface Berry force must be zero. Moreover, if properly applied, this mean-field Berry force yields roughly the correct asymptotic motion for scattering through an avoided crossing. That being said, within the context of a ground-state calculation, several nuances do arise as far interpreting the Berry force correctly, and as a practical matter, the Berry force diverges near the Coulson-Fischer point (which can lead to numerical instabilities). We do not address magnetic fields here.

Electron transfer and spin-orbit coupling: Can nuclear motion lead to spin selective rates?

We investigate a spin-boson inspired model of electron transfer, where the diabatic coupling is given by a position-dependent phase, e^iWx. We consider both equilibrium and nonequilibrium initial conditions. We show that, for this model, all equilibrium results are completely invariant to the sign of W (to infinite order). However, the nonequilibrium results do depend on the sign of W, suggesting that photo-induced electron transfer dynamics with spin-orbit coupling can exhibit electronic spin polarization (at least for some time).

Energy, Momentum, and Angular Momentum Transfer between Electrons and Nuclei

The recently developed exact factorization approach condenses all electronic effects on the nuclear subsystem into scalar and vector potentials that appear in an effective time dependent Schrödinger equation. Starting from this equation, we derive subsystem Ehrenfest identities characterizing the energy, momentum, and angular momentum transfer between electrons and nuclei. An effective electromagnetic force operator induced by the electromagnetic field corresponding to the effective scalar and vector potentials appears in all three identities. The effective magnetic field has two components that can be identified with the Berry curvature calculated with (a) different Cartesian coordinates of the same nucleus and (b) arbitrary Cartesian coordinates of two different nuclei. (a) has a classical interpretation as the induced magnetic field felt by the nucleus, while (b) has no classical analog. Subsystem Ehrenfest identities are ideally suited for quantifying energy transfer in electron-phonon systems. With two explicit examples we demonstrate the usefulness of the new identities.

Current-Induced One-Dimensional Diffusion of Co Adatoms on Graphene Nanoribbons

One-dimensional diffusion of Co adatoms on graphene nanoribbons has been induced and investigated by means of scanning tunnelling microscopy (STM). To this end, the nanoribbons and the Co adatoms have been imaged before and after injecting current pulses into the nanoribbons, with the STM tip in direct contact with the ribbon. We observe current-induced motion of the Co atoms along the nanoribbons, which is approximately described by a distribution expected for a thermally activated one-dimensional random walk. This indicates that the nanoribbons reach temperatures far beyond 100 K, which is well above the temperature of the underlying Au substrate. This model system can be developed further for the study of electromigration at the single-atom level.

Phonon Helicity Induced by Electronic Berry Curvature in Dirac Materials

In two-dimensional insulators with time-reversal (TR) symmetry, a nonzero local Berry curvature of low-energy massive Dirac fermions can give rise to nontrivial spin and charge responses, even though the integral of the Berry curvature over all occupied states is zero. In this Letter, we present a new effect induced by the electronic Berry curvature. By studying electron-phonon interactions in BaMnSb_{2}, a prototype two-dimensional Dirac material possessing two TR-related massive Dirac cones, we find that the nonzero local Berry curvature of electrons can induce a phonon angular momentum. The direction of this phonon angular momentum is locked to the phonon propagation direction, and thus we refer to it as "phonon helicity" in a way that is reminiscent of electron helicity in spin-orbit-coupled electronic systems. We discuss possible experimental probes of such phonon helicity.

Unraveling current-induced dissociation mechanisms in single-molecule junctions

Understanding current-induced bond rupture in single-molecule junctions is both of fundamental interest and a prerequisite for the design of molecular junctions, which are stable at higher-bias voltages. In this work, we use a fully quantum mechanical method based on the hierarchical quantum master equation approach to analyze the dissociation mechanisms in molecular junctions. Considering a wide range of transport regimes, from off-resonant to resonant, non-adiabatic to adiabatic transport, and weak to strong vibronic coupling, our systematic study identifies three dissociation mechanisms. In the weak and intermediate vibronic coupling regime, the dominant dissociation mechanism is stepwise vibrational ladder climbing. For strong vibronic coupling, dissociation is induced via multi-quantum vibrational excitations triggered either by a single electronic transition at high bias voltages or by multiple electronic transitions at low biases. Furthermore, the influence of vibrational relaxation on the dissociation dynamics is analyzed and strategies for improving the stability of molecular junctions are discussed.

Current-induced forces in single-resonance systems

In recent years, there has been an increasing interest in nanoelectromechanical devices, current-driven quantum machines, and the mechanical effects of electric currents on nanoscale conductors. Here, we carry out a thorough study of the current-induced forces and the electronic friction of systems whose electronic effective Hamiltonian can be described by an archetypal model, a single energy level coupled to two reservoirs. Our results can help better understand the general conditions that maximize the performance of different devices modeled as a quantum dot coupled to two electronic reservoirs. Additionally, they can be useful to rationalize the role of current-induced forces in the mechanical deformation of one-dimensional conductors.

First-passage time theory of activated rate chemical processes in electronic molecular junctions

Confined nanoscale spaces, electric fields, and tunneling currents make the molecular electronic junction an experimental device for the discovery of new out-of-equilibrium chemical reactions. Reaction-rate theory for current-activated chemical reactions is developed by combining the Keldysh nonequilibrium Green's function treatment of electrons, Fokker-Planck description of the reaction coordinate, and Kramers first-passage time calculations. The nonequilibrium Green's functions (NEGF) provide an adiabatic potential as well as a diffusion coefficient and temperature with local dependence on the reaction coordinate. Van Kampen's Fokker-Planck equation, which describes a Brownian particle moving in an external potential in an inhomogeneous medium with a position-dependent friction and diffusion coefficient, is used to obtain an analytic expression for the first-passage time. The theory is applied to several transport scenarios: a molecular junction with a single reaction coordinate dependent molecular orbital and a model diatomic molecular junction. We demonstrate the natural emergence of Landauer's blowtorch effect as a result of the interplay between the configuration dependent viscosity and diffusion coefficients. The resultant localized heating in conjunction with the bond-deformation due to current-induced forces is shown to be the determining factors when considering chemical reaction rates, each of which results from highly tunable parameters within the system.

Non-adiabatic effects of nuclear motion in quantum transport of electrons: A self-consistent Keldysh-Langevin study

The molecular junction geometry is modeled in terms of nuclear degrees of freedom that are embedded in a stochastic quantum environment of non-equilibrium electrons. The time-evolution of the molecular geometry is governed via a mean force, a frictional force, and a stochastic force, forces arising from many electrons tunneling across the junction for a given nuclear vibration. Conversely, the current-driven nuclear dynamics feed back to the electronic current, which can be captured according to the extended expressions for the current that have explicit dependences on classical nuclear velocities and accelerations. Current-induced nuclear forces and the non-adiabatic electric current are computed using non-equilibrium Green's functions via a timescale separation solution of Keldysh-Kadanoff-Baym equations in the Wigner space. Applying the theory to molecular junctions demonstrated that non-adiabatic corrections play an important role when nuclear motion is considered non-equilibrium and, in particular, showed that non-equilibrium and equilibrium descriptions of nuclear motion produce significantly different current characteristics. It is observed that non-equilibrium descriptions generally produce heightened conductance profiles relative to the equilibrium descriptions and provide evidence that the effective temperature is an effective measure of the steady-state characteristics. Finally, we observe that the non-equilibrium descriptions of nuclear motion can give rise to the Landauer blowtorch effect via the emergence of multi-minima potential energy surfaces in conjunction with non-uniform temperature profiles. The Landauer blowtorch effect and its impact on the current characteristics, waiting times, and the Fano factor are explored for an effective adiabatic potential that morphs between a single, double, and triple potential as a function of voltage.

Cooling molecular electronic junctions by AC current

Electronic current flowing in a molecular electronic junction dissipates significant amounts of energy to vibrational degrees of freedom, straining and rupturing chemical bonds and often quickly destroying the integrity of the molecular device. The infamous mechanical instability of molecular electronic junctions critically limits performance and lifespan and raises questions as to the technological viability of single-molecule electronics. Here, we propose a practical scheme for cooling the molecular vibrational temperature via application of an AC voltage over a large, static operational DC voltage bias. Using nonequilibrium Green's functions, we computed the viscosity and diffusion coefficient experienced by nuclei surrounded by a nonequilibrium "sea" of periodically driven, current-carrying electrons. The effective molecular junction temperature is deduced by balancing the viscosity and diffusion coefficients. Our calculations show the opportunity of achieving in excess of 40% cooling of the molecular junction temperature while maintaining the same average current.

Voltage-Induced Rearrangements in Atomic-Size Contacts

We study voltage-induced conductance changes of Pb, Au, Al, and Cu atomic contacts. The experiments are performed in vacuum at low temperature using mechanically controllable break junctions. We determine switching histograms, i.e., distribution functions of switching voltages and switching currents, as a function of the conductance. We observe a clear material dependence: Au reveals the highest and almost conductance-independent switching voltage, while Al has the lowest with a pronounced dependence on the conductance. The theoretical study uses density functional theory and a generalized Langevin equation considering the pumping of particular phonon modes. We identify a runaway voltage as the threshold at which the pumping destabilizes the atomic arrangement. We find qualitative agreement between the average switching voltage and the runaway voltage regarding the material and conductance dependence and contact-to-contact variation of the average characteristic voltages, suggesting that the phonon pumping is a relevant mechanism driving the rearrangements in the experimental contacts.

Nonthermal vibrations in biased molecular junctions

We study vibrational statistics in current-carrying model molecular junctions using a master equation approach. In particular, we concentrate on the validity of using an effective temperature T_{eff} to characterize the nonequilibrium steady state of a vibrational mode. We identify cases in which a single T_{eff} cannot fully describe one vibrational state. In such cases, the probability distribution among different vibrational states does not follow the Boltzmann type. Consequently, the actual entropy (free energy) of the vibrational mode is lower (higher) than the corresponding thermal value given by T_{eff}, indicating extra work can be extracted from these states. Our results will be useful for the study of a nonthermal vibrational state in the thermodynamics of nanoscale systems, and its usage in nanoscale heat engines.

Thermodynamics and Steady State of Quantum Motors and Pumps Far from Equilibrium

In this article, we briefly review the dynamical and thermodynamical aspects of different forms of quantum motors and quantum pumps. We then extend previous results to provide new theoretical tools for a systematic study of those phenomena at far-from-equilibrium conditions. We mainly focus on two key topics: (1) The steady-state regime of quantum motors and pumps, paying particular attention to the role of higher order terms in the nonadiabatic expansion of the current-induced forces. (2) The thermodynamical properties of such systems, emphasizing systematic ways of studying the relationship between different energy fluxes (charge and heat currents and mechanical power) passing through the system when beyond-first-order expansions are required. We derive a general order-by-order scheme based on energy conservation to rationalize how every order of the expansion of one form of energy flux is connected with the others. We use this approach to give a physical interpretation of the leading terms of the expansion. Finally, we illustrate the above-discussed topics in a double quantum dot within the Coulomb-blockade regime and capacitively coupled to a mechanical rotor. We find many exciting features of this system for arbitrary nonequilibrium conditions: a definite parity of the expansion coefficients with respect to the voltage or temperature biases; negative friction coefficients; and the fact that, under fixed parameters, the device can exhibit multiple steady states where it may operate as a quantum motor or as a quantum pump, depending on the initial conditions.

Circular current and induced force in a molecular ring junction

We consider bias-induced circular current in a molecular ring junction. It is natural to define circular current as a component of ring current that acts as a sole source of magnetic flux induced in the ring. Alternatively, the bias-induced circular current can also be determined from the magnetic response of the ring junction to an external flux in the zero-flux limit. This leads to determination of bias-induced circular current without actually calculating the bond currents. We also explore the possibility of circular current-induced force rupturing the covalent bonds in the ring leading to ultimate breakdown of the ring junction. Our calculations underscore the reliability problem posed by the current magnification effect in the molecular ring structures.

Waiting time between charging and discharging processes in molecular junctions

When electric current flows through a molecular junction, the molecule constantly charges and discharges by tunneling electrons. These charging and discharging events occur at specific but random times and are separated by stochastic time intervals. These time intervals can be associated with the dwelling time for a charge (electron or hole) to reside on the molecule. In this paper, the statistical properties of these time intervals are studied and a general formula for their distribution is derived. The theory is based on the Markovian master equation which takes into account transitions between the vibrational states of charged and neutral molecules in the junction. Two quantum jump operators are identified from the Liouvillian of the master equation-one corresponds to charging of the molecule and the other discharges the molecule back to the neutral state. The quantum jump operators define the conditional probability that given that the molecule was charged by a tunneling electron at time t, the molecule becomes neutral at a later time t + τ discharging the electron to the drain electrode. Statistical properties of these time intervals τ are studied with the use of this distribution.

Fast quantitative optical detection of heat dissipation by surface plasmon polaritons

Heat management at the nanoscale is an issue of increasing importance. In optoelectronic devices the transport and decay of plasmons contribute to the dissipation of heat. By comparison of experimental data and simulations we demonstrate that it is possible to gain quantitative information about excitation, propagation and decay of surface plasmon polaritons (SPPs) in a thin gold stripe supported by a silicon membrane. The temperature-dependent optical transmissivity of the membrane is used to determine the temperature distribution around the metal stripe with high spatial and temporal resolution. This method is complementary to techniques where the propagation of SPPs is monitored optically, and provides additional information which is not readily accessible by other means. In particular, we demonstrate that the thermal conductivity of the membrane can also be derived from our analysis. The results presented here show the high potential of this tool for heat management studies in nanoscale devices.

Perspective: How to understand electronic friction

Electronic friction is a correction to the Born-Oppenheimer approximation, whereby nuclei in motion experience a drag in the presence of a manifold of electronic states. The notion of electronic friction has a long history and has been (re-)discovered in the context of a wide variety of different chemical and physical systems including, but not limited to, surface scattering events, surface reactions or chemisorption, electrochemistry, and conduction through molecular-(or nano-) junctions. Over the years, quite a few different forms of electronic friction have been offered in the literature. In this perspective, we briefly review these developments of electronic friction, highlighting the fact that we can now isolate a single, unifying form for (Markovian) electronic friction. We also focus on the role of electron-electron interactions for understanding frictional effects and offer our thoughts on the strengths and weaknesses of using electronic friction to model dynamics in general.

Structure and local charging of electromigrated Au nanocontacts

We study the structure and the electronic properties of Au nanocontacts created by controlled electromigration of thin film devices, a method frequently used to contact molecules. In contrast to electromigration testing, a current is applied in a cyclic fashion and during each cycle the resistance increase of the metal upon heating is used to avoid thermal runaway. In this way, nanometer sized-gaps are obtained. The thin film devices with an optimized structure at the origin of the electromigration process are made by shadow evaporation without contamination by organic materials. Defining rounded edges and a thinner area in the center of the device allow to pre-determine the location where the electromigration takes place. Scanning force microscopy images of the pristine Au film and electromigrated contact show its grainy structure. Through electromigration, a 1.5 μm-wide slit is formed, with extensions only on the anode side that had previously not been observed in narrower structures. It is discussed whether this could be explained by asymmetric heating of both electrodes. New grains are formed in the slit and on the extensions on both, the anode and the cathode side. The smaller structures inside the slit lead to an electrode distance below 150 nm. Kelvin probe force microscopy images show a local work function difference with fluctuations of 70 mV on the metal before electromigration. Between the electrodes, disconnected through electromigration, a work function difference of 3.2 V is observed due to charging. Some of the grains newly formed by electromigration are electrically disconnected from the electrodes.

Shot Noise of 1,4-Benzenedithiol Single-Molecule Junctions

We report measurements of the shot noise on single-molecule Au-1,4-benzenedithiol-Au junctions, fabricated with the mechanically controllable break junction (MCBJ) technique at 4.2 K in a wide range of conductance values from 10(-2) to 0.24 conductance quanta. We introduce a simple measurement scheme using a current amplifier and a spectrum analyzer and that does not imply special requirements regarding the electrical leads. The experimental findings provide evidence that the current is carried by a single conduction channel throughout the whole conductance range. This observation suggests that the number of channels is limited by the Au-thiol bonds and that contributions due to direct tunneling from the Au to the π-system of the aromatic ring are negligible also for high conductance. The results are supported by quantum transport calculations using density functional theory.

Current-induced runaway vibrations in dehydrogenated graphene nanoribbons

We employ a semi-classical Langevin approach to study current-induced atomic dynamics in a partially dehydrogenated armchair graphene nanoribbon. All parameters are obtained from density functional theory. The dehydrogenated carbon dimers behave as effective impurities, whose motion decouples from the rest of carbon atoms. The electrical current can couple the dimer motion in a coherent fashion. The coupling, which is mediated by nonconservative and pseudo-magnetic current-induced forces, change the atomic dynamics, and thereby show their signature in this simple system. We study the atomic dynamics and current-induced vibrational instabilities using a simplified eigen-mode analysis. Our study illustrates how armchair nanoribbons can serve as a possible testbed for probing the current-induced forces.

Evidence for non-conservative current-induced forces in the breaking of Au and Pt atomic chains

This experimental work aims at probing current-induced forces at the atomic scale. Specifically it addresses predictions in recent work regarding the appearance of run-away modes as a result of a combined effect of the non-conservative wind force and a 'Berry force'. The systems we consider here are atomic chains of Au and Pt atoms, for which we investigate the distribution of break down voltage values. We observe two distinct modes of breaking for Au atomic chains. The breaking at high voltage appears to behave as expected for regular break down by thermal excitation due to Joule heating. However, there is a low-voltage breaking mode that has characteristics expected for the mechanism of current-induced forces. Although a full comparison would require more detailed information on the individual atomic configurations, the systems we consider are very similar to those considered in recent model calculations and the comparison between experiment and theory is very encouraging for the interpretation we propose.

Current-induced forces: a new mechanism to induce negative differential resistance and current-switching effect in molecular junctions

Current-induced forces can excite molecules, polymers and other low-dimensional materials, which in turn leads to an effective gate voltage through Holstein interaction. Here, by taking a short asymmetric DNA junction as an example, and using the Langevin approach, we find that when suppression of charge transport by the effective gate voltage surpasses the current increase from an elevated voltage bias, the current-voltage (I-V) curves display strong negative differential resistance (NDR) and perfect current-switching characteristics. The asymmetric DNA chain differs in mechanical stability under inverse voltages and the I-V curve is asymmetric about inverse biases, which can be used to understand recent transport experiments on DNA chains, and meanwhile provides a new strategy to realize NDR in molecular junctions and other low-dimensional quantum systems.

Nonconservative current-driven dynamics: beyond the nanoscale

Long metallic nanowires combine crucial factors for nonconservative current-driven atomic motion. These systems have degenerate vibrational frequencies, clustered about a Kohn anomaly in the dispersion relation, that can couple under current to form nonequilibrium modes of motion growing exponentially in time. Such motion is made possible by nonconservative current-induced forces on atoms, and we refer to it generically as the waterwheel effect. Here the connection between the waterwheel effect and the stimulated directional emission of phonons propagating along the electron flow is discussed in an intuitive manner. Nonadiabatic molecular dynamics show that waterwheel modes self-regulate by reducing the current and by populating modes in nearby frequency, leading to a dynamical steady state in which nonconservative forces are counter-balanced by the electronic friction. The waterwheel effect can be described by an appropriate effective nonequilibrium dynamical response matrix. We show that the current-induced parts of this matrix in metallic systems are long-ranged, especially at low bias. This nonlocality is essential for the characterisation of nonconservative atomic dynamics under current beyond the nanoscale.

Current-induced forces and hot spots in biased nanojunctions

We investigate theoretically the interplay of current-induced forces (CIFs), Joule heating, and heat transport inside a current-carrying nanoconductor. We find that the CIFs, due to the electron-phonon coherence, can control the spatial heat dissipation in the conductor. This yields a significant asymmetric concentration of excess heating (hot spot) even for a symmetric conductor. When coupled to the electrode phonons, CIFs drive different phonon heat flux into the two electrodes. First-principles calculations on realistic biased nanojunctions illustrate the importance of the effect.

A current-driven single-atom memory

The possibility of fabricating electronic devices with functional building blocks of atomic size is a major driving force of nanotechnology. The key elements in electronic circuits are switches, usually realized by transistors, which can be configured to perform memory operations. Electronic switches have been miniaturized all the way down to the atomic scale. However, at such scales, three-terminal devices are technically challenging to implement. Here we show that a metallic atomic-scale contact can be operated as a reliable and fatigue-resistant two-terminal switch. We apply a careful electromigration protocol to toggle the conductance of an aluminium atomic contact between two well-defined values in the range of a few conductance quanta. Using the nonlinearities of the current-voltage characteristics caused by superconductivity in combination with molecular dynamics and quantum transport calculations, we provide evidence that the switching process is caused by the reversible rearrangement of single atoms. Owing to its hysteretic behaviour with two distinct states, this two-terminal switch can be used as a non-volatile information storage element.

Adiabatic quantum motors

When parameters are varied periodically, charge can be pumped through a mesoscopic conductor without applied bias. Here, we consider the inverse effect in which a transport current drives a periodic variation of an adiabatic degree of freedom. This provides a general operating principle for adiabatic quantum motors which we discuss here in general terms. We relate the work performed per cycle on the motor degree of freedom to characteristics of the underlying quantum pump and discuss the motors' efficiency. Quantum motors based on chaotic quantum dots operate solely due to quantum interference, and motors based on Thouless pumps have ideal efficiency.

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.

Observation of intramolecular vibrations cooperating with the magnetic phase transition in a nickel-bis-dithiolene compound

A new one-dimensional (1-D) ion-pair compound, [1,7-bis(1-methylimidazolium)heptane][Ni(mnt)(2)](2) (mnt(2-) = maleonitriledithiolate), was synthesized and characterized structurally and magnetically. This compound shows a spin-Peierls-type transition at around 235 K. Its crystal structure belongs to the monoclinic system with space group C2/c and the magnetic [Ni(mnt)(2)](-) anions form uniform stacks in the high-temperature (HT) phase. The crystal undergoes a transformation into the triclinic space group P1 accompanied by the magnetic transition and the anion stacks become dimerized in the low-temperature (LT) phase. The entropy changes (ΔS) are estimated to be 0.772 J K(-1) mol(-1) for the spin-Peierls-type transition, from DSC data, which is much less than the spin entropy change (ΔS = R ln 2 ≈ 5.76 J K(-1) mol(-1)), indicating that a substantial short-range order persists above the transition temperature. The variable temperature IR spectra showed that the peak positions and intensities for the bands near 1160 and 725 cm(-1), which correspond respectively to the ν(C-C) + ν(C-S) mode of the mnt(2-) ligands and the rocking vibration mode of the methylene group γ(r)(CH(2)) in the cation moiety, undergo an abrupt change at around 240 K, close to the transition temperature. This observation demonstrates that the intramolecular vibrations of both the anion and the counter-cation probably couple with the spins to cooperate with the spin-Peierls-type phase transition in this 1-D spin system.

Nonequilibrium thermodynamics of interacting tunneling transport: variational grand potential, density functional formulation and nature of steady-state forces

The standard formulation of tunneling transport rests on an open-boundary modeling. There, conserving approximations to nonequilibrium Green function or quantum statistical mechanics provide consistent but computational costly approaches; alternatively, the use of density-dependent ballistic-transport calculations (e.g., Lang 1995 Phys. Rev. B 52 5335), here denoted 'DBT', provides computationally efficient (approximate) atomistic characterizations of the electron behavior but has until now lacked a formal justification. This paper presents an exact, variational nonequilibrium thermodynamic theory for fully interacting tunneling and provides a rigorous foundation for frozen-nuclei DBT calculations as a lowest-order approximation to an exact nonequilibrium thermodynamic density functional evaluation. The theory starts from the complete electron nonequilibrium quantum statistical mechanics and I identify the operator for the nonequilibrium Gibbs free energy which, generally, must be treated as an implicit solution of the fully interacting many-body dynamics. I demonstrate a minimal property of a functional for the nonequilibrium thermodynamic grand potential which thus uniquely identifies the solution as the exact nonequilibrium density matrix. I also show that the uniqueness-of-density proof from a closely related Lippmann-Schwinger collision density functional theory (Hyldgaard 2008 Phys. Rev. B 78 165109) makes it possible to express the variational nonequilibrium thermodynamic description as a single-particle formulation based on universal electron-density functionals; the full nonequilibrium single-particle formulation improves the DBT method, for example, by a more refined account of Gibbs free energy effects. I illustrate a formal evaluation of the zero-temperature thermodynamic grand potential value which I find is closely related to the variation in the scattering phase shifts and hence to Friedel density oscillations. This paper also discusses the difference between the here-presented exact thermodynamic forces and the often-used electrostatic forces. Finally the paper documents an inherent adiabatic nature of the thermodynamic forces and observes that these are suited for a nonequilibrium implementation of the Born-Oppenheimer approximation.

Spin-orbit coupling induced spin-transfer torque and current polarization in topological-insulator/ferromagnet vertical heterostructures

We predict an unconventional spin-transfer torque (STT) acting on the magnetization of a free ferromagnetic (F) layer within N/TI/F vertical heterostructures, which originates from strong spin-orbit coupling on the surface of a three-dimensional topological insulator (TI), as well as from charge current becoming spin polarized in the direction of transport as it flows perpendicularly from the normal metal (N) across the bulk of the TI layer. The STT vector has both in-plane and perpendicular components that are comparable in magnitude to conventional torque in F'/I/F (where I stands for insulator) magnetic tunnel junctions, while not requiring additional spin-polarizing F' layer with fixed magnetization, which makes it advantageous for spintronics applications. Our principal formal result is a derivation of the nonequilibrium Green function-based formula and the corresponding gauge-invariant nonequilibrium density matrix, which makes it possible to analyze the components of the STT vector in the presence of arbitrary strong spin-orbit coupling either in the bulk or at the interface of the free F layer.

An ignition key for atomic-scale engines

A current-carrying resonant nanoscale device, simulated by non-adiabatic molecular dynamics, exhibits sharp activation of non-conservative current-induced forces with bias. The result, above the critical bias, is generalized rotational atomic motion with a large gain in kinetic energy. The activation exploits sharp features in the electronic structure, and constitutes, in effect, an ignition key for atomic-scale motors. A controlling factor for the effect is the non-equilibrium dynamical response matrix for small-amplitude atomic motion under current. This matrix can be found from the steady-state electronic structure by a simpler static calculation, providing a way to detect the likely appearance, or otherwise, of non-conservative dynamics, in advance of real-time modelling.

Geometric heat flux for classical thermal transport in interacting open systems

We study classical heat conduction in a dissipative open system composed of interacting oscillators. By exactly solving a twisted Fokker-Planck equation which describes the full counting statistics of heat flux flowing through the system, we identify the geometric-phase-like effect and examine its impact on the classical heat transport. We find that the nonlinear interaction as well as the closely related temperature dependence of system parameters are crucial in manifesting the geometric-phase contribution of heat flux. Finally, we propose an electronic experiment based on RC circuits to verify our theoretical predictions.

Current-induced forces in mesoscopic systems: A scattering-matrix approach

Nanoelectromechanical systems are characterized by an intimate connection between electronic and mechanical degrees of freedom. Due to the nanoscopic scale, current flowing through the system noticeably impacts upons the vibrational dynamics of the device, complementing the effect of the vibrational modes on the electronic dynamics. We employ the scattering-matrix approach to quantum transport in order to develop a unified theory of nanoelectromechanical systems out of equilibrium. For a slow mechanical mode the current can be obtained from the Landauer-Büttiker formula in the strictly adiabatic limit. The leading correction to the adiabatic limit reduces to Brouwer's formula for the current of a quantum pump in the absence of a bias voltage. The principal results of the present paper are the scattering-matrix expressions for the current-induced forces acting on the mechanical degrees of freedom. These forces control the Langevin dynamics of the mechanical modes. Specifically, we derive expressions for the (typically nonconservative) mean force, for the (possibly negative) damping force, an effective "Lorentz" force that exists even for time-reversal-invariant systems, and the fluctuating Langevin force originating from Nyquist and shot noise of the current flow. We apply our general formalism to several simple models that illustrate the peculiar nature of the current-induced forces. Specifically, we find that in out-of-equilibrium situations the current-induced forces can destabilize the mechanical vibrations and cause limit-cycle dynamics.

Current-induced dynamics in carbon atomic contacts

BACKGROUND

The effect of electric current on the motion of atoms still poses many questions, and several mechanisms are at play. Recently there has been focus on the importance of the current-induced nonconservative forces (NC) and Berry-phase derived forces (BP) with respect to the stability of molecular-scale contacts. Systems based on molecules bridging electrically gated graphene electrodes may offer an interesting test-bed for these effects.

RESULTS

We employ a semi-classical Langevin approach in combination with DFT calculations to study the current-induced vibrational dynamics of an atomic carbon chain connecting electrically gated graphene electrodes. This illustrates how the device stability can be predicted solely from the modes obtained from the Langevin equation, including the current-induced forces. We point out that the gate offers control of the current, independent of the bias voltage, which can be used to explore current-induced vibrational instabilities due the NC/BP forces. Furthermore, using tight-binding and the Brenner potential we illustrate how Langevin-type molecular-dynamics calculations including the Joule heating effect for the carbon-chain systems can be performed. Molecular dynamics including current-induced forces enables an energy redistribution mechanism among the modes, mediated by anharmonic interactions, which is found to be vital in the description of the electrical heating.

CONCLUSION

We have developed a semiclassical Langevin equation approach that can be used to explore current-induced dynamics and instabilities. We find instabilities at experimentally relevant bias and gate voltages for the carbon-chain system.

Nonconservative current-induced forces: A physical interpretation

We give a physical interpretation of the recently demonstrated nonconservative nature of interatomic forces in current-carrying nanostructures. We start from the analytical expression for the curl of these forces, and evaluate it for a point defect in a current-carrying system. We obtain a general definition of the capacity of electrical current flow to exert a nonconservative force, and thus do net work around closed paths, by a formal noninvasive test procedure. Second, we show that the gain in atomic kinetic energy over time, generated by nonconservative current-induced forces, is equivalent to the uncompensated stimulated emission of directional phonons. This connection with electron-phonon interactions quantifies explicitly the intuitive notion that nonconservative forces work by angular momentum transfer.

Organic-based molecular switches for molecular electronics

In a general sense, molecular electronics (ME) is the branch of nanotechnology which studies the application of molecular building blocks for the fabrication of electronic components. Among the different types of molecules, organic compounds have been revealed as promising candidates for ME, due to the easy access, great structural diversity and suitable electronic and mechanical properties. Thanks to these useful capabilities, organic molecules have been used to emulate electronic devices at the nanoscopic scale. In this feature article, we present the diverse strategies used to develop organic switches towards ME with special attention to non-volatile systems.

The phonon Hall effect: theory and application

We present a systematic theory of the phonon Hall effect in a ballistic crystal lattice system, and apply it on the kagome lattice which is ubiquitous in various real materials. By proposing a proper second quantization for the non-Hermitian in the polarization-vector space, we obtain a new heat current density operator with two separate contributions: the normal velocity responsible for the longitudinal phonon transport, and the anomalous velocity manifesting itself as the Hall effect of transverse phonon transport. As exemplified in kagome lattices, our theory predicts that the direction of Hall conductivity at low magnetic field can be reversed by tuning the temperatures, which we hope can be verified by experiments in the future. Three phonon-Hall-conductivity singularities induced by phonon-band-topology change are discovered as well, which correspond to the degeneracies at three different symmetric center points, Γ, K, X, in the wavevector space of the kagome lattice.

Laserlike vibrational instability in rectifying molecular conductors

We study the damping of molecular vibrations due to electron-hole pair excitations in donor-acceptor (D-A) type molecular rectifiers. At finite voltage additional nonequilibrium electron-hole pair excitations involving both electrodes become possible, and contribute to the stimulated emission and absorption of phonons. We point out a generic mechanism for D-A molecules, where the stimulated emission can dominate beyond a certain voltage due to the inverted position of the D and A quantum resonances. This leads to current-driven amplification (negative damping) of the phonons similar to laser action. We investigate the effect in realistic molecular rectifier structures using first-principles calculations.

Scattering theory of current-induced forces in mesoscopic systems

We develop a scattering theory of current-induced forces exerted by the conduction electrons of a general mesoscopic conductor on slow "mechanical" degrees of freedom. Our theory describes the current-induced forces both in and out of equilibrium in terms of the scattering matrix of the phase-coherent conductor. Under general nonequilibrium conditions, the resulting mechanical Langevin dynamics is subject to both nonconservative and velocity-dependent Lorentz-like forces, in addition to (possibly negative) friction. We illustrate our results with a two-mode model inspired by hydrogen molecules in a break junction which exhibits limit-cycle dynamics of the mechanical modes.