Effective Charging Energy Research Articles

Pair tunnelling through a molecule: linear thermopower

We present the calculations of the linear thermopower in single electron molecular transistors. The molecule with its vibrational internal degrees of freedom used as central object in a single electron transistor can in some cases be characterised by negative effective charging energy. This allows to model the system by Anderson Hamiltonian with negative U. Here we extend the previous calculations of the conductance of such system and study the linear thermopower of a dot characterised by negative value of the on-dot interaction U. We focus on the weak tunnelling limit, for which a rate equation approach is valid.

Precise implementation of cluster transfer matrix method in the single electron box

The partition function of the single electron box (SEB), a small metallic island connected by a tunnel junction to the source lead and by a gate capacitor to the gate, can be expressed in path-integral form, which contains the effective action of the collective variable, phase, after integrating out the background electron degrees of freedom. The cluster transfer matrix method (CTM) is applied to the SEB. By using an improved numerical algorithm and more intensive calculations with larger cluster size, we obtained a highly accurate result for the effective charging energy of SEB up to a large barrier conductance. With a clear converging tendency and the fact that we do not use any approximation in calculation of the partition function, our CTM calculation is systematic and exact. The result is in excellent agreement with the real time renormalization group method of König and Schoeller.

Effective charge and free energy of DNA inside an ion channel

Translocation of a single stranded DNA (ssDNA) through an alpha -hemolysin channel in a lipid membrane driven by applied transmembrane voltage V was extensively studied recently. While the bare charge of the ssDNA piece inside the channel is approximately 12 (in units of electron charge) measurements of different effective charges resulted in values between one and two. We explain these challenging observations by a large self-energy of a charge in the narrow water filled gap between ssDNA and channel walls, related to large difference between dielectric constants of water and lipid, and calculate effective charges of ssDNA. We start from the most fundamental stall charge q(s), which determines the force F(s)=q(s)V/L stalling DNA against the voltage V ( L is the length of the channel). We show that the stall charge q(s) is proportional to the ion current blocked by DNA, which is small due to the self-energy barrier. Large voltage V reduces the capture barrier which DNA molecule should overcome in order to enter the channel by /q(c)/V, where q(c) is the effective capture charge. We expressed it through the stall charge q(s). We also relate the stall charge q(s) to two other effective charges measured for ssDNA with a hairpin in the back end: the charge q(u) responsible for reduction of the barrier for unzipping of the hairpin and the charge q(e) responsible for DNA escape in the direction of hairpin against the voltage. At small V we explain reduction of the capture barrier with the salt concentration.

Interplay between exchange interactions and charging effects in metallic grains

We study the effect of strong antiferromagnetic exchange interactions in metallic grains in the Coulomb blockade regime. These interactions can be large in superconducting systems or in metallic antiferromagnetic particles. We extend the standard description of the grain in terms of a single collective variable, the charge and its conjugated phase, to include the spin degree of freedom. The suppression of spin fluctuations enhances the tendency towards Coulomb blockade. The effective charging energy and conductance are calculated numerically in the regime of large grain-lead coupling.

Universal scaling behaviour of the single electron box in the strong tunnellinglimit

We perform a numerical analysis of recently proposed scaling functions for the singleelectron box. Specifically, we study the ‘magnetic’ susceptibility as a function oftunnelling conductance and gate charge, and the effective charging energy atzero gate charge as a function of tunnelling conductance in the strong tunnellinglimit. Our Monte Carlo results confirm the accuracy of the theoretical predictions.

Pair Tunneling through Single Molecules

By a polaronic energy shift, the effective charging energy of molecules can become negative, favoring ground states with even numbers of electrons. Here we show that charge transport through such molecules near ground-state degeneracies is dominated by tunneling of electron pairs which coexists with (featureless) single-electron cotunneling. Because of the restricted phase space for pair tunneling, the current-voltage characteristics exhibit striking differences from the conventional Coulomb blockade. In asymmetric junctions, pair tunneling can be used for gate-controlled current rectification and switching.

Effective charging energy for a regular granular metal array

We study the Ambegaokar-Eckern-Sch\"{o}n (AES) model for a regular array of metallic grains coupled by tunnel junctions of conductance $g$ and calculate both paramagnetic and diamagnetic terms in the Kubo formula for the conductivity. We find analytically, and confirm by numerical path integral Monte Carlo methods, that for $0<g<4$ the conductivity obeys an Arrhenius law $\sigma(T)\sim\exp[-E^{*}(g)/T]$ with an effective charging energy $E^{*} (g)$ when the temperature is sufficiently low, due to a subtle cancellation between $T^2$ inelastic-cotunneling contributions in the paramagnetic and diamagnetic terms. We present numerical results for the effective charging energy and compare the results with recent theoretical analyses. We discuss the different ways in which the experimentally observed $\sigma(T)\sim\exp[-\sqrt{T_{0}/T}]$ law could be attributed to disorder.

Model for the onset of transport in systems with distributed thresholds for conduction

We present a model supported by simulation to explain the effect of temperature on the conduction threshold in disordered systems. Arrays with randomly distributed local thresholds for conduction occur in systems ranging from superconductors to metal nanocrystal arrays. Thermal fluctuations provide the energy to overcome some of the local thresholds, effectively erasing them as far as the global conduction threshold for the array is concerned. We augment this thermal energy reasoning with percolation theory to predict the temperature at which the global threshold reaches zero. We also study the effect of capacitive nearest-neighbor interactions on the effective charging energy. Finally, we present results from Monte Carlo simulations that find the lowest-cost path across an array as a function of temperature. The main result of the paper is the linear decrease of conduction threshold with increasing temperature: ${V}_{t}(T)={V}_{t}(0)[1\ensuremath{-}4.8{k}_{B}TP(0)∕{p}_{c}]$, where $1∕P(0)$ is an effective charging energy that depends on the particle radius and interparticle distance, and ${p}_{c}$ is the percolation threshold of the underlying lattice. The predictions of this theory compare well to experiments in one- and two-dimensional systems.

Effective charging energy of the single-electron box

We present numerical results on electron tunnelling in a single-electron box at lowtemperature. The effective action of this device is equivalent to the Hamiltonian of a classicalXY spin chain with long-ranged interactions. Using an efficient cluster algorithm and a newtransition matrix Monte Carlo approach, we are able to compute the effective charging energyEC* in the limit of very small tunnelling resistance. While previous Monte Carlo simulations wererestricted to the weak- and intermediate-tunnelling regimes, our method extends the range ofEC*-valuesby more than 30 orders of magnitude. This allows us to clearly observe the exponential suppression ofEC* with increasingtunnelling conductance α. For large but fixed α, the correction to the leading exponential behaviour exhibits a crossover from anintermediate-temperature behaviour at to zero-temperature behaviour at . We determine this correction in both regimes and compare the numerical results to thenumerous and controversial theoretical predictions for the strong-tunnelling limit.

Single-electron transistors in electromagnetic environments

The current--voltage $(I--V)$ characteristics of single-electron transistors (SETs) have been measured in various electromagnetic environments. Some SETs were biased with one-dimensional arrays of dc superconducting quantum interference devices (SQUIDs). The purpose was to provide the SETs with a magnetic-field-tunable environment in the superconducting state, and a high-impedance environment in the normal state. The comparison of SETs with SQUID arrays and those without arrays in the normal state confirmed that the effective charging energy of SETs in the normal state becomes larger in the high-impedance environment, as expected theoretically. In SETs with SQUID arrays in the superconducting state, as the zero-bias resistance of the SQUID arrays was increased to be much larger than the quantum resistance ${R}_{K}\ensuremath{\equiv}{h/e}^{2}\ensuremath{\approx}26\mathrm{k}\ensuremath{\Omega},$ a sharp Coulomb blockade was induced, and the current modulation by the gate-induced charge was changed from e periodic to $2e$ periodic at a bias point $0&lt;|V|&lt;2{\ensuremath{\Delta}}_{0}/e,$ where ${\ensuremath{\Delta}}_{0}$ is the superconducting energy gap. The author discusses the Coulomb blockade and its dependence on the gate-induced charge in terms of the single Josephson junction with gate-tunable junction capacitance.

Coulomb blockade with dispersive interfaces.

What quantity controls the Coulomb blockade oscillations if the dot-lead conductance is essentially frequency dependent? We argue that it is the conductance at the imaginary frequency given by the effective charging energy. The latter may be very different from the bare charging energy due to the interface-induced capacitance (or inductance). These observations are supported by a number of examples, considered from the weak and strong coupling (perturbation theory versus instanton calculus) perspectives.

Weak charge quantization on a superconducting island

We consider Coulomb blockade on a superconductive quantum dot strongly coupled to a lead through a tunneling barrier and/or normal diffusive metal. Andreev transport of the correlated pairs leads to quantum fluctuations of the charge on the dot. These fluctuations result in exponential renormalization of the effective charging energy. We employ two complimentary ways to approach the problem: the instanton and the functional renormalization group treatment of the nonlinear $\ensuremath{\sigma}$ model. We show that these two different methods produce identical results. We also derive the charging energy renormalization in terms of the arbitrary transmission matrix of the multichannel interface.

Charge fluctuations in the single-electron box

Quantum fluctuations of the charge in the single-electron box are investigated. Based on a diagrammatic expansion we calculate the average island charge number and the effective charging energy in third order in the tunneling conductance. Near the degeneracy point where the energy of two charge states coincides, the perturbative approach fails, and we explicitly resum the leading logarithmic divergencies to all orders. The predictions for zero temperature are compared with Monte Carlo data and with recent renormalization group results. While good agreement between the third-order result and numerical data justifies the perturbative approach in most of the parameter regime relevant experimentally, near the degeneracy point and at zero temperature the resummation is shown to be insufficient to describe strong tunneling effects quantitatively. We also determine the charge noise spectrum by employing a projection operator technique. Former perturbative and semiclassical results are extended by the approach.

Quantum Charge Fluctuations in Quantum Dots

Influence of the quantum charge fluctuations in a quantum dot on its charging effect has been investigated by using a quantum-dot device having four quantum point contacts (QPC's) which connect the dot to the reservoirs. The charging effect was detectable at combined tunnel conductance of four QPC's up to near 8 e 2 / h beyond the intuitive criterion e 2 / h . We observed anomalously nonlinear dependences of the conductances at the tops ( G top ) and bottoms ( G bot ) of the Coulomb oscillation on the tunnel conductances of QPC's, G QPC 's. The result on G top indicates that a transition from Coulombically regulated tunnelings to non-correlated tunnelings occurs by increasing G QPC 's. The result on G bot shows the existence of leakage conductance beyond the 2nd-order cotunneling contribution. The offset voltage in the current-voltage characteristics of the device showed significant decrease with the increase of G QPC 's, indicating the shrinkage of the effective charging energy. The results on G top and ...

Thermopower of quantum chaos

The thermopower of a chaotic quantum dot has been studied in the Coulomb and the ballistic transport regime. Theoretical examinations predict distinct features for quantum dots where the electron trajectories are chaotic. Accordingly, we give experimental evidence for a residual effective charging energy in the case of asymmetric ajusted leads ( G⩽2 e 2/ h) and for non-Gaussian thermopower fluctuation distributions in the ballistic regime ( G=4 e 2/ h).

Strong charge fluctuations in the single-electron box: A quantum Monte Carlo analysis

We study strong electron tunneling in the single-electron box, a small metallic island coupled to an electrode by a tunnel junction, by means of quantum Monte Carlo simulations. We obtain results, at arbitrary tunneling strength, for the free energy of this system and the average charge on the island as a function of an external bias voltage. In much of the parameter range an extrapolation to the ground state is possible. Our results for the effective charging energy for strong tunneling are compared to earlier -- in part controversial -- theoretical predictions and Monte Carlo simulations.

Coulomb Blockade without Tunnel Junctions

We find that tunnel junctions are not needed to provide single electron effects in a metallic island. Eventually the tunnel junction may be replaced by an arbitrary scatterer. It is important that even a {\it diffusive} scatterer provides a sufficient isolation for single electron effects to persist. To formulate this in exact terms, we derive and analyze the effective action that describes an arbitrary scatterer. We also consider the fluctuations of the effective charging energy.

Charging Energy of a Chaotic Quantum Dot

The scaling behavior of the charging energy of a quantum dot with asymmetrically adjusted tunnel barriers is measured through the amplitude of the Coulomb oscillations in the thermovoltage. For weak coupling between the dot and the reservoirs, we observe a linear scaling of the effective charging energy when the transmission probability of one tunnel barrier is increased. At higher transmission probabilities, we find a deviation from the linear scaling and a crossover to a constant value. This behavior is caused by the chaotic nature of the electron trajectories within the dot.

Effective charging energy and conductance of ultrasmall tunnel junctions coupled to an external electromagnetic environment

Tunneling processes in ultrasmall tunnel junctions surrounded by an electromagnetic environment have been investigated with a nonperturbative approach. The derived functional integral representation of the transport current as a function of the junction voltage clearly indicates that the effective charging energy and the effective external conductance depend on the junction conductance. Via these effective parameters, we can map the nonperturbative formula of the action onto the perturbative one. Consequently, the tunneling current can be calculated for the first time beyond the perturbation theory. Our theory provides a better understanding of the measured current–voltage characteristics.

Effective charge and electronic energy loss of heavy ions from a modelof an ion embedded in jellium

A model of an ion embedded in jellium is presented. The static charge state of a heavy ion is determined self-consistently. The effective charge of a heavy ion at low velocities is calculated, which is incorporated with the Brandt-Kitagawa effective charge theory to take the velocity dependence of the effective charge into account. The quantal harmonic oscillator model is generalized to calculate the electronic energy loss of heavy ions colliding with a carbon target. The results are compared with available experimental data.