Emergence of Boltzmann Subspaces in Open Quantum Systems Far from Equilibrium.

Single molecule junctions are important examples of complex out-of-equilibrium many-body quantum systems. We identify a nontrivial clustering of steady state populations into distinctive subspaces with Boltzmann-like statistics, which persist far from equilibrium. Such Boltzmann subspaces significantly reduce the information needed to describe the steady state, enabling modeling of high-dimensional systems that are otherwise beyond the reach of current computations. The emergence of Boltzmann subspaces is demonstrated analytically and numerically for fermionic transport systems of increasing complexity.

How an electrical current can stabilize a molecular nanojunction.

The stability of molecular junctions under transport is of the utmost importance for the field of molecular electronics. This question is often addressed within the paradigm of current-induced heating of nuclear degrees of freedom or current-induced forces acting upon the nuclei. At the same time, an essential characteristic of the failure of a molecular electronic device is its changing conductance - typically from a finite value for the intact device to zero for a device that lost its functionality. In this publication, we focus on the current-induced changes in the molecular conductance, which are inherent to molecular junctions at the limit of mechanical stability. We employ a numerically exact framework based on the hierarchical equations of motion approach, which treats both electronic and nuclear degrees of freedom on an equal footing and does not impose additional assumptions. Studying generic model systems for molecular junctions with dissociative potentials for a wide range of parameters spanning the adiabatic and the nonadiabatic regime, we find that molecular junctions that exhibit a decrease in conductance upon dissociation are more stable than junctions that are more conducting in their dissociated state. This represents a new mechanism that stabilizes molecular junctions under current. Moreover, we identify characteristic signatures in the current of breaking junctions related to the interplay between changes in the conductance and the nuclear configuration and show how these are related to properties of the leads rather than characteristics of the molecule itself.

Nonequilibrium reaction rate theory: Formulation and implementation within the hierarchical equations of motion approach.

The study of chemical reactions in environments under nonequilibrium conditions has been of interest recently in a variety of contexts, including current-induced reactions in molecular junctions and scanning tunneling microscopy experiments. In this work, we outline a fully quantum mechanical, numerically exact approach to describe chemical reaction rates in such nonequilibrium situations. The approach is based on an extension of the flux correlation function formalism to nonequilibrium conditions and uses a mixed real and imaginary time hierarchical equations of motion approach for the calculation of rate constants. As a specific example, we investigate current-induced intramolecular proton transfer reactions in a molecular junction for different applied bias voltages and molecule-lead coupling strengths.

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.

The porphyrin ring rather than the metal ion dictates long-range electron transport across proteins suggesting coherence-assisted mechanism.

The fundamental biological process of electron transfer (ET) takes place across proteins with common ET pathways of several nanometers. Recent discoveries push this limit and show long-range extracellular ET over several micrometers. Here, we aim in deciphering how protein-bound intramolecular cofactors can facilitate such long-range ET. In contrast to natural systems, our protein-based platform enables us to modulate important factors associated with ET in a facile manner, such as the type of the cofactor and its quantity within the protein. We choose here the biologically relevant protoporphyrin molecule as the electron mediator. Unlike natural systems having only Fe-containing protoporphyrins, i.e., heme, as electron mediators, we use here porphyrins with different metal centers, or lacking a metal center. We show that the metal redox center has no role in ET and that ET is mediated solely by the conjugated backbone of the molecule. We further discuss several ET mechanisms, accounting to our observations with possible contribution of coherent processes. Our findings contribute to our understanding of the participation of heme molecules in long-range biological ET.

Mechanical Stabilization of Nanoscale Conductors by Plasmon Oscillations.

External driving of the Fermion reservoirs interacting with a nanoscale charge-conductor is shown to enhance its mechanical stability during resonant tunneling. This counterintuitive cooling effect is predicted despite the net energy flow into the device. Field-induced plasmon oscillations stir the energy distribution of charge carriers near the reservoir's chemical potentials into a nonequilibrium state with favored transport of low-energy electrons. Consequently, excess heating of mechanical degrees of freedom in the conductor is suppressed. We demonstrate and analyze this effect for a generic model of mechanical instability in nanoelectronic devices, covering a broad range of parameters. Plasmon-induced stabilization is suggested as a feasible strategy to confront a major problem of current-induced heating and breakdown of nanoscale systems operating far from equilibrium.

Ballistic transport and quantum unfurling in molecular junctions via minimal representations of quantum master equations.

Quantum furling and unfurling are inelastic transitions between localized and delocalized electronic states. We predict scenarios where these processes govern charge transport through donor-bridge-acceptor molecular junctions. Like in the case of ballistic transport, the resulting currents are nearly independent of the molecular bridge length. However, currents involving quantum furling and unfurling processes can be controlled by the coupling to vibrations in the intra-molecular and the extra-molecular environment, which can be experimentally tuned. Our study is based on rate equations for exchange of energy (bosons) and particles (fermions) between the molecular bridge and its environment. An efficient algorithm is introduced for a compact representation of the relevant rate equations, which utilizes the redundancies in the rate matrix and the sparsity of the creation and annihilation operators in the molecular Fock space.

Coherence-assisted electron diffusion across the multi-heme protein-based bacterial nanowire.

Biological electron transfer (ET) is one of the most studied biochemical processes due to its immense importance in biology. For many years, biological ET was explained using the classical incoherent transport mechanism, i.e. sequential hopping. One of the relatively recent major observations in this field is long-range extracellular ET (EET), where some bacteria were shown to mediate electrons for extremely long distances on the micrometer length scales across individual nanowires. This fascinating finding has resulted in several suggested mechanisms that might explain this intriguing EET. More recently, the structure of a conductive G. sulfurreducens nanowire has been solved, which showed a highly ordered quasi-1D wire of a hexaheme cytochrome protein, named OmcS. Based on this new structure, we suggest here several electron diffusion models for EET, involving either purely hopping or several degrees of mixed hopping and coherent transport, in which the coherent part is due to a local rigidification of the protein structure, associated with a decrease in the local reorganization energy. The effect is demonstrated for two closely packed heme sites as well as for longer chains containing up to several dozens porphyrins. We show that the pure hopping model probably cannot explain the reported conductivity values of the G. sulfurreducens nanowire using conventional values of reorganization energy and electronic coupling. On the other hand, we show that for a wide range of the latter energy values, the mixed hopping-coherent model results in superior electron diffusion compared to the pure hopping model, and especially for long-range coherent transport, involving multiple porphyrin sites.

Quantum transport in the presence of contact vibrations.

We explore the transport of fermions through a quantum conductor in the presence of contact vibrations. The latter are coupled to charge transfer between the fermion reservoirs and the conductor but remain inert to the charging state of the conductor itself. We derive explicit expressions for charge transfer rates into and out of the conductor which extend the scope of rate theories of inelastic transport to the presence of contact vibrations. Implementing the theory to a simple model with a uniform vibronic coupling at different contact orbitals, we demonstrate and analyze the effect of such vibrations on the charge current. Asymmetry between contact vibrations at the two reservoirs is shown to induce a pronounced current rectification, especially in the limit of floppy (low frequencies) contacts. At high frequencies, vibrational quantization is shown to suppress the effect, in accord with the increasing contact rigidity. This quantum result requires corrections beyond the classical theory of charge hopping.

Breaking Down Resonance: Nonlinear Transport and the Breakdown of Coherent Tunneling Models in Single Molecule Junctions.

The promise of the field of single-molecule electronics is to reveal a new class of quantum devices that leverages the strong electronic interactions inherent to subnanometer scale systems. Here, we form Au-molecule-Au junctions using a custom scanning tunneling microscope and explore charge transport through current-voltage measurements. We focus on the resonant tunneling regime of two molecules, one that is primarily an electron conductor and one that conducts primarily holes. We find that in the high bias regime, junctions that do not rupture demonstrate reproducible and pronounced negative differential resistance (NDR)-like features followed by hysteresis with peak-to-valley ratios exceeding 100 in some cases. Furthermore, we show that both junction rupture and NDR are induced by charging of the molecular orbital dominating transport and find that the charging is reversible at lower bias and with time with kinetic time scales on the order of hundreds of milliseconds. We argue that these results cannot be explained by existing models of charge transport and likely require theoretical advances describing the transition from coherent to sequential tunneling. Our work also suggests new rules for operating single-molecule devices at high bias to obtain highly nonlinear behavior.

Formulation of Long-Range Transport Rates through Molecular Bridges: From Unfurling to Hopping.

Weak fluctuations about the rigid equilibrium structure of ordered molecular bridges drive charge transfer in donor-bridge-acceptor systems via quantum unfurling, which differs from both hopping and ballistic transfer, yet static disorder (low frequency motions) in the bridge is shown to induce a change of mechanism from unfurling to hopping when local fluctuations along the molecular bridge are uncorrelated. Remarkably, these two different transport mechanisms manifest in similar charge-transfer rates, which are nearly independent of the molecular bridge length. We propose an experimental test for distinguishing unfurling from hopping in DNA models with different helix directionality. A unified formulation explains the apparent similarity in the length dependence of the transfer rate despite the difference in the underlying transport mechanisms.

High-Voltage-Assisted Mechanical Stabilization of Single-Molecule Junctions.

Resonant tunneling is an efficient mechanism for charge transport through nanoscale conductance junctions due to the relatively high currents involved. However, continuous charging and discharging cycles of the nanoconductor during resonant tunneling often lead to mechanical instability. The realization of efficient nanoscale electronic components therefore depends to a large extent on the ability to mechanically stabilize them during resonant transport. In this work, we focus on single-molecule junctions, demonstrating that their mechanical stability during resonant transport can be increased by increasing the bias voltage. This counter-intuitive effect is attributed to the energy dependence of the molecule-lead coupling densities, which promote the rate of transport-induced cooling of molecular vibrations at higher voltages. The required energy dependence is characteristic of realistic electrodes (such as graphene), which cannot be modeled within the commonly invoked wide-band approximation. Our research provides new guidelines for the design of mechanically stable molecular devices operating in the regime of resonant charge transport and demonstrates these guidelines while considering realistic features of single-molecule junctions.

Quantum Dot Coupling in a Vertical Transport Device under Ambient Conditions.

The semiconductor device industry is constantly challenged by the demands of miniaturization. Therefore, the use of nanomaterials, such as quantum dots (QDs), is expected. At these scales, quantum effects are anticipated under industrial working conditions. Here, we present a simple fabrication method for integrating colloidal coupled QDs as components in a vertical device. Characterization of the fundamental properties of QDs as an ensemble of isolated particles and as layered QD hybrid structures is demonstrated. For the case of layered QD hybrid structures, coupling between dots is on average stronger with typical energy band gaps reduced by more than 200 meV. The shown device offers a straightforward method to measure and establish a strong coupling transport system under ambient conditions.

Length-independent transport rates in biomolecules by quantum mechanical unfurling.

Experiments on hole transfer in DNA between donor and acceptor moieties revealed transfer rates which are independent of the molecular bridge length (within experimental error). However, the physical origin of this intriguing observation is still unclear. The hopping model implies that the hole propagates in multiple steps along the bridge from one localized state to another, and therefore the longer the bridge, the slower the transfer. This can explain weak length-dependence but not a length-independent transfer rate. We show that the rigid molecular structure of a poly-A bridge supports single step transitions from a localized hole state to delocalized states, spread over the entire bridge. Since propagation to the bridge end is a single step process (termed quantum unfurling) the transfer rate becomes independent of the bridge length. This explanation is consistent with experimental results, and emphasizes the importance of structural order in charge transfer through bio-molecular systems.

Negative Differential Resistance Probe for Interdot Interactions in a Double Quantum Dot Array.

Colloidal quantum dots are free-standing nanostructures with chemically tunable electronic properties. In this work, we consider a new STM tip-double quantum dot (DQD)-surface setup with a unique connectivity, in which the tip is coupled to a single dot and the coupling to the surface is shared by both dots. Our theoretical analysis reveals a unique negative differential resistance (NDR) effect attributed to destructive interference during charge transfer from the DQD to the surface. This NDR can be used as a sensitive probe for interdot interactions in DQD arrays.

Pump-Probe Noise Spectroscopy of Molecular Junctions.

The slow response of electronic components in junctions limits the direct applicability of pump-probe type spectroscopy in assessing the intramolecular dynamics. Recently the possibility of getting information on a sub-picosecond time scale from dc current measurements was proposed. We revisit the idea of picosecond resolution by pump-probe spectroscopy from dc measurements and show that any intramolecular dynamics not directly related to charge transfer in the current direction is missed by current measurements. We propose a pump-probe dc shot noise spectroscopy as a suitable alternative. Numerical examples of time-dependent and average responses of junctions are presented for generic models.

Charge transport-induced recoil and dissociation in double quantum dots.

Colloidal quantum dots (CQDs) are free-standing nanostructures with chemically tunable electronic properties. This combination of properties offers intriguing new possibilities for nanoelectromechanical devices that were not explored yet. In this work, we consider a new scanning tunneling microscopy setup for measuring ligand-mediated effective interdot forces and for inducing motion of individual CQDs within an array. Theoretical analysis of a double quantum dot structure within this setup reveals for the first time voltage-induced interdot recoil and dissociation with pronounced changes in the current. Considering realistic microscopic parameters, our approach enables correlating the onset of mechanical motion under bias voltage with the effective ligand-mediated binding forces.

Ballistic charge transport through bio-molecules in a dissipative environment.

The question whether dissipative bio-molecular systems can support efficient coherent (phase-conserving) charge transport is raised again following recent experiments on electron-energy transfer in bio-molecules. In this work we formulate conditions under which the current due to coherent ballistic resonant charge transport through DNA molecular junctions can be measured in spite of coupling to the dissipative environment.

Coherently controlled molecular junctions.

Within a generic model, we discuss the possibility of coherent control of charge fluxes in unbiased molecular junctions. The control is induced by resonances between the Rabi frequency due to a pumping laser field and internal characteristic frequencies of pre-designed molecular donor-bridge-acceptor complexes. Two models are considered: a coherently controlled molecular charge pump and a molecular switch. The study generalizes previous consideration of light induced current [M. Galperin and A. Nitzan, Phys. Rev. Lett. 95, 206802 (2005)] and of a molecular electron pump [R. Volkovich and U. Peskin, Phys. Rev. B 83, 033403 (2011)] and accounts for the coherently driven charge transport in an unbiased molecular junction with symmetric coupling to leads. Numerical examples demonstrate the feasibility of the control mechanism for realistic junctions parameters.

Bias-controlled selective excitation of vibrational modes in molecular junctions: a route towards mode-selective chemistry.

We show that individual vibrational modes in single-molecule junctions with asymmetric molecule-lead coupling can be selectively excited by applying an external bias voltage. Thereby, a non-statistical distribution of vibrational energy can be generated, that is, a mode with a higher frequency can be stronger excited than a mode with a lower frequency. This is of particular interest in the context of mode-selective chemistry, where one aims to break specific (not necessarily the weakest) chemical bond in a molecule. Such mode-selective vibrational excitation is demonstrated for two generic model systems representing asymmetric molecular junctions and/or scanning tunneling microscopy experiments. To this end, we employ two complementary theoretical approaches, a nonequilibrium Green's function approach and a master equation approach. The comparison of both methods reveals good agreement in describing resonant electron transport through a single-molecule contact, where differences between the approaches highlight the role of non-resonant transport processes, in particular co-tunneling and off-resonant electron-hole pair creation processes.