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.

Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space

We extend the twin-space formulation of the hierarchical equations of motion approach in combination with the matrix product state representation (introduced in J. Chem. Phys. 150, 234102, [2019]) to nonequilibrium scenarios where the open quantum system is coupled to a hybrid fermionic and bosonic environment. The key ideas used in the extension are a reformulation of the hierarchical equations of motion for the auxiliary density matrices into a time-dependent Schrödinger-like equation for an augmented multi-dimensional wave function as well as a tensor decomposition into a product of low-rank matrices. The new approach facilitates accurate simulations of non-equilibrium quantum dynamics in larger and more complex open quantum systems. The performance of the method is demonstrated for a model of a molecular junction exhibiting current-induced mode-selective vibrational excitation.

Pathways for charge transport through material interfaces

Modeling charge transport across material interfaces is important for understanding the limitations of electronic devices such as transistors, electrochemical cells, sensors, and batteries. However, modeling the entire structure and full dimensionality of an interface can be computationally demanding. In this study, we investigate the validity of an efficient reduced one-dimensional Hamiltonian for calculating charge transport along interfaces by comparing to a two-dimensional model that accounts for additional charge transport pathways. We find that the one-dimensional model successfully predicts the qualitative trend of charge transmission probability among Pt/Fe₂O₃ and Ag/Fe₂O₃ interfaces. However, the two-dimensional model provides additional information on possible pathways that are not perpendicular to the interface direction. These charge transport pathways are directed along the lowest potential energy profile of the interface that correlates with the crystal structure of the constituting materials. However, the two-dimensional paths are longer and take more scattering time. Therefore, the one-dimensional model may hold sufficient information for qualitative estimation of charge transport through some material interfaces.

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.

Beyond Marcus theory and the Landauer-Büttiker approach in molecular junctions. II. A self-consistent Born approach

Marcus and Landauer-Büttiker approaches to charge transport through molecular junctions describe two contrasting mechanisms of electronic conduction. In previous work, we have shown how these charge transport theories can be unified in the single-level case by incorporating lifetime broadening into the second-order quantum master equation. Here, we extend our previous treatment by incorporating lifetime broadening in the spirit of the self-consistent Born approximation. By comparing both theories to numerically converged hierarchical-equations-of-motion results, we demonstrate that our novel self-consistent approach rectifies shortcomings of our earlier framework, which are present especially in the case of relatively strong electron-vibrational coupling. We also discuss circumstances under which the theory developed here simplifies to the generalized theory developed in our earlier work. Finally, by considering the high-temperature limit of our new self-consistent treatment, we show how lifetime broadening can also be self-consistently incorporated into Marcus theory. Overall, we demonstrate that the self-consistent approach constitutes a more accurate description of molecular conduction while retaining most of the conceptual simplicity of our earlier framework.

Extending the hierarchical quantum master equation approach to low temperatures and realistic band structures

The hierarchical quantum master equation (HQME) approach is an accurate method to describe quantum transport in interacting nanosystems. It generalizes perturbative master equation approaches by including higher-order contributions as well as non-Markovian memory and allows for the systematic convergence to the numerically exact result. As the HQME method relies on a decomposition of the bath correlation function in terms of exponentials, however, its application to systems at low temperatures coupled to baths with complexer band structures has been a challenge. In this publication, we outline an extension of the HQME approach, which uses re-summation over poles and can be applied to calculate transient currents at a numerical cost that is independent of temperature and band structure of the baths. We demonstrate the performance of the extended HQME approach for noninteracting tight-binding model systems of increasing complexity as well as for the spinless Anderson-Holstein model.

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.

Origin of Vibrational Instabilities in Molecular Wires with Separated Electronic States

Current-induced heating in molecular junctions stems from the interaction between tunneling electrons and localized molecular vibrations. If the electronic excitation of a given vibrational mode exceeds heat dissipation, a situation known as vibrational instability is established, which can seriously compromise the integrity of the junction. Using out of equilibrium first-principles calculations, we demonstrate that vibrational instabilities can take place in the general case of molecular wires with separated unoccupied electronic states. From the ab initio results, we derive a model to characterize unstable vibrational modes and construct a diagram that maps mode stability. These results generalize previous theoretical work and predict vibrational instabilities in a new regime.

Reconciling perturbative approaches in phonon-assisted transport junctions

We present consistent results for molecular conduction using two central-complementary approaches: the non-equilibrium Green's function technique and the quantum master equation method. Our model describes electronic conduction in a donor-acceptor junction in which electron transfer is coupled to nuclear motion, modeled by a harmonic vibrational mode. This primary mode is further coupled to secondary phonon modes, a thermal bath. Assuming weak electron-phonon coupling but an arbitrary large molecule-metal hybridization, we compute several non-equilibrium transport quantities: the mean phonon number of the primary mode, charge current statistics. We further present scaling relations for the cumulants valid in the large voltage regime. Our analysis illustrates that the non-equilibrium Green's function technique and the quantum master equation method can be worked out consistently, when taking into account corresponding scattering processes.

The effect of Duschinsky rotation on charge transport properties of molecular junctions in the sequential tunneling regime

We present here a systematic theoretical study on the effect of Duschinsky rotation on charge transport properties of molecular junctions in the sequential tunneling regime. In the simulations we assume that only two electronic charging states each coupled to a two dimensional vibrational potential energy surface (PES) are involved in the transport process. The Duschinsky rotation effect is accounted by varying the rotational angle between the two sets of displaced PESs. Both harmonic potential and anharmonic Morse potential have been considered for the cases of the intermediate to strong electron-vibration couplings. Our calculations show that the inclusion of the Duschinsky rotation effect can significantly change the charge transport properties of a molecular junction. Such an effect makes the otherwise symmetric Coulomb diamond become asymmetric in harmonic potentials. Depending on the angle of the rotation, the low bias current could be significantly suppressed or enhanced. This effect is particularly prominent in the Franck-Condon (FC) blockade regime where the electron-vibration coupling is strong. These changes are caused by the variation of the FC factors which are closely related to the rotational angle between the two sets of PESs involved in the charge transport process. For a molecular junction with Morse potentials, the changes caused by Duschinsky rotation are much more complicated. Both the amplitude and shape of the Coulomb diamond are closely dependent on the rotational angle in the whole range from 0 to 2π. One interesting result is that with a rotation angle of π (and also π/2 for certain cases) symmetric Coulomb diamonds can even be formed from the intrinsically asymmetric Morse potential. These results could be important for the interpretation of experimental observations.

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.

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.