Mesoscopic Tunnel Junctions Research Articles

Mesoscopic quantum transport: Resonant tunneling in the presence of a strong Coulomb interaction.

Coulomb-blockade phenomena and quantum fluctuations are studied in mesoscopic metallic tunnel junctions with high charging energies. If the resistance of the barriers is large compared to the quantum resistance, transport can be described by sequential tunneling. Here we study the influence of quantum fluctuations. They are strong when the resistance is small or the temperature is very low. A real-time approach is developed that allows the diagrammatic classification of resonant tunneling processes where different electrons tunnel coherently back and forth between the leads and the metallic island. With the help of a nonperturbative resummation technique we evaluate the spectral density, which describes the charge excitations of the system. From it, physical quantities of interest such as current and average charge can be deduced. Our main conclusions are as follows: An energy renormalization leads to a logarithmic temperature dependence of the renormalized system parameters. A finite lifetime broadening can change the classical picture drastically. It gives rise to a strong flattening of the Coulomb oscillations for low resistances, but in the Coulomb-blockade regime inelastic electron cotunneling persists. The effects become important at temperatures that are accessible in experiments.

Resonant tunneling and charge fluctuations in mesoscopic tunnel junctions

Quantum fluctuations in mesoscopic tunnel junctions are studied in the presence of high charging energies. The processes of sequential tunneling, electron cotunneling and resonant tunneling are analyzed within a new nonperturbative resummation technique. The current and the average charge are shown to be related to the spectral density describing the charge excitations of the single electron transistor. An energy-dependent finite lifetime is obtained which leads to the theory of inelastic electron cotunneling and gives important corrections to the classical result for strong tunneling and finite temperatures. An additional energy renormalization leads to a logarithmic temperature dependence of the renormalized system parameters. Several formulas for the line shape of the conductance oscillations are presented which show the possibility to observe experimentally quantum fluctuation effects at realistic temperatures.

Transport properties of mesoscopic tunnel junctions: nonperturbative analysis

The correlation functions and transport properties of a small normal tunnel junction are investigated. In the flow frequency limit the junction response is found to be purely capacitive for both weak and strong electron tunneling. The junction static conductance vanishes exponentially with the temperature T and shows a crossover between the Coulomb blockade and metallic behavior at T∼ e 2/ C eff, where C eff is the renormalized junction capacitance.

Charge fluctuations in systems of mesoscopic tunnel junctions

We study the effect of an external circuit on electron cotunneling and show that the cotunneling rate can be strongly suppressed by the external impedance. For a system with N normal tunnel junctions the cotunneling contribution to the I- V curve is found to be I ∝ V 2 N−1+1/2 as x, a s is the dimensionless conductance of the external leads. We also evaluate the I- V characteristic of a multijunction system beyond the perturbation theory in the junction conductance. The offset on this characteristic essentially depends on the form of the external impedance.

Phase transition in small metallic junctions with quasiparticle dissipation.

The results of Monte Carlo simulations of a mesoscopic tunnel junction at T=0 are reported, showing some evidence of a dissipative phase transition. In the strong dissipation regime the predictions of the self consistent spin wave theory turn out to be correct and the algebraic decay of correlations leads to quasi-long range order (absence of a voltage threshold for the Coulomb blockade). We estimated the critical junction resistance to be Rt≈0.53 kΩ.

Inelastic tunneling effects in current-driven mesoscopic tunnel junctions.

We theoretically study ideally current-driven single mesoscopic tunnel junctions, including an inelastic tunneling conduction path. Energy considerations demand that the usual peaks in the ${\mathit{d}}^{2}$I/${\mathit{dV}}^{2}$ versus voltage spectrum are shifted by the charging energy of the junction. We also find the peaks to be broadened by single-electron-tunneling oscillations and shot noise. We propose that these effects can be used experimentally to determine the effective external driving source of a junction.

Analytic solution for the current-voltage characteristic of two mesoscopic tunnel junctions coupled in series.

We present a theoretical analysis for a system composed of two mesoscopic tunnel junctions coupled in series. We show that the current-voltage characteristic for this system can be obtained analytically. The usefulness of the model is demonstrated through the fit of experimental data acquired with a cryogenic (4.2 K) scanning tunneling microscope. A simple extension of the model predicts additional structure in the system characteristics when discrete middle electrode states are present.

Probability-density-function description of mesoscopic normal tunnel junctions.

Conventional treatments of the dynamics of mesoscopic normal tunnel junctions mainly reduce the problem to a stochastic master equation and finally resort to computer simulation. This paper presents a new methodology based on probability-density functions to solve the problem in a fully analytic manner. Analytic expressions of the charge distribution across the junction, current-voltage characteristics, and the degree of randomness of the single-electron-tunneling oscillations are obtained under an arbitrary bias condition, where the degree of randomness is defined as the ratio of the standard deviation of dwell times to their mean value. In particular, the minimum degree of randomness achievable under the constant-current-bias condition is found to be (${\mathit{R}}_{\mathit{T}}$${\mathit{CI}}_{\mathrm{dc}}$/e${)}^{1/2}$, where e is the electronic charge, ${\mathit{R}}_{\mathit{T}}$ is the tunnel resistance, C is the junction capacitance, and ${\mathit{I}}_{\mathrm{dc}}$ is the bias current.

Charge solitons in 1-D array of mesoscopic tunnel junctions

We study the dynamics of a one-dimensional array of mesoscopic normal tunnel junctions using the semiclassical picture. We show that the charging effect on a single electron tunneling through a single junction together with capacitive coupling to a substrate lead to the existence of soliton-like modes of charge transfer along the array. These modes are manifested by the appearance of clear Coulomb steps in the current-voltage characteristics (for a range of junction parameters) which can be directly verified experimentally.

Charge effect solitons

We present an effective circuit model of a chain of mesoscopic tunnel junctions. We show that the system possesses a soliton solution. The propagation of the soliton corresponds to the tunneling of a single charge along the system. We study the properties of this charged soliton and calculate the resulting I–V characteristics. We discuss possible experimental realizations of the model and its relevance to other systems.

The charge-effect transistor

We present a theoretical study of the current-voltage characteristic of a new transistor based upon the ‘‘Coulomb blockade.’’ In mesoscopic (submicron) tunnel junctions the flow of current can be blocked by the electrostatic charging energy of a single electron. The charge-effect transistor is composed of two mesoscopic tunnel junctions connected in series with a gate terminal capacitively coupled to the interjunction region. Such a device has been shown to lead to a Coulomb staircase in the current-voltage characteristic when the gate voltage is zero. Here we study the effect of the gate voltage on the current through the device for various ranges of junction parameters. We study junctions made from both normal metal and superconductors. We examine the current noise at different operating points and find it comparable to, but lower than, that in ordinary shot-noise devices.

The dynamics of mesoscopic normal tunnel junctions

We first review the dynamics of mesoscopic tunnel junctions within the semiclassical approach, outlining the method and its assumptions. We examine the case of a single junction driven by a constant current source, and its non-linear I–V characteristic. We then consider a single junction driven by a direct and an alternating current source, and show that it can be used as a phase-voltage converter. We also apply the approach to two junctions in series, showing that such a configuration has a non-linear I–V characteristic that can be used in electronic devices. We subsequently investigate the dynamics of such systems when the phase breaking time is large and the semiclassical approach does not apply. We first review the standard Zener tunneling calculations, and then show the effect of dissipation. We define and calculate the Zener time, a measure of the width of non-adiabatic transitions. We investigate the dynamics of systems whose energy spectrum consists of a set of periodic bands, for the cases where the phase breaking time is larger and smaller than the period of the band, but larger than the Zener time.