Experimental measurements of electron transport properties of molecular junctions are often performed in solvents. Solvent-molecule coupling and physical properties of the solvent can be used as the external stimulus to control electric current through a molecule. In this paper, we propose a model, which includes dynamical effects of solvent-molecule interaction in the non-equilibrium Green's function calculations of electric current. The solvent is considered as a macroscopic dipole moment that reorients stochastically and interacts with the electrons tunnelling through the molecular junction. The Keldysh-Kadanoff-Baym equations for electronic Green's functions are solved in time-domain with subsequent averaging over random realisations of rotational variables using Furutsu-Novikov method for exact closure of infinite hierarchy of stochastic correlation functions. The developed theory requires the use of wide-band approximation as well as classical treatment of solvent degrees of freedom. The theory is applied to a model molecular junction. It is demonstrated that not only electrostatic interaction between molecular junction and solvent but also solvent viscosity can be used to control electrical properties of the junction. Aligning of the rotating dipole moment breaks particle-hole symmetry of the transmission favouring either hole or electron transport channels depending upon the aligning potential.
Recent experiments have shown that transport properties of molecular-scale devices can be reversibly altered by the surrounding solvent. Here, we use a combination of first-principles calculations and experiment to explain this change in transport properties through a shift in the local electrostatic potential at the junction caused by nearby conducting and solvent molecules chemically bound to the electrodes. This effect is found to alter the conductance of bipyridine - gold junctions by more than 50%. Moreover, we develop a general electrostatic model that quantitatively predicts the relatio…
We consider a single molecule circuit embedded into solvent. The Born dielectric solvation model is combined with Keldysh nonequilibrium Green's functions to describe the electron transport properties of the system. Depending on the dielectric constant, the solvent induces multiple nonequilibrium steady states with corresponding hysteresis in molecular current-voltage characteristics as well as negative differential resistance. We identify the physical range of solvent and molecular parameters where the effects are present. The position of the negative differential resistance peak can be contr…
After evaporation of the organic solvents, benzene, toluene, and cyclohexane on gold substrates, Scanning Tunneling Microscope (STM) shows the presence of a remaining adsorbed layer. The different solvent molecules were individually observed at ambient conditions, and their electronic transport properties characterized through the STM in the Break Junction approach. The combination of both techniques reveals, on one hand, that solvents are not fully evaporated over the gold electrode and, secondly, determines the role of the electronic transport of the solvents in molecular electronics.
Electronic current flowing in a molecular electronic junction dissipates significant amounts of energy to vibrational degrees of freedom, straining and rupturing chemical bonds and often quickly destroying the integrity of the molecular device. The infamous mechanical instability of molecular electronic junctions critically limits performance, lifespan, and raises questions as to the technological viability of single-molecule electronics. Here we propose a practical scheme for cooling the molecular vibrational temperature via application of an AC voltage over a large, static operational DC vol…
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 t…
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 adjusting the charging state of a molecular metal complex in the context of a density functional theory description of coherent electron transport through single molecule junctions, we correct for self interaction effects by fixing the charge on a counterion, which in our calculations mimics the effect of the gate in an electrochemical STM setup, with two competing methods, namely the generalized $Δ$ SCF technique and screening with solvation shells. One would expect a transmission peak to be pinned at the Fermi energy for a nominal charge of +1 on the molecule in the junction but we find …
Electronic excitations in dilute solutions of poly para phenylene ethynylene (poly-PPE) are studied using a QM/MM approach combining many-body Green's functions theory within the $GW$ approximation and the Bethe-Salpeter equation with polarizable force field models. Oligomers up to a length of 7.5\,nm (10 repeat units) functionalized with nonyl side chains are solvated in toluene and water, respectively. After equilibration using atomistic molecular dynamics (MD), the system is partitioned into a quantum region (backbone) embedded into a classical (side chains and solvent) environment. Optical…
Transition metal dichalcogenides (TMDCs) are promising materials for applications in nanoelectronics and correlated fields, where their metallic edge states play a fundamental role in the electronic transport. In this work, we investigate the transport properties of MoS$_2$ zigzag nanoribbons under a butadiene (C$_4$H$_6$) atmosphere, as this compound has been used to obtain MoS$_2$ flakes by exfoliation. We use density functional theory combined with non-equilibrium Green's function techniques, in a methodology contemplating disorder and different coverages. Our results indicate a strong modu…
We present electronic transport measurements through thiolated C$_{60}$ molecules in liquid environment. The molecules were placed within a mechanically controllable break junction using a single anchoring group per molecule. When varying the electrode separation of the C$_{60}$-modified junctions, we observed a peak in the conductance traces. The shape of the curves is strongly influenced by the environment of the junction as shown by measurements in two distinct solvents. In the framework of a simple resonant tunneling model, we can extract the electronic tunneling rates governing the transp…
In molecular electronic conduction, exotic lattice morphologies often give rise to exotic behaviors. Among 2D systems, graphene is a notable example. Recently, a stable amorphous version of graphene called Monolayer Amorphous Carbon (MAC) was synthesized. MAC poses a new set of questions regarding the effects of disorder on conduction. In this Letter, we perform ensemble-level computational analysis of the coherent electronic transmission through MAC nano-fragments in search of defining characteristics. Our analysis, relying on a semi-empirical Hamiltonian (Pariser-Parr-Pople) and Landauer the…
Confined nanoscale spaces, electric fields and tunneling currents make the molecular electronic junction an experimental device for the discovery of new, out-of-equilibrium chemical reactions. Reaction-rate theory for current-activated chemical reactions is developed by combining a Keldysh nonequilibrium Green's functions treatment of electrons, Fokker-Planck description of the reaction coordinate, and Kramers' first-passage time calculations. The NEGF provide an adiabatic potential as well as a diffusion coefficient and temperature with local dependence on the reaction coordinate. Van Kampen'…
Molecule-electrode interfaces in molecular electronic junctions are prone to chemical reactions, structural changes, and localized heating effects caused by electric current. These can be exploited for device functionality or may be degrading processes that limit performance and device lifetime. We develop a nonequilibrium Green's function based transport theory in which the central region atoms and, more importantly, atoms on molecule-electrode interfaces are allowed to move. The separation of time-scales of slow nuclear motion and fast electronic dynamics enables the algebraic solution of th…
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…
Few layer black phosphorus is a new two-dimensional material which is of great interest for applications, mainly in electronics. However, its lack of stability severely limits our ability to synthesise and process this material. Here we demonstrate that high-quality, few-layer black phosphorus nanosheets can be produced in large quantities by liquid phase exfoliation in the solvent N-cyclohexyl-2-pyrrolidone (CHP). We can control nanosheet dimensions and have developed metrics to estimate both nanosheet size and thickness spectroscopically. When exfoliated in CHP, the nanosheets are remarkably…
We expand iterative numerically-exact influence functional path-integral tools and present a method capable of following the nonequilibrium time evolution of subsystems coupled to multiple bosonic and fermionic reservoirs simultaneously. Using this method, we study the real-time dynamics of charge transfer and vibrational mode excitation in an electron conducting molecular junction. We focus on nonequilibrium vibrational effects, particularly, the development of vibrational instability in a current-rectifying junction. Our simulations are performed by assuming large molecular vibrational anhar…
The interaction between electronic and vibrational degrees of freedom in single-molecule junctions may result from the dependence of the electronic energies or the electronic states of the molecular bridge on the nuclear displacement. The latter mechanism leads to a direct coupling between different electronic states and is referred to as nonadiabatic electronic-vibrational coupling. Employing a perturbative nonequilibrium Green's function approach, we study the influence of nonadiabatic electronic-vibrational coupling in model molecular junctions. Thereby we distinguish between systems with w…
The energy and charge fluxes carried by electrons in a two-terminal junction subjected to a random telegraph noise, produced by a single electronic defect, are analyzed. The telegraph processes are imitated by the action of a stochastic electric field that acts on the electrons in the junction. Upon averaging over all random events of the telegraph process, it is found that this electric field supplies, on the average, energy to the electronic reservoirs, which is distributed unequally between them: the stronger is the coupling of the reservoir with the junction, the more energy it gains. Thus…
The interaction between electronic and nuclear degrees of freedom in single-molecule junctions is an essential mechanism, which may result in the current-induced rupture of chemical bonds. As such, it is fundamental for the stability of molecular junctions and for the applicability of molecular electronic devices. In this publication, we study current-induced bond rupture in molecular junctions using a numerically exact scheme, which is based on the hierarchical quantum master equation (HQME) method in combination with a discrete variable representation for the nuclear degrees of freedom. Empl…
The influence of multiple vibrational modes on current fluctuations in electron transport through single-molecule junctions is investigated. Our analysis is based on a generic model of a molecular junction, which comprises a single electronic state on the molecular bridge coupled to multiple vibrational modes and fermionic leads, and employs a master equation approach. The results reveal that in molecular junctions with multiple vibrational modes already weak to moderate electronic-vibrational coupling may result in high noise levels, especially at the onset of resonant transport, in accordanc…
Electromigrated nanoscale junctions have proven very useful for studying electronic transport at the single-molecule scale. However, confirming that conduction is through precisely the molecule of interest and not some contaminant or metal nanoparticle has remained a persistent challenge, typically requiring a statistical analysis of many devices. We review how transport mechanisms in both purely electronic and optical measurements can be used to infer information about the nanoscale junction configuration. The electronic response to optical excitation is particularly revealing. We briefly dis…
Electronic Whispering Gallery Modes (EWGMs) have been recently observed in several circular graphene junctions, pn and pp0, created in scanning tunnelling microscope experiments. By computing the local density of states within the Dirac-Weyl formalism for massless fermions we demonstrate that the EWGMs may really be emerged in any type of the electrostatic potential induced circular graphene junctions, including uni-junctions (e.g. np- or pp0-junctions) as well as bipolar-junctions (e.g. pnp-heterojunctions). Surprisingly, quantitative analyses show that for all the EWGMs identified (regardles…
The exact ground-state exchange-correlation functional of Kohn-Sham density functional theory yields the exact transmission through an Anderson junction at zero bias and temperature. The exact impurity charge susceptibility is used to construct the exact exchange-correlation potential. We analyze the successes and limitations of various types of approximations, including smooth and discontinuous functionals of the occupation, as well as symmetry-broken approaches.
Using a model comprising a 2-level bridge connecting free electron reservoirs we show that coupling of a molecular bridge to electron-hole excitations in the leads can markedly effect the source-drain current through a molecular junction.In some cases, e.g. molecules that exhibit strong charge transfer transitions, the contribution from electron-hole excitations can exceed the Landauer elastic current and dominate the observed conduction.
We investigated a suspended bilayer graphene where the bottom (top) layer is doped by boron (nitrogen) substitutional atoms by using Density Functional Theory (DFT) calculations. We found that at high dopant concentration (one B-N pair every 32 C atoms) the electronic structure of the bilayer does not depend on the B-N distance but on the relative occupation of the bilayer graphene sub-lattices by B and N. We found that a large built in electric field is established between layers, giving rise to an energy gap. We further investigated the transport properties and found that intra-layer electro…
We use simultaneous electronic transport and optical characterization measurements to reveal new information about electronic and optical processes in nanoscale junctions fabricated by electromigration. Comparing electronic tunneling and photocurrents allows us to infer the optical frequency potential difference produced by the plasmon response of the junction. Together with the measured tunneling conductance, we can then determine the locally enhanced electric field within the junction. In similar structures containing molecules, anti-Stokes and Stokes Raman emission allow us to infer the eff…
We investigate the conductance of normal-conductor/graphene/normal-conductor (NGN) junctions for arbitrary on-site potentials in the normal and graphitic parts of the system. We find that a ballistic NGN junction can display insulating behavior even when the charge-carrier density in the graphene part is finite. This effect originates in the different k intervals supporting propagating modes in graphene and a normal conductor, and persists for moderate levels of bulk, edge, or interface disorder. The ensuing conductance thresholds could be used as an electronic tool to map out details of the g…
We propose to correlate transmittance maps and spectral-density maps of planar junctions, in order to analyze quantitatively and in detail spin-dependent transport calculations. Since spectral-density maps can be resolved with respect to atom, angular momentum, and spin, the resulting correlation coefficients reveal unequivocally, e.g., which layers or which orbitals determine the tunnel conductances. Our method can be used for transport calculations within the Landauer-Büttiker formalism. Its properties and features will be discussed by means of a pure bcc Fe(001) lead as well as an extensive…
We carry out a layer-by-layer investigation to understand electron transport across metal-insulator-metal junctions. Interfacial structures of junctions were studied and characterized using first-principles density functional theory within the generalized gradient approximation. We found that as a function of the number of crystal layers the calculated transmission coefficients of multilayer silicene junctions decay much slower than for BN-based junctions We revisited the semiclassical Boltzmann theory of electronic transport and applied to multilayer silicene and BN-based junctions. The calcu…
Electronic conduction through single molecules is affected by the molecular electronic structure as well as by other information that is extremely difficult to assess, such as bonding geometry and chemical environment. The lack of an independent diagnostic technique has long hampered single-molecule conductance studies. We report simultaneous measurement of the conductance and the Raman spectra of nanoscale junctions used for single-molecule electronic experiments. Blinking and spectral diffusion in the Raman response of both para-mercaptoaniline and a fluorinated oligophenylyne ethynylene cor…
Fluctuations pose fundamental limitations in making sensitive measurements, yet at the same time, noise unravels properties that are inaccessible at the level of the averaged signal. In electronic devices, shot noise arises from the discrete nature of charge carriers and it increases linearly with the applied voltage according to the celebrated Schottky formula. Nonetheless, measurements of shot noise in atomic-scale junctions at high voltage reveal significant nonlinear (anomalous) behavior, which varies from sample to sample, and has no specific trend. Here, we provide a viable, unifying exp…
Understanding and controlling the flow of heat is a major challenge in nanoelectronics. When a junction is driven out of equilibrium by light or the flow of electric charge, the vibrational and electronic degrees of freedom are, in general, no longer described by a single temperature[1-6]. Moreover, characterizing the steady-state vibrational and electronic distributions {\it in situ} is extremely challenging. Here we show that surface-enhanced Raman emission may be used to determine the effective temperatures for both the vibrational modes and the flowing electrons in a biased metallic nanosc…
The accurate determination of electronic temperatures in metallic nanostructures is essential for many technological applications, like plasmon-enhanced catalysis or lithographic nanofabrication procedures. In this Letter we demonstrate that the electronic temperature can be accurately measured by the shape of the tunnel electroluminescence emission edge in tunnel plasmonic nanocavities, which follows a universal thermal distribution with the bias voltage as the chemical potential of the photon population. A significant deviation between electronic and lattice temperatures is found below 30 K …
The non-centrosymmetric semiconductor BiTeI exhibits two distinct surface terminations that support spin-split Rashba surface states. Their ambipolarity can be exploited for creating spin-polarized $p$-$n$ junctions at the boundaries between domains with different surface terminations. We use scanning tunneling microscopy/spectroscopy (STM/STS) to locate such junctions and investigate their atomic and electronic properties. The Te- and I-terminated surfaces are identified owing to their distinct chemical reactivity, and an apparent height mismatch of electronic origin. The Rashba surface state…
We investigate the electronic transport properties of a ferromagnet/normal/ferromagnet junction on the surface of a topological insulator with a gate voltage exerted on the normal segment. It is found that the conductance oscillates with the width of normal segment and gate voltage, and the maximum of conductance gradually decreases while the minimum of conductance approaches zero as the width increases. The conductance can be controlled by tuning the gate voltage like a spin field-effect transistor. It is found that the magnetoresistance ratio can be very large, and can also be negative owing…
Micro-refrigerators that operate in the sub-kelvin regime are a key device in quantum technology. A well-studied candidate, an electronic cooler using Normal metal - Insulator - Superconductor (NIS) tunnel junctions offers substantial performance and power. However, its superconducting electrodes are severely overheated due to exponential suppression of their thermal conductance towards low temperatures, and the cooler performs unsatisfactorily - especially in powerful devices needed for practical applications. We employ a second NIS cooling stage to thermalize the hot superconductor at the ba…
Nanoscale molecular-electronic devices and machines are emerging as promising functional elements, naturally flexible and efficient, for next generation technologies. A deeper understanding of carrier dynamics in molecular junctions is expected to benefit many fields of nanoelectronics and power-devices. We determine time-resolved charge current flowing at donor- acceptor interface in molecular junctions connected to metallic electrodes by means of quantum transport simulations. The current is induced by the interaction of the donor with a Gaussian-shape femtosecond laser pulse. Effects of the…
Spatial manipulation of current flow in graphene could be achieved through the use of a tilted pn junction. We show through numerical simulation that a pseudo-Hall effect (i.e. non-equilibrium charge and current density accumulating along one of the sides of a graphene ribbon) can be observed under these conditions. The tilt angle and the pn transition length are two key parameters in tuning the strength of this effect. This phenomenon can be explained using classical trajectory via ray analysis, and is therefore relatively robust against disorder. Lastly, we propose and simulate a three termi…
The generalized Kadanoff-Baym ansatz (GKBA) offers a computationally inexpensive approach to simulate out-of-equilibrium quantum systems within the framework of nonequilibrium Green's functions. For finite systems the limitation of neglecting initial correlations in the conventional GKBA approach has recently been overcome [Phys. Rev. B 98, 115148 (2018)]. However, in the context of quantum transport the contacted nature of the initial state, i.e., a junction connected to bulk leads, requires a further extension of the GKBA approach. In this work, we lay down a GKBA scheme which includes initi…
We study the influence of superconducting correlations on the electronic specific heat in a diffusive superconductor-normal metal-superconductor Josephson junction. We present a description of this system in the framework of the diffusive-limit Green's function theory, taking into account finite temperatures, phase difference as well as junction parameters. We find that proximity effect may lead to a substantial deviation of the specific heat as compared to that in the normal state, and that it can be largely tuned in magnitude by changing the phase difference between the superconductors. A me…
When biased at a voltage just below a superconductor's energy gap, a tunnel junction between this superconductor and a normal metal cools the latter. While the study of such devices has long been focussed to structures of submicron size and consequently cooling power in the picoWatt range, we have led a thorough study of devices with a large cooling power up to the nanoWatt range. Here we describe how their performance can be optimized by using a quasi-particle drain and tuning the cooling junctions' tunnel barrier.
We investigate transport through molecular wires whose energy levels are affected by environmental fluctuations. We assume that the relevant fluctuations are so slow that they, within a tight-binding description, can be described by disordered, Gaussian distributed onsite energies. For long wires, we find that the corresponding current distribution can be rather broad even for a small energy variance. Moreover, we analyse with a Floquet master equation the interplay of laser excitations and static disorder. Then the disorder leads to spatial asymmetries such that the laser diving can induce a …
Vibrational nonequilibrium effects in charge transport through single-molecule junctions are investigated. Focusing on molecular bridges with multiple electronic states, it is shown that electronic-vibrational coupling triggers a variety of vibronic emission and absorption processes, which influence the conductance properties and mechanical stability of single-molecule junctions profoundly. Employing a master equation and a nonequilibrium Green's function approach, these processes are analyzed in detail for a generic model of a molecular junction and for benzenedibutanethiolate bound to gold e…
In electronic cooling with superconducting tunnel junctions, the cooling power is counterbalanced by the interaction with phonons and by the heat flow from the overheated leads. We study aluminium-based coolers that are equipped with a suspended normal metal and an efficient quasi-particle drain. At intermediate temperatures, the phonon bath of the suspended normal metal is cooled. At lower temperatures, by adjusting the junction transparency, we control the injection current, and thus the superconductor temperature. The device shows a strong cooling from 150 mK down to about 30 mK, a factor o…
We present a theory of molecular motors based on the Ehrenfest dynamics for the nuclear coordinates and the adiabatic limit of the Kadanoff-Baym equations for the current-induced forces. Electron-electron interactions can be systematically included through many-body perturbation theory, making the nonequilibrium Green's functions formulation suitable for first-principles treatments of realistic junctions. The method is benchmarked against simulations via real-time Kadanoff-Baym equations, finding an excellent agreement. Results on a paradigmatic model of molecular motor show that correlations …
We have developed a device fabrication process to pattern graphene into nanostructures of arbitrary shape and control their electronic properties using local electrostatic gates. Electronic transport measurements have been used to characterize locally gated bipolar graphene $p$-$n$-$p$ junctions. We observe a series of fractional quantum Hall conductance plateaus at high magnetic fields as the local charge density is varied in the $p$ and $n$ regions. These fractional plateaus, originating from chiral edge states equilibration at the $p$-$n$ interfaces, exhibit sensitivity to inter-edge backsc…
Electronic transport across n-Si-alkyl monolayer/Hg junctions is, at reverse and low forward bias, independent of alkyl chain-length from 18 down to 1 or 2 carbons! This and further recent results indicate that electron transport is minority, rather than majority carrier-dominated, occurs via generation and recombination, rather than (the earlier assumed) thermionic emission and, as such is rather insensitive to interface properties. The (m)ethyl results show that binding organic molecules directly to semiconductors provides semiconductor/metal interface control options, not accessible otherwi…
Using density functional theory and non-equilibrium Greens function technique, we performed theoretical investigations on the transport properties of several ZAZ SiNRs junctions,a similar kind of silicene molecules junction combined by zigzag and armchair silicene nanoribbons. It is found that the differential conductances of the three systems decrease with an order of 5-ZAZ>4-ZAZ>3-ZAZ.Particularly,the Negative differential resistance can be observed within certain bias voltage range only in 3-ZAZ SiNRs. In order to elucidate the mechanism the NDR behavior, the transmission spectra and molecu…
Monte Carlo simulations and an analytical approach within the framework of a semiclassical model are presented which permit the determination of Coulomb blockade and single electron charging effects for multiple tunnel junctions coupled in series. The Coulomb gap in the I(V) curves can be expressed as a simple function of the capacitances in the series. Furthermore, the magnitude of the differential conductivity at current onset is calculated in terms of the model. The results are discussed with respect to the number of junctions.
The influence of vibrational motion on electron conduction through single molecules bound to metal electrodes is investigated employing first-principles electronic-structure calculations and projection-operator Green's function methods. Considering molecular junctions where a central phenyl ring is coupled via (alkane)thiol-bridges to gold electrodes, it is shown that -- depending on the distance between the electronic $π$-system and the metal -- electronic-vibrational coupling may result in pronounced vibrational substructures in the transmittance, a significantly reduced current as well as a…
Electronic and Thermoelectric Properties of Molecular Junctions Incorporating Organometallic Complexes: Implications for Thermoelectric Energy Conversion
Using density functional theory and nonequilibrium Greens functions-based methods we investigated the electronic and transport properties of monolayer TiS3 pn-junction. We constructed a lateral pn-junction in monolayer TiS3 by using Li and F adatoms. An applied bias voltage caused significant variability in the electronic and transport properties of the TiS3 pn-junction. In addition, spin dependent current-voltage characteristics of the constructed TiS3 pn-junction were analyzed. Important device characteristics were found such as negative differential resistance and rectifying diode behaviors…
The sensitivity of superconducting qubits allows for spectroscopy and coherence measurements on individual two-level systems present in the disordered tunnel barrier of an $\mathrm{Al/AlO_x/Al}$ Josephson junction. We report experimental evidence for the decoherence of two-level systems by Bogoliubov quasiparticles leaking into the insulating $\mathrm{AlO_x}$ barrier. We control the density of quasiparticles in the junction electrodes either by the sample temperature or by injecting them using an on-chip dc-SQUID driven to its resistive state. The decoherence rates were measured by observing t…
The description of transport phenomena in devices consisting of arrays of tunnel junctions, and the experimental confirmation of these predictions is one of the great successes of mesoscopic physics. The aim of this paper is to give a self-consistent review of sequential transport processes in such devices, based on the so-called "orthodox" model. We calculate numerically the current-voltage (I-V) curves, the conductance versus bias voltage (G-V) curves, and the associated thermal transport in symmetric and asymmetric two-junction arrays such as Coulomb-blockade thermometers (CBTs), supercondu…
