Closed-form Green functions, surface effects, and the importance of dimensionality in tight-binding metals

A Green's Function Approach for Determining Surface Induced Broadening and Shifting of Molecular Energy Levels

Upon adsorption of a molecule onto a surface, the molecular energy levels (MELs) broaden and change their alignment. This phenomenon directly affects electron transfer across the interface and is, therefore, a fundamental observable that influences electrochemical device performance. Here, we propose a rigorous parameter-free framework, built upon the theoretical construct of Green's functions, for studying the interface between a molecule and a bulk surface and its effect on MELs. The method extends beyond the usual wide-band limit approximation, and its generality allows its use with any level of electronic structure theory. We demonstrate its ability to predict the broadening and shifting of MELs as a function of intramolecular coupling, molecule/surface coupling, and the surface density of states for a molecule with two MELs adsorbed on a one-dimensional model metal surface. The new approach could help provide guidelines for the design and experimental characterization of electrochemical devices with optimal electron transport.

Estimation of π-π Electronic Couplings from Current Measurements

The π-π interactions between organic molecules are among the most important parameters for optimizing the transport and optical properties of organic transistors, light-emitting diodes, and (bio-) molecular devices. Despite substantial theoretical progress, direct experimental measurement of the π-π electronic coupling energy parameter t has remained an old challenge due to molecular structural variability and the large number of parameters that affect the charge transport. Here, we propose a study of π-π interactions from electrochemical and current measurements on a large array of ferrocene-thiolated gold nanocrystals. We confirm the theoretical prediction that t can be assessed from a statistical analysis of current histograms. The extracted value of t ≈35 meV is in the expected range based on our density functional theory analysis. Furthermore, the t distribution is not necessarily Gaussian and could be used as an ultrasensitive technique to assess intermolecular distance fluctuation at the subangström level. The present work establishes a direct bridge between quantum chemistry, electrochemistry, organic electronics, and mesoscopic physics, all of which were used to discuss results and perspectives in a quantitative manner.

A unified perspective of complex band structure: interpretations, formulations, and applications

Complex band structure generalizes conventional band structure by also considering wavevectors with complex components. In this way, complex band structure describes both the bulk-propagating states from conventional band structure and the evanescent states that grow or decay from one unit cell to the next. Even though these latter states are excluded by translational symmetry, they become important when translational symmetry is broken via, for example, a surface or impurity. Many studies over the last 80 years have directly or indirectly developed complex band structure for an impressive range of applications, but very few discuss its fundamentals or compare its various results. In this work we build upon these previous efforts to expose the physical foundation of complex band structure, which mathematically implies its existence. We find that a material's static and dynamic electronic structure are both completely described by complex band structure. Furthermore, we show that complex band structure reflects the minimal, intrinsic information contained in the material's Hamiltonian. These realizations then provide a context for comparing and unifying the different formulations and applications of complex band structure that have been reported over the years. Ultimately, this discussion introduces the idea of examining the amount of information contained in a material's Hamiltonian so that we can find and exploit the minimal information necessary for understanding a material's properties.

Molecule-lead coupling at molecular junctions: relation between the real- and state-space perspectives

We present insights into the lead-molecule coupling scheme in molecular electronics junctions. Using a "site-to-state" transformation that provides direct access to the coupling matrix elements between the molecular states and the eigenstate manifold of each lead, we find coupling bands whose character depends on the geometry and dimensionality of the lead. We use a standard tight-binding model to elucidate the origin of the coupling bands and explain their nature via simple "particle-in-a-box" type considerations. We further show that these coupling bands can shed light on the charge transport behavior of the junction. The picture presented in this study is not limited to the case of molecular electronics junctions and is relevant to any scenario where a finite molecular entity is coupled to a (semi)infinite system.

Signatures of cooperative effects and transport mechanisms in conductance histograms

We present a computational investigation into the line shapes of peaks in conductance histograms, finding that they possess high information content. In particular, the histogram peak associated with conduction through a single molecule elucidates the electron transport mechanism and is generally well-described by beta distributions. A statistical analysis of the peak corresponding to conduction through two molecules reveals the presence of cooperative effects between the molecules and also provides insight into the underlying conduction channels. This work describes tools for extracting additional interpretations from experimental statistical data, helping us better understand electron transport processes.

Carrier Transport in Heterojunction Nanocrystals Under Strain

We present a theory for carrier transport in semiconducting nanoscale heterostructures that emphasizes the effects of strain at the interface between two different crystal structures. An exactly solvable model shows that the interface region, or junction, acts as a scattering potential that facilitates charge separation. As a case study, we model a type-II CdS/ZnSe heterostructure. After advancing a theory similar to that employed in model molecular conductance calculations, we calculate the electron and hole photocurrents and conductances, including nonlinear effects, through the junction at steady state.

Molecular conduction through adlayers: cooperative effects can help or hamper electron transport

We use a one-electron, tight-binding model of a molecular adlayer sandwiched between two metal electrodes to explore how cooperative effects between molecular wires influence electron transport through the adlayer. When compared to an isolated molecular wire, an adlayer exhibits cooperative effects that generally enhance conduction away from an isolated wire's resonance and diminish conductance near such a resonance. We also find that the interwire distance (related to the adlayer density) is a key quantity. Substrate-mediated coupling induces most of the cooperative effects in dense adlayers, whereas direct, interwire coupling (if present) dominates in sparser adlayers. In this manner, cooperative effects through dense adlayers cannot be removed, suggesting an optimal adlayer density for maximizing conduction.