Ab initiostudy of the alternating current impedance of a molecular junction

Electron Dynamics in Open Quantum Systems: The Driven Liouville-von Neumann Methodology within Time-Dependent Density Functional Theory

A first-principles approach to describe electron dynamics in open quantum systems driven far from equilibrium via external time-dependent stimuli is introduced. Within this approach, the driven Liouville-von Neumann methodology is used to impose open boundary conditions on finite model systems whose dynamics is described using time-dependent density functional theory. As a proof of concept, the developed methodology is applied to simple spin-compensated model systems, including a hydrogen chain and a graphitic molecular junction. Good agreement between steady-state total currents obtained via direct propagation and those obtained from the self-consistent solution of the corresponding Sylvester equation indicates the validity of the implementation. The capability of the new computational approach to analyze, from first principles, non-equilibrium dynamics of open quantum systems in terms of temporally and spatially resolved current densities is demonstrated. Future extensions of the approach toward the description of dynamical magnetization and decoherence effects are briefly discussed.

A projection-based reduced-order method for electron transport problems with long-range interactions

Long-range interactions play a central role in electron transport. At the same time, they present a challenge for direct computer simulations since sufficiently large portions of the bath have to be included in the computation to accurately compute the Coulomb potential. This article presents a reduced-order approach by deriving an open quantum model for the reduced density matrix. To treat the transient dynamics, the problem is placed in a reduced-order framework. The dynamics described by the Liouville-von Neumann equation is projected to subspaces using a Petrov-Galerkin projection. In order to recover the global electron density profile as a vehicle to compute the Coulomb potential, we propose a domain decomposition approach, where the computational domain also includes segments of the bath that are selected using logarithmic grids. This approach leads to a multi-component self-energy that enters the effective Hamiltonian. We demonstrate the accuracy of the reduced model using a molecular junction built from lithium chains.

Photoinduced Carrier Dynamics at the Interface of Black Phosphorus and Bismuth Vanadate

Two-dimensional (2D) heterostructures of black phosphorus (BP)/bismuth vanadate (BVO) have attracted much attention due to their potential uses in photocatalytic water splitting. However, the interfacial photoinduced electron- and hole-transfer dynamics are not explored computationally. Herein, we have used density functional theory (DFT) calculations and DFT-based fewest-switches surface-hopping dynamics simulations to investigate the light-driven electron and hole dynamics taking place at the interface of BP and the BVO(010) surface. Our results show that the BP monolayer is adsorbed on BVO(010) via van der Waals interaction. Upon irradiation, the electron transfer takes place from BP to BVO(010) within 500 fs but with two distinct processes. In the first phase, the electron transfer proceeds adiabatically and is mainly driven by atomic motions. In the second phase, the electron transfer decays very slowly. The hole-transfer dynamics from BVO(010) to BP exhibits a similar ultrafast decay in the first stage followed by a slow decay; however, there is a comparable amount of hole trapped in a BP state due to a large energy gap from its higher state. These insights may be useful for the design of novel photocatalytic water-splitting materials.

Imaging Time-Dependent Electronic Currents through a Graphene-Based Nanojunction

To assist the design of efficient molecular junctions, a precise understanding of the charge transport mechanisms through nanoscaled devices is of prime importance. In the present contribution, we present time- and space-resolved electron transport simulations through a nanojunction under time-dependent potential biases. We use the driven Liouville-von Neumann approach to simulate the time evolution of the one-electron density matrix under nonequilibrium conditions, which allows us to capture the ultrafast scattering dynamics, the electronic relaxation process, and the quasi-stationary current limit from the same simulation. Using local projection techniques, we map the coherent electronic current density, unraveling insightful mechanistic details of the transport on time scales ranging from atto- to picoseconds. Memory effects dominate the early time transport process, and they reveal different current patterns on short time scales in comparison to those in the long-time regime. For nanotransistors with high switching rates, the scattering perspective on electron transport should thus be favored.

Photoinduced Carrier Dynamics at the Interface of Pentacene and Molybdenum Disulfide

Understanding of photoinduced interfacial carrier dynamics in organic-transition metal dichalcogenides heterostructures is very important for the enhancement of their potential photoelectronic conversion efficiencies. In this work we have used density functional theory (DFT) calculations and DFT-based fewest-switches surface-hopping dynamics simulations to explore the photoinduced hole transfer and subsequent nonadiabatic electron-hole recombination dynamics taking place at the interface of pentacene and MoS₂ in pentacene@MoS₂. Upon photoexcitation the electronic transition mainly occurs on the MoS₂ monolayer, which corresponds to moving an electron to the MoS₂ conduction band. As a result, a hole is left in the valence band. This hole state is energetically lower than certain occupied states of the pentacene molecule; thus, the interfacial hole transfer from MoS₂ to pentacene is favorable in energy. In terms of nonadiabatic dynamics simulations, the hole transfer time to the HOMO-1 state of the pentacene is estimated to be about 600 fs; however, the following hole relaxation process from HOMO-1 to HOMO takes much longer time of ca. 15 ps due to the large energy gap between HOMO-1 and HOMO. Moreover, our results also show that the subsequent radiationless recombination process between the hole transferred to the pentacene molecule and the remaining electron on the MoS₂ CBM needs about 10.2 ns. The computational results shed important mechanistic insights on the interfacial carrier dynamics of mixed-dimensional pentacene@MoS₂. These insights could help to design excellent interfaces for organic-TMDs heterostructures.

Time-resolved impurity-invisibility in graphene nanoribbons

We investigate time-resolved charge transport through graphene nanoribbons supplemented with adsorbed impurity atoms. Depending on the location of the impurities with respect to the hexagonal carbon lattice, the transport properties of the system may become invisible to the impurity due to the symmetry properties of the binding mechanism. This motivates a chemical sensing device since dopants affecting the underlying sublattice symmetry of the pristine graphene nanoribbon introduce scattering. Using the time-dependent Landauer-Büttiker formalism, we extend the stationary current-voltage picture to the transient regime, where we observe how the impurity invisibility takes place at sub-picosecond time scales further motivating ultrafast sensor technology. We further characterize time-dependent local charge and current profiles within the nanoribbons, and we identify rearrangements of the current pathways through the nanoribbons due to the impurities. We finally study the behavior of the transients with ac driving which provides another way of identifying the lattice-symmetry breaking caused by the impurities.

Absorbing boundary conditions for time-dependent Schrödinger equations: A density-matrix formulation

This paper presents some absorbing boundary conditions for simulations based on the time-dependent Schrödinger equations. The boundary conditions are expressed in terms of the elements of the density-matrix, and it is derived from the full model over a much larger domain. To make the implementation much more efficient, several approximations for the convolution integral will be constructed with guaranteed stability. These approximations lead to modified density-matrix equations at the boundary. The effectiveness is examined via numerical tests.

Emergence of Landauer transport from quantum dynamics: A model Hamiltonian approach

The Landauer expression for computing current-voltage characteristics in nanoscale devices is efficient but not suited to transient phenomena and a time-dependent current because it is applicable only when the charge carriers transition into a steady flux after an external perturbation. In this article, we construct a very general expression for time-dependent current in an electrode-molecule-electrode arrangement. Utilizing a model Hamiltonian (consisting of the subsystem energy levels and their electronic coupling terms), we propagate the Schrödinger wave function equation to numerically compute the time-dependent population in the individual subsystems. The current in each electrode (defined in terms of the rate of change of the corresponding population) has two components, one due to the charges originating from the same electrode and the other due to the charges initially residing at the other electrode. We derive an analytical expression for the first component and illustrate that it agrees reasonably with its numerical counterpart at early times. Exploiting the unitary evolution of a wavefunction, we construct a more general Landauer style formula and illustrate the emergence of Landauer transport from our simulations without the assumption of time-independent charge flow. Our generalized Landauer formula is valid at all times for models beyond the wide-band limit, non-uniform electrode density of states and for time and energy-dependent electronic coupling between the subsystems. Subsequently, we investigate the ingredients in our model that regulate the onset time scale of this steady state. We compare the performance of our general current expression with the Landauer current for time-dependent electronic coupling. Finally, we comment on the applicability of the Landauer formula to compute hot-electron current arising upon plasmon decoherence.

Near omni-conductors and insulators: Alternant hydrocarbons in the SSP model of ballistic conduction

Within the source-and-sink-potential model, a complete characterisation is obtained for the conduction behaviour of alternant π-conjugated hydrocarbons (conjugated hydrocarbons without odd cycles). In this model, an omni-conductor has a molecular graph that conducts at the Fermi level irrespective of the choice of connection vertices. Likewise, an omni-insulator is a molecular graph that fails to conduct for any choice of connections. We give a comprehensive classification of possible combinations of omni-conducting and omni-insulating behaviour for molecular graphs, ranked by nullity (number of non-bonding orbitals). Alternant hydrocarbons are those that have bipartite molecular graphs; they cannot be full omni-conductors or full omni-insulators but may conduct or insulate within well-defined subsets of vertices (unsaturated carbon centres). This leads to the definition of "near omni-conductors" and "near omni-insulators." Of 81 conceivable classes of conduction behaviour for alternants, only 14 are realisable. Of these, nine are realised by more than one chemical graph. For example, conduction of all Kekulean benzenoids (nanographenes) is described by just two classes. In particular, the catafused benzenoids (benzenoids in which no carbon atom belongs to three hexagons) conduct when connected to leads via one starred and one unstarred atom, and otherwise insulate, corresponding to conduction type CII in the near-omni classification scheme.

Transport through correlated systems with density functional theory

We present recent advances in density functional theory (DFT) for applications in the field of quantum transport, with particular emphasis on transport through strongly correlated systems. We review the foundations of the popular Landauer-Büttiker(LB)  +  DFT approach. This formalism, when using approximations to the exchange-correlation (xc) potential with steps at integer occupation, correctly captures the Kondo plateau in the zero bias conductance at zero temperature but completely fails to capture the transition to the Coulomb blockade (CB) regime as the temperature increases. To overcome the limitations of LB  +  DFT, the quantum transport problem is treated from a time-dependent (TD) perspective using TDDFT, an exact framework to deal with nonequilibrium situations. The steady-state limit of TDDFT shows that in addition to an xc potential in the junction, there also exists an xc correction to the applied bias. Open shell molecules in the CB regime provide the most striking examples of the importance of the xc bias correction. Using the Anderson model as guidance we estimate these corrections in the limit of zero bias. For the general case we put forward a steady-state DFT which is based on one-to-one correspondence between the pair of basic variables, steady density on and steady current across the junction and the pair local potential on and bias across the junction. Like TDDFT, this framework also leads to both an xc potential in the junction and an xc correction to the bias. Unlike TDDFT, these potentials are independent of history. We highlight the universal features of both xc potential and xc bias corrections for junctions in the CB regime and provide an accurate parametrization for the Anderson model at arbitrary temperatures and interaction strengths, thus providing a unified DFT description for both Kondo and CB regimes and the transition between them.

Driven Liouville von Neumann Equation in Lindblad Form

The Driven Liouville von Neumann approach [J. Chem. Theory Comput. 2014, 10, 2927-2941] is a computationally efficient simulation method for modeling electron dynamics in molecular electronics junctions. Previous numerical simulations have shown that the method can reproduce the exact single-particle dynamics while avoiding density matrix positivity violation found in previous implementations. In this study we prove that in the limit of infinite lead models the underlying equation of motion can be cast in Lindblad form. This provides a formal justification for the numerically observed density matrix positivity conservation.

Echenique P, Aizpurua J, Borisov AG. Active quantum plasmonics

The ability of localized surface plasmons to squeeze light and engineer nanoscale electromagnetic fields through electron-photon coupling at dimensions below the wavelength has turned plasmonics into a driving tool in a variety of technological applications, targeting novel and more efficient optoelectronic processes. In this context, the development of active control of plasmon excitations is a major fundamental and practical challenge. We propose a mechanism for fast and active control of the optical response of metallic nanostructures based on exploiting quantum effects in subnanometric plasmonic gaps. By applying an external dc bias across a narrow gap, a substantial change in the tunneling conductance across the junction can be induced at optical frequencies, which modifies the plasmonic resonances of the system in a reversible manner. We demonstrate the feasibility of the concept using time-dependent density functional theory calculations. Thus, along with two-dimensional structures, metal nanoparticle plasmonics can benefit from the reversibility, fast response time, and versatility of an active control strategy based on applied bias. The proposed electrical manipulation of light using quantum plasmonics establishes a new platform for many practical applications in optoelectronics.

Plasmon-Mediated Electron Transport in Tip-Enhanced Raman Spectroscopic Junctions

We combine experiment, theory, and first-principles-based calculations to study the light-induced plasmon-mediated electron transport characteristics of a molecular-scale junction. The experimental data show a nonlinear increase in electronic current perturbation when the focus of a chopped laser beam moves laterally toward the tip-sample junction. To understand this behavior and generalize it, we apply a combined theory of the electronic nonequilibrium formed upon decoherence of an optically triggered plasmon and first-principles transport calculations. Our model illustrates that the current via an adsorbed molecular monolayer increases nonlinearly as more energy is pumped into the junction due to the increasing availability of virtual molecular orbital channels for transport with higher injection energies. Our results thus illustrate light-triggered, plasmon-enhanced tunneling current in the presence of a molecular linker.

Nanooptics of Plasmonic Nanomatryoshkas: Shrinking the Size of a Core-Shell Junction to Subnanometer

Quantum effects in plasmonic systems play an important role in defining the optical response of structures with subnanometer gaps. Electron tunneling across the gaps can occur, altering both the far-field optical response and the near-field confinement and enhancement. In this study, we experimentally and theoretically investigate plasmon coupling in gold "nanomatryoshka" (NM) nanoparticles with different core-shell separations. Plasmon coupling effects between the core and the shell become significant when their separation decreases to 15 nm. When their separation decreases to below 1 nm, the near- and far-field properties can no longer be described by classical approaches but require the inclusion of quantum mechanical effects such as electron transport through the self-assembled monolayer of molecular junction. In addition, surface-enhanced Raman scattering measurements indicate strong electron-transport induced charge transfer across the molecular junction. Our quantum modeling provides an estimate for the AC conductances of molecules in the junction. The insights acquired from this work pave the way for the development of novel quantum plasmonic devices and substrates for surface-enhanced Raman scattering.

Towards a full ab initio theory of strong electronic correlations in nanoscale devices

In this paper I give a detailed account of an ab initio methodology for describing strong electronic correlations in nanoscale devices hosting transition metal atoms with open d- or f-shells. The method combines Kohn-Sham density functional theory for treating the weakly interacting electrons on a static mean-field level with non-perturbative many-body methods for the strongly interacting electrons in the open d- and f-shells. An effective description of the strongly interacting electrons in terms of a multi-orbital Anderson impurity model is obtained by projection onto the strongly correlated subspace properly taking into account the non-orthogonality of the atomic basis set. A special focus lies on the ab initio calculation of the effective screened interaction matrix U for the Anderson model. Solution of the effective Anderson model with the one-crossing approximation or other impurity solver techniques yields the dynamic correlations within the strongly correlated subspace giving rise e.g. to the Kondo effect. As an example the method is applied to the case of a Co adatom on the Cu(0 0 1) surface. The calculated low-bias tunnel spectra show Fano-Kondo lineshapes similar to those measured in experiments. The exact shape of the Fano-Kondo feature as well as its width depend quite strongly on the filling of the Co 3d-shell. Although this somewhat hampers accurate quantitative predictions regarding lineshapes and Kondo temperatures, the overall physical situation can be predicted quite reliably.

Time-dependent density functional theory for open systems with a positivity-preserving decomposition scheme for environment spectral functions

Understanding electronic dynamics on material surfaces is fundamentally important for applications including nanoelectronics, inhomogeneous catalysis, and photovoltaics. Practical approaches based on time-dependent density functional theory for open systems have been developed to characterize the dissipative dynamics of electrons in bulk materials. The accuracy and reliability of such approaches depend critically on how the electronic structure and memory effects of surrounding material environment are accounted for. In this work, we develop a novel squared-Lorentzian decomposition scheme, which preserves the positive semi-definiteness of the environment spectral matrix. The resulting electronic dynamics is guaranteed to be both accurate and convergent even in the long-time limit. The long-time stability of electronic dynamics simulation is thus greatly improved within the current decomposition scheme. The validity and usefulness of our new approach are exemplified via two prototypical model systems: quasi-one-dimensional atomic chains and two-dimensional bilayer graphene.

State Representation Approach for Atomistic Time-Dependent Transport Calculations in Molecular Junctions

We propose a new method for simulating electron dynamics in open quantum systems out of equilibrium, using a finite atomistic model. The proposed method is motivated by the intuitive and practical nature of the driven Liouville-von-Neumann equation approach of Sánchez et al. [J. Chem. Phys. 2006, 124, 214708] and Subotnik et al. [J. Chem. Phys. 2009, 130, 144105]. A key ingredient of our approach is a transformation of the Hamiltonian matrix from an atomistic to a state representation of the molecular junction. This allows us to uniquely define the bias voltage across the system while maintaining a proper thermal electronic distribution within the finite lead models. Furthermore, it allows us to investigate complex molecular junctions, including multilead configurations. A heuristic derivation of our working equation leads to explicit expressions for the damping and driving terms, which serve as appropriate electron sources and sinks that effectively "open" the finite model system. Although the method does not forbid it, in practice we find neither violation of Pauli's exclusion principles nor deviation from density matrix positivity throughout our numerical simulations of various tight-binding model systems. We believe that the new approach offers a practical and physically sound route for performing atomistic time-dependent transport calculations in realistic molecular junction models.

An efficient solution of Liouville-von Neumann equation that is applicable to zero and finite temperatures

Application of quantum dissipation theory to electronic dynamics has been limited to model systems with few energy levels, and its numerical solutions are mostly restricted to high temperatures. A highly accurate and efficient numerical algorithm, which is based on the Chebyshev spectral method, is developed to integrate a single-particle Liouville-von Neumann equation, and the two long-standing limitations of quantum dissipation theory are resolved in the context of quantum transport. Its computational time scales to O(N(3)) with N being the number of orbitals involved, which leads to a reality for the quantum mechanical simulation of real open systems containing hundreds or thousands of atomic orbitals. More importantly, the algorithm spans both finite and zero temperatures. Numerical calculations are carried out to simulate the transient current through a metallic wire containing up to 1000 orbitals.

Expeditious stochastic calculation of multiexciton generation rates in semiconductor nanocrystals

A stochastic method is developed to calculate the multiexciton generation (MEG) rates in semiconductor nanocrystals (NCs). The numerical effort scales near-linearly with system size allowing the study of MEG rates up to diameters and exciton energies previously unattainable using atomistic calculations. Illustrations are given for CdSe NCs of sizes and energies relevant to current experimental setups, where direct methods require treatment of over 10(11) states. The approach is not limited to the study of MEG and can be applied to calculate other correlated electronic processes.

Dynamical Coulomb blockade and the derivative discontinuity of time-dependent density functional theory

The role of the discontinuity of the exchange-correlation potential of density functional theory is studied in the context of electron transport and shown to be intimately related to Coulomb blockade. By following the time evolution of an interacting nanojunction attached to biased leads, we find that, instead of evolving to a steady state, the system reaches a dynamical state characterized by correlation-induced current oscillations. Our results establish a dynamical picture of Coulomb blockade manifesting itself as a periodic sequence of charging and discharging of the nanostructure.

Exchange and correlation in molecular wire conductance: nonlocality is the key

We study real-time electron dynamics in a molecular junction with a variety of approximations to the electronic structure, toward the ultimate aim of determining what ingredients are crucial for the accurate prediction of charge transport. We begin with real-time, all electron simulations using some common density functionals that differ in how they treat long-range Hartree-Fock exchange. We find that the inclusion or exclusion of nonlocal exchange is the dominant factor determining the transport behavior, with all semilocal contributions having a smaller effect. In order to study nonlocal correlation, we first map our junction onto a simple Pariser-Parr-Pople (PPP) model Hamiltonian. The PPP dynamics are shown to faithfully reproduce the all electron results, and we demonstrate that nonlocal correlation can be readily included in the model space using the generator coordinate method (GCM). Our PPP-GCM simulations suggest that nonlocal correlation has a significant impact on the I-V character that is not captured even qualitatively by any of the common semilocal approximations to exchange and correlation. The implications of our results for transport calculations are discussed.

The influence of initial conditions on charge transfer dynamics

In this work we address the influence of the initial state on electron transfer dynamics by comparing two different ways of setting up the initial state, namely by taking an electron from the HOMO of a DFT ground state, or by using constrained DFT to self-consistently create the initial state. We solve the TDKS equations for the benzyl-pentafluorobenzene cation. The neutral molecule has a localised HOMO, which gives a natural partitioning in donor and acceptor group. We compare the electronic dynamics for varying angle between donor and acceptor and for varying basis set. We show that the methods lead to essentially equivalent results, but that the use of cDFT gives higher currents and a more consistent initial state with respect to variation of basis set and geometry.

Distribution of multiexciton generation rates in CdSe and InAs nanocrystals

The distribution of rates of multiexciton generation following photon absorption is calculated for semiconductor nanocrystals (NCs). The rates of biexciton generation are calculated using Fermi's golden rule with all relevant Coulomb matrix elements, taking into account proper selection rules within a screened semiempirical pseudopotential approach. In CdSe and InAs NCs, we find a broad distribution of biexciton generation rates depending strongly on the exciton energy and size of the NC. Multiexciton generation becomes inefficientfor NCs exceeding 3 nm in diameter in the photon energy range of 2-3 times the band gap.

Linear scaling calculation of an n-type GaAs quantum dot

A linear scale method for calculating electronic properties of large and complex systems is introduced within a local density approximation. The method is based on the Chebyshev polynomial expansion and the time-dependent method, which is tested on the calculation of the electronic structure of a model n-type GaAs quantum dot.

Molecular conduction: do time-dependent simulations tell you more than the Landauer approach?

A dynamical method for simulating steady-state conduction in atomic and molecular wires is presented which is both computationally and conceptually simple. The method is tested by calculating the current-voltage spectrum of a simple diatomic molecular junction, for which the static Landauer approach produces multiple steady-state solutions. The dynamical method quantitatively reproduces the static results and provides information on the stability of the different solutions.

Nonlinear signal mixing in a three-terminal molecular wire

The authors study the electronic response of two simple molecular devices to a bichromatic field, where the device acts as a mixer. Two closely related model systems are considered: one is a benzene molecule and the other is a single grapheme sheet, and in both cases the systems are connected to three polyacetylene chains. The electronic response to the dichromatic alternating electric fields is studied by following the electron density fluctuation along the chain lengths. In both cases the electron transfer follows the field frequency at low electric fields. At higher amplitude, a significant amount of nonlinear mixing resulting in new combinations of the input frequencies is found in the spectrum. The influence of gating on the output frequencies is also shown.

A well-tempered density functional theory of electrons in molecules

This Invited Article reports extensions of a recently developed approach to density functional theory with correct long-range behavior (R. Baer and D. Neuhauser, Phys. Rev. Lett., 2005, 94, 043002). The central quantities are a splitting functional gamma[n] and a complementary exchange-correlation functional E[n]. We give a practical method for determining the value of gamma in molecules, assuming an approximation for E is given. The resulting theory shows good ability to reproduce the ionization potentials for various molecules. However it is not of sufficient accuracy for forming a satisfactory framework for studying molecular properties. A somewhat different approach is then adopted, which depends on a density-independent gamma and an additional parameter w eliminating part of the local exchange functional. The values of these two parameters are obtained by best-fitting to experimental atomization energies and bond lengths of the molecules in the G2(1) database. The optimized values are gamma = 0.5 a and w = 0.1. We then examine the performance of this slightly semi-empirical functional for a variety of molecular properties, comparing to related works and experiment. We show that this approach can be used for describing in a satisfactory manner a broad range of molecular properties, be they static or dynamic. Most satisfactory is the ability to describe valence, Rydberg and inter-molecular charge-transfer excitations.