We present a consistent theory of energy balance and conversion in a single-molecule junction with strong interactions between electrons on the molecular linker (dot) and phonons in the nuclear environment where the Marcus-type electron hopping processes predominate in the electron transport. It is shown that the environmental reorganization and relaxation that accompany electron hopping energy exchange between the electrodes and the nuclear (molecular and solvent) environment may bring a moderate local cooling of the latter in biased systems. The effect of a periodically driven dot level on the heat transport and power generated in the system is analyzed and energy conservation is demonstrated both within and beyond the quasistatic regime. Finally, a simple model of atomic scale engine based on a Marcus single-molecule junction with a driven electron level is suggested and discussed.
Charge transport through molecular junctions is often described either as a purely coherent or a purely classical phenomenon, and described using the Landauer-Büttiker formalism or Marcus theory, respectively. Using a generalised quantum master equation, we here derive an expression for current through a molecular junction modelled as a single electronic level coupled to a collection of thermalised vibrational modes. We demonstrate that the aforementioned theoretical approaches can be viewed as two limiting cases of this more general expression, and present a series of approximations of this r…
Marcus and Landauer-Buttiker 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 (HEOM) results, we demonstrate that our …
Thermoelectric energy conversion is perhaps the most promising of the potential applications of molecular electronics. Ultimately, it is desirable for this technology to operate at around room temperature, and it is therefore important to consider the role of dissipative effects in these conditions. Here, we develop a theory of thermoelectricity which accounts for the vibrational coupling within the framework of Marcus theory. We demonstrate that the inclusion of lifetime broadening is necessary in the theoretical description of this phenomenon. We further show that the Seebeck coefficient and…
Redox molecular junctions are molecular conduction junctions that involve more than one oxidation state of the molecular bridge. This property is derived from the ability of the molecule to transiently localize transmitting electrons, implying relatively weak molecule-leads coupling and, in many cases, the validity of the Marcus theory of electron transfer. Here we study the implications of this property on the non-linear transport properties of such junctions. We obtain an analytical solution of the integral equations that describe molecular conduction in the Marcus kinetic regime and use it …
Experimental studies on single-molecule junctions are typically in need of a simple theoretical approach that can reproduce or be fitted to experimentally measured transport data. In this context, the single-level variant of the Landauer approach is most commonly used but methods based on Marcus theory are also gaining in popularity. Recently, a generalized theory unifying these two approaches has also been developed. In the present work, we extend this theory so that it includes entropic effects (which can be important when polar solvents are involved, but are likely minor for solid-state sys…
We determine the zero-frequency charge current noise in a metal-molecule-metal junction embedded in a thermal environment, e.g., a solvent, dominated by sequential charge transmission described by a classical master equation, and study its dependence of specific model parameters, i.e., the environmental reorganization energy and relaxation behavior. Interestingly, the classical current noise term has the same structure as its quantum analog which reflects a charge correlation due to the bridging molecule. We further determine the thermodynamic uncertainty relation (TUR) which defines a bound o…
For defining the conductance of single molecule junctions with a redox functionality in an electrochemical cell, two conceptually different electron transport mechanisms, namely coherent tunnelling and vibrationally induced hopping compete with each other, where implicit parameters of the setup such as the length of the molecule and the applied gate voltage decide which mechanism is the dominant one. Although coherent tunnelling is most efficiently described within Landauer theory, while the common theoretical treatment of electron hopping is based on Marcus theory, both theories are adequate …
There are various quantum chemical approaches for an ab initio description of transfer integrals within the framework of Marcus theory in the context of electron transfer reactions. In our article we aim to calculate transfer integrals in redox-active single molecule junctions, where we focus on the coherent tunneling limit with the metal leads taking the position of donor and acceptor and the molecule acting as a transport mediating bridge. This setup allows us to derive a conductance, which can be directly compared with recent results from a non-equilibrium Green's function approach. Compare…
Off-resonant charge transport through molecular junctions has been extensively studied since the advent of single-molecule electronics and it is now well understood within the framework of the non-interacting Landauer approach. Conversely, gaining a qualitative and quantitative understanding of the resonant transport regime has proven more elusive. Here, we study resonant charge transport through graphene-based zinc-porphyrin junctions. We experimentally demonstrate an inadequacy of the non-interacting Landauer theory as well as the conventional single-mode Franck-Condon model. Instead, we mod…
We present a theoretical analysis aimed at understanding electrical conduction in molecular tunnel junctions. We focus on discussing the validity of coherent versus incoherent theoretical formulations for single-level tunneling to explain experimental results obtained under a wide range of experimental conditions, including measurements in individual molecules connecting the leads of electromigrated single-electron transistors and junctions of self-assembled monolayers (SAM) of molecules sandwiched between two macroscopic contacts. We show that the restriction of transport through a single lev…
In this work we present and discuss theoretical models of redox molecular junctions that account for recent observations of nonlinear charge transport phenomena, such as hysteresis and hysteretic negative differential resistance (NDR). A defining feature in such models is the involvement of at least two conduction channels - a slow channel that determines transitions between charge states of the bridge and a fast channel that dominates its conduction. Using Marcus theory of heterogeneous electron transfer (ET) at metal-molecule interfaces we identify and describe different regimes of nonlinear…
Sequential tunneling model is used to study electron transport in molecular rectifiers based on structures of donor-bridge-acceptor type. The device is made of two metallic electrodes connected by a molecule, which contains acceptor and donor subunits, separated by insulating bridge. Both subunits are modeled as quantum dots with discrete energy levels, isolated from each other by potential barrier and weakly coupled to both electrodes through tunnel junctions. Intervalence donor-acceptor tunneling process is treated as a superexchange mechanism or equivalently through the use of Marcus theory…
In this contribution we demonstrate structural control over a transport resonance in HS(CH$_{2}$)$_{n}$[1,4 - C$_{6}$H$_{4}$](CH$_{2}$)$_{n}$SH (n = 1, 3, 4, 6) metal - molecule - metal junctions, fabricated and tested using the scanning tunnelling microscopy-based $I(z)$ method. The Breit-Wigner resonance originates from one of the arene $π$-bonding orbitals, which sharpens and moves closer to the contact Fermi energy as $n$ increases. Varying the number of methylene groups thus leads to a very shallow decay of the conductance with the length of the molecule. We demonstrate that the electrica…
The relativistic nature of charge carriers in graphene is expected to lead to an angle- dependent transmission through a potential barrier, where Klein tunneling involves annihilation of an electron and a hole at the edges of the barrier. The signatures of Klein tunneling have been observed in gated graphene devices, but the angle dependence of the transmission probability has not been directly observed. Here we show measurements of the angle-dependent transmission through quasi-ballistic graphene heterojunctions with straight and angled leads, in which the barrier height is controlled by a sh…
We study the response of high-critical current proximity Josephson junctions to a microwave excitation. Electron over-heating in such devices is known to create hysteretic dc voltage-current characteristics. Here we demonstrate that it also strongly influences the ac response. The interplay of electron over-heating and ac Josephson dynamics is revealed by the evolution of the Shapiro steps with the microwave drive amplitude. Extending the resistively shunted Josephson junction model by including a thermal balance for the electronic bath coupled to phonons, a strong electron over-heating is obt…
The hot carrier dynamics and its effect on the device performance of GaAs solar cell and InAs/GaAs quantum dot solar cell (QDSC) was investigated. At first, the fundamental operation feature of conventional hot carrier solar cell was simulated based on the detailed balance thermodynamic model. Then we investigated the hot carrier dynamics in the normal junction based solar cell using hydrodynamic/energy Boltzmann transportation model (HETM) where the two temperature (carrier temperature and lattice temperature are treated separately. For the first time, we report an inherent quasi-equivalence …
