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.

Control and Enhancement of Single-Molecule Electroluminescence through Strong Light-Matter Coupling

The energetic positions of molecular electronic states at molecule/electrode interfaces are crucial factors for determining the transport and optoelectronic properties of molecular junctions. Strong light-matter coupling offers a potential for manipulating these factors, enabling a boost in the efficiency and versatility of these junctions. Here, we investigate electroluminescence from single-molecule junctions in which the molecule is strongly coupled with the vacuum electromagnetic field in a plasmonic nanocavity. We demonstrate an improvement in the electroluminescence efficiency by employing the strong light-matter coupling in conjunction with the characteristic feature of single-molecule junctions to selectively control the formation of the lowest-energy excited state. The mechanism of efficiency improvement is discussed based on the energetic position and composition of the formed polaritonic states. Our findings indicate the possibility to manipulate optoelectronic conversion in molecular junctions by strong light-matter coupling and contribute to providing design principles for developing efficient molecular optoelectronic devices.

Plasmon Squeezing in Single-Molecule Junctions

Scanning tunneling microscope (STM)-induced luminescence provides an ideal platform for electrical generation and the atomic-scale manipulation of nonclassical states of light. However, despite its extreme importance in quantum technologies, squeezed light emission with reduced quantum fluctuations has hitherto not been demonstrated in such a platform. Here, we theoretically predict that the emitted light from the plasmon mode can be squeezed in an STM single molecular junction subject to an external laser drive. Going beyond the traditional paradigm that generates squeezing with the quadratic interaction of photons, our prediction explores the molecular coherence involved in an anharmonic energy spectrum of a coupled plasmon-molecule-exciton system. Furthermore, we show that, by selectively exciting the energy ladder, the squeezed plasmon can show either sub- or super-Poissonian statistical properties. We also demonstrate that, following the same principle, the molecular excitonic mode can be squeezed simultaneously.

Optical suppression of energy barriers in single molecule-metal binding

Transient bonds between molecules and metal surfaces underpin catalysis, bio/molecular sensing, molecular electronics, and electrochemistry. Techniques aiming to characterize these bonds often yield conflicting conclusions, while single-molecule probes are scarce. A promising prospect confines light inside metal nanogaps to elicit in operando vibrational signatures through surface-enhanced Raman scattering. Here, we show through analysis of more than a million spectra that light irradiation of only a few microwatts on molecules at gold facets is sufficient to overcome the metallic bonds between individual gold atoms and pull them out to form coordination complexes. Depending on the molecule, these light-extracted adatoms persist for minutes under ambient conditions. Tracking their power-dependent formation and decay suggests that tightly trapped light transiently reduces energy barriers at the metal surface. This opens intriguing prospects for photocatalysis and controllable low-energy quantum devices such as single-atom optical switches.

Orbital-resolved visualization of single-molecule photocurrent channels

Given its central role in utilizing light energy, photoinduced electron transfer (PET) from an excited molecule has been widely studied^1-6. However, even though microscopic photocurrent measurement methods^7-11 have made it possible to correlate the efficiency of the process with local features, spatial resolution has been insufficient to resolve it at the molecular level. Recent work has, however, shown that single molecules can be efficiently excited and probed when combining a scanning tunnelling microscope (STM) with localized plasmon fields driven by a tunable laser^12,13. Here we use that approach to directly visualize with atomic-scale resolution the photocurrent channels through the molecular orbitals of a single free-base phthalocyanine (FBPc) molecule, by detecting electrons from its first excited state tunnelling through the STM tip. We find that the direction and the spatial distribution of the photocurrent depend sensitively on the bias voltage, and detect counter-flowing photocurrent channels even at a voltage where the averaged photocurrent is near zero. Moreover, we see evidence of competition between PET and photoluminescence¹², and find that we can control whether the excited molecule primarily relaxes through PET or photoluminescence by positioning the STM tip with three-dimensional, atomic precision. These observations suggest that specific photocurrent channels can be promoted or suppressed by tuning the coupling to excited-state molecular orbitals, and thus provide new perspectives for improving energy-conversion efficiencies by atomic-scale electronic and geometric engineering of molecular interfaces.

Beaming Elastic and SERS Emission from Bent-Plasmonic Nanowire on a Mirror Cavity

We report on the experimental observation of beaming elastic and surface enhanced Raman scattering (SERS) emission from a bent-nanowire on a mirror (B-NWoM) cavity. The system was probed with polarization resolved Fourier plane and energy-momentum imaging to study the spectral and angular signature of the emission wavevectors. The out-coupled elastically scattered light from the kink occupies a narrow angular spread. We used a self-assembled monolayer of molecules with a well-defined molecular orientation to utilize the out-of-plane electric field in the cavity for enhancing Raman emission from the molecules and in achieving beaming SERS emission. Calculated directionality for elastic scattering and SERS emission was found to be 16.2 and 12.5 dB, respectively. The experimental data were corroborated with three-dimensional numerical finite element and finite difference time domain based numerical simulations. The results presented here may find relevance in understanding coupling of emitters with elongated plasmonic cavities and in designing on-chip optical antennas.

Energy, Particle, and Photon Fluxes in Molecular Junctions

Electroluminescence from a current-carrying molecular junction at steady state is simulated. (Charge) particle conservation and energy conservation are satisfied by a perturbative expansion in the radiation/matter coupling. Our approach makes it possible to adopt standard tools of traditional (equilibrium) spectroscopy to study signals from open systems such as molecular junctions. The nonperturbative analysis of spontaneous light emission signals coincides with the perturbative approach for weak molecule-field coupling.

Electron Transfer Methods in Open Systems

Utilization of electron transfer methods for description of quantum transport is popular due to simplicity of the formulation and its ability to account for basic physics of electron exchange between the system and baths. At the same time, the necessity to go beyond simple golden rule-type expressions for rates was indicated in the literature and ad hoc formulations were proposed. Similarly, kinetic schemes for quantum transport beyond the usual second-order Lindblad/Redfield considerations were discussed. Here we utilize recently introduced the nonequilibrium Hubbard Green's function diagrammatic technique to analyze the construction of rates in open systems. We show that previous considerations for rates of second and fourth order can be obtained as a particular case of zero- and second-order Green's function diagrammatic series with bare diagrams. We discuss limitations of previous considerations, stress advantages of the Hubbard Green's function approach in constructing the rates, and indicate that standard dressing of the diagrams is a natural way to account for additional baths/degrees of freedom in the formulation of generalized expressions for the rates.

Many-Body State Description of Single-Molecule Electroluminescence Driven by a Scanning Tunneling Microscope

Electron transport and optical properties of a single molecule in contact with conductive materials have attracted considerable attention because of their scientific importance and potential applications. With the recent progress in experimental techniques, especially by virtue of scanning tunneling microscope (STM)-induced light emission, where the tunneling current of the STM is used as an atomic-scale source for induction of light emission from a single molecule, it has become possible to investigate single-molecule properties at subnanometer spatial resolution. Despite extensive experimental studies, the microscopic mechanism of electronic excitation of a single molecule in STM-induced light emission has yet to be clarified. Here we present a formulation of single-molecule electroluminescence driven by electron transfer between a molecule and metal electrodes based on a many-body state representation of the molecule. The effects of intramolecular Coulomb interaction on conductance and luminescence spectra are investigated using the nonequilibrium Hubbard Green's function technique combined with first-principles calculations. We compare simulation results with experimental data and find that the intramolecular Coulomb interaction is crucial for reproducing recent experiments for a single phthalocyanine molecule. The developed theory provides a unified description of the electron transport and optical properties of a single molecule in contact with metal electrodes driven out of equilibrium, and thereby, it contributes to a microscopic understanding of optoelectronic conversion in single molecules on solid surfaces and in nanometer-scale junctions.

Hubbard Nonequilibrium Green's Function Analysis of Photocurrent in Nitroazobenzene Molecular Junction

We present a combined experimental and theoretical study of photoinduced current in molecular junctions consisting of monolayers of nitroazobenzene oligomers chemisorbed on carbon surfaces and illuminated by ultraviolet-visible light through a transparent electrode. Experimentally observed dependence of the photocurrent on light frequency, temperature, and monolayer thickness is analyzed within first-principles simulations employing the Hubbard nonequilibrium Green's function diagrammatic technique. We reproduce qualitatively correct behavior and discuss mechanisms leading to the characteristic behavior of dark and photoinduced currents in response to changes in bias, frequency of radiation, temperature, and thickness of molecular layer.

Quantitative Evaluation of Surface-Enhanced Raman Scattering Nanoparticles for Intracellular pH Sensing at a Single Particle Level

Intracellular pH is one of the key factors for understanding various biological processes in biological cells. Plasmonic gold and silver nanoparticles (NPs) have been extensively studied for surface-enhanced Raman scattering (SERS) applications for pH sensing as a local pH probe in a living cell. However, the SERS performance of NPs depends on material, size, and shape, which can be controlled by chemical synthesis. Here, we synthesized 18 types of gold and silver NPs with different morphologies such as sphere, rod, flower, star, core/shell, hollow, octahedra, core/satellites, and chainlike aggregates, and quantitatively compared their SERS performance for pH sensing. The SERS intensity from the most commonly utilized SERS probe molecule ( para-mercaptobenzoic acid, p-MBA) for pH sensing was measured at the single nanoparticle level under the same measurement parameters such as low laser power (0.5 mW/μm²), short integration time (100 ms) at wavelengths of 405, 488, 532, 584, 676, and 785 nm. In our measurement, the Ag chain, Ag core/satellites, Ag@Au core/satellites, and Au core/satellites nanoassemblies showed efficient pH sensing at the single particle level. By using p-MBA-conjugated Au@Ag core/satellites, we performed time-lapse pH measurements during apoptosis of HeLa cells. These experimental results confirmed that the pH measurement using p-MBA-conjugated Au@Ag core/satellites can be applied for long-term measurements of intracellular pH during cellular events.

Long-Range Activationless Photostimulated Charge Transport in Symmetric Molecular Junctions

Molecular electronic junctions consisting of nitroazobenzene oligomers covalently bonded to a conducting carbon surface using an established "all-carbon" device design were illuminated with UV-vis light through a partially transparent top electrode. Monitoring junction conductance with a DC bias imposed permitted observation of photocurrents while varying the incident wavelength, light intensity, molecular layer thickness, and temperature. The photocurrent spectrum tracked the in situ absorption spectrum of nitroazobenzene, increased linearly with light intensity, and depended exponentially on applied bias. The electronic characteristics of the photocurrent differed dramatically from those of the same device in the dark, with orders of magnitude higher conductance and very weak attenuation with molecular layer thickness (β = 0.14 nm^-1 for thickness above 5 nm). The temperature dependence of the photocurrent was opposite that of the dark current, with a 35% decrease in conductance between 80 and 450 K, while the dark current increased by a factor of 4.5 over the same range. The photocurrent was similar to the dark current for thin molecular layers but greatly exceeded the dark current for low bias and thick molecular layers. We conclude that the light and dark mechanisms are additive, with photoexcited carriers transported without thermal activation for a thickness range of 5-10 nm. The inverse temperature dependence is likely due to scattering or recombination events, both of which increase with temperature and in turn decrease the photocurrent. Photostimulated resonant transport potentially widens the breadth of conceivable molecular electronic devices and may have immediate value for wavelength-specific photodetection.

CHEERS: a tool for correlated hole-electron evolution from real-time simulations

We put forward a practical nonequilibrium Green's function (NEGF) scheme to perform real-time evolutions of many-body interacting systems driven out of equilibrium by external fields. CHEERS is a computational tool to solve the NEGF equation of motion in the so called generalized Kadanoff-Baym ansatz and it can be used for model systems as well as first-principles Hamiltonians. Dynamical correlation (or memory) effects are added to the Hartree-Fock dynamics through a many-body self-energy. Applications to time-dependent quantum transport, time-resolved photoabsorption and other ultrafast phenomena are discussed.

On the Fano Line Shape of Single Molecule Electroluminescence Induced by a Scanning Tunneling Microscope

The coupling between molecular exciton and gap plasmons plays a key role in single molecular electroluminescence induced by a scanning tunneling microscope (STM). But it has been difficult to clarify the complex experimental phenomena. By employing the nonequilibrium Green's function method, we propose a general theoretical model to understand the light emission spectrum of single molecule and gap plasmons from an energy transport point of view. The coherent interaction between gap plasmons and molecular exciton leads to a prominent Fano resonance in the emission spectrum. We analyze the dependence of the Fano line shape on the system parameters, based on which we provide a unified account of several recent experimental observations. Moreover, we highlight the effect of the tip-molecule electronic coupling on the spectrum.

Photoinduced Anomalous Coulomb Blockade and the Role of Triplet States in Electron Transport through an Irradiated Molecular Transistor

In this study, we explore photoinduced electron transport through a molecule weakly coupled to two electrodes by combining first-principles quantum chemistry calculations with a Pauli master equation approach that accounts for many-electron states. In the incoherent limit, we demonstrate that energy-level alignment of triplet and charged states plays a crucial role, even when the rate of intersystem crossing is much smaller than the rate of fluorescence. Furthermore, the field intensity dependence and an upper bound to the photoinduced electric current can be analytically derived in our model. Under an optical field, the conductance spectra (charge stability diagrams) exhibit unusual Coulomb diamonds, which are associated with molecular excited states, and their widths can be expressed in terms of energies of the molecular electronic states. This study offers new directions for exploring optoelectronic response in nanoelectronics.

Towards Noise Simulation in Interacting Nonequilibrium Systems Strongly Coupled to Baths

Progress in experimental techniques at nanoscale makes measurements of noise in molecular junctions possible. These data are important source of information not accessible through average flux measurements. The emergence of optoelectronics, the recently shown possibility of strong light-matter couplings, and developments in the field of quantum thermodynamics are making measurements of transport statistics even more important. Theoretical methods for noise evaluation in first principles simulations can be roughly divided into approaches for weak intra-system interactions, and those treating strong interactions for systems weakly coupled to baths. We argue that due to structure of its diagrammatic expansion, and the use of many-body states as a basis of its formulation, the recently introduced nonequilibrium diagrammatic technique for Hubbard Green functions is a relatively inexpensive method suitable for evaluation of noise characteristics in first principles simulations over a wide range of parameters. We illustrate viability of the approach by simulations of noise and noise spectrum within generic models for non-, weakly and strongly interacting systems. Results of the simulations are compared to exact data (where available) and to simulations performed within approaches best suited for each of the three parameter regimes.

Electromagnetic theories of surface-enhanced Raman spectroscopy

A fundamental theoretical understanding of SERS, and SERS hotspots, leads to new design principles for SERS substrates and new applications in nanomaterials and chemical analysis.