Single electron tunneling rates in multijunction circuits

The rate of electron tunneling through normal metal tunnel junctions is calculated for the case of ultrasmall junction capacitances. The so-called Coulomb blockade of electron tunneling at low temperatures is shown to be strongly affected by the external electrical circuit. Under the common experimental condition of a low impedance environment the Coulomb blockade is suppressed for single tunnel junctions. However, a Coulomb gap structure emerges for junctions embedded in a high impedance environment. For a double junction setup a Coulomb blockade of tunneling arises even for low impedance environments due to the charge quantization on the metallic island between the junctions. An approach using circuit analysis is presented which allows to reduce the calculation of tunneling rates in multijunction circuits to those of a single junction in series with an effective capacitance. The range of validity of the socalled local rule and global rule rates is clarified. It is found that the tunneling rate tends towards the global rule rate as the number of junctions is increased. Some specific results are given for a one-dimensional array of tunnel junctions.     

Time domain capacitance spectroscopy of tunneling electrons in the two-dimensional electron gas

We have developed a technique capable of measuring the tunneling current into both localized and conducting states in a 2D electron system (2DES). The method yields I-V characteristics for tunneling with no distortions arising from low 2D in-plane conductivity. We have used the technique to determine the pseudogap energy spectrum for electron tunneling into and out of a 2D system and, further, we have demonstrated that such tunneling measurements reveal spin relaxation times within the 2DEG. Pseudogap: In a 2DEG in perpendicular magnetic field, a pseudogap develops in the tunneling density of states at the Fermi energy. We resolve a linear energy dependence of this pseudogap at low excitations. The slopes of this linear gap are strongly field dependent. No existing theory predicts the observed behavior. Spin relaxation: We explore the characteristics of equilibrium tunneling of electrons from a 3D electrode into a high mobility 2DES. For most 2D Landau level filling factors, we find that electrons tunnel with a single, well-defined tunneling rate. However, for spin-polarized quantum Hall states (ν=1, 3 and 1/3) tunneling occurs at two distinct rates that differ by up to two orders of magnitude. The dependence of the two rates on temperature and tunnel barrier thickness suggests that slow in-plane spin relaxation creates a bottleneck for tunneling of electrons.     

Coherent Cooper pair tunneling in systems of Josephson junctions: Effects of quasiparticle tunneling and of the electromagnetic environment

Small capacitance tunnel junctions show single electron effects and, in the superconducting state, the coherent tunneling of Cooper pairs. We study these effects in a system of two Josephson junctions, driven by a voltage source with a finite impedance. Novel features show up in theI?V characteristics, in particular pronounced structures at subgap voltages. These are due to Cooper pair tunneling, combined with tunneling of quasiparticles or with excitation of the electromagnetic environment.     

Intrinsic tunnelling effects in self-doped La0.89MnO3 single crystals

Transport properties of self-doped La_0.89MnO₃ single crystals with Néel temperature of T_N ≈139 K have been investigated in wide temperature range 10–300 K. Data suggests that current at low temperature is conducted through a strongly temperature-dependent, but almost bias independent channel operating in parallel with a bias controlled but temperature independent channel. The first channel is associated with transport across an insulating antiferromagnetic matrix while the latter one represents tunnel conductivity through intrinsic tunnel junctions appearing due to interruption of conducting percolating paths by phase separated insulating inclusions. Tunnel character of the conductivity manifests itself in nonlinear current-voltage characteristics and appearance of a zero-bias anomaly in the form of a prominent conductance peak in the vicinity of zero bias. Zero bias anomaly and V-shaped characteristics of the differential conductance at high voltages are ascribed to the formation of local magnetic states in the insulating region of the tunneling junction.     

Tunneling through narrow-gap semiconductor Sb2Te3 barrier

Tunnel experiments have been performed on Au/Sb₂Te₃/Al tunnel junctions to study elastic interelectrode tunneling through the small energy gap of a narrow-gap semiconductor. Tunnel conductance exhibited narrow width conductance peak at zero bias voltage. This behaviour is in accordance with the result of the theoretically calculated tunnel conductance, in which the nonparabolic dispersion relation within the energy gap of the narrow-gap semiconductor used as a tunnel barrier in a metal/narrow-gap semiconductor/metal tunnel structure is included. And some interesting structures are also observed in the conductance curves.     

Conductance anomalies of small tunnel junctions inside the Coulomb gap

A small-capacitance normal tunnel deviates significantly from equilibrium because each tunneling event turns the junction voltage almost upside-down. If such a sudden perturbation occurs locally, Fermi liquid theory guarantees that infinitely many electron-hole pairs should be created near the Fermi surface. It is predicted that such an infrared-divergent shake-up combined with the electromagnetic environment leads to subgap conductance anomalies for two categories of junctions. For symmetric junctions whose electrodes have the same electronic properties, a nonvanishing subgap conductance is shown to be inevitable even if the environmental impedance is infinite. This effect smoothes the current-voltage (I–V) characteristic and shifts the Coulomb offset extrapolated back from the high-voltage part of theI–V curve. For asymmetric junctions, whose electrodes have different electronic affinities, tunneling conductance is enhanced in one direction and suppressed in the other; that is, the junctions exhibit a diode effect. In particular, when the tunneling resistance is much smaller than the resistance quantum and the current flows in the favorable direction, a strong tendency towards establishing phase coherence is shown to emerge, as in Josephson junctions, resulting in infinite differential conductance at zero bias voltage.     

Quasiparticle and Cooper pair tenneling in small capacitance Josephson junctions

The tunneling of single electrons in small capacitance tunnel junctions is influenced by charging effects and by the fluctuations of the elecromagnetic environment. We study the effect of an external circuit with arbitrary impedance on the tunneling of quasiparticles and Cooper pairs in voltage driven Josephson junctions. We present results at finite temperatures and also consider an acdriven system.     

Energy-exchange processes by tunneling electrons

Resistive heating, emission heating or cooling (e.g., the Nottingham effect), and thermal fluctuation radiation are examples of energy exchange processes which are fundamental in electron field emission and in tunneling junctions of scanning tunneling microscopy. These exchange processes are analyzed for both electronic tunneling processes. We first discuss the energy delivered by a monoatomic tip in the field emission process. Strong phonon excitation is expected for field emission currents exceeding 1 nA. Secondly we present a theoretical calculation of the thermal deposition associated with the Nottingham effect in a tunneling junction. The calculation is based on the free electron model for the electrode materials and the tunneling process across a planar vacuum gap. Our results show that the thermal power is deposited not only at the electron receiving electrode but also at the emitting electrode. This originates from a finite probability for electrons below the Fermi level to tunnel through the tunneling barrier replaced by electrons starting from the Fermi level. The comparison between the calculations and the recent STM measurements is given. Finally we discuss the other energy exchange processes in the tunneling junction, and conclude that the thermal coupling between the tip and the sample of STM is extremely small under UHV conditions. This is important for high temperature STM.     

Effect of spin-flip scattering on electrical transport in magnetic tunnel junctions

By means of the nonequilibrium Green function technique, the effect of spin-flip scatterings on the spin-dependent electrical transport in ferromagnet–insulator–ferromagnet (FM–I–FM) tunnel junctions is investigated. It is shown that Jullière's formula for the tunnel conductance must be modified when including the contribution from the spin-flip scatterings. It is found that the spin-flip scatterings could lead to an angular shift of the tunnel conductance, giving rise to the junction resistance not being the largest when the orientations of magnetizations in the two FM electrodes are antiparallel, which may offer an alternative explanation for such a phenomenon observed previously in experiments in some FM–I–FM junctions. The spin-flip assisted tunneling is also observed.     

Flux-dependent transport through an Aharonov-Bohm interferometer with embedded multiple coupled quantum dots

The electron transport through an Aharonov-Bohm (AB) interferometer with embedded four coupled quantum dots (QDs) is studied with the Green's function technique. The QDs are coupled to each other by the hopping integral tc. Two among them connect with the left lead and the other two with the right lead by the tunneling matrix element T which incorporates the effects of the applied magnetic field φ. The linear conductance spectra swap between the molecular levels and the atomic states by adjusting tc and T. Fano effect appears when the electrons tunnel through different channels contributed by different QDs energy levels, and the Fano resonance peaks split for large tc. The Fano factor can be manipulated by tc, T, φ, and the QD energy levels.     

A comparison of barrier type tunnel junction and point contact tunnel junction formed on the same highT c material

By making a combination of both point contact and barrier type tunnel junctions on a single sample of the highT _c superconductor BSCCO (2212) single crystal, we have shown that as the tunneling tip is slowly retracted from the surface a point contact junction gradually evolves from a N-S short to a high resistance tunnel junction. The scaled dynamic conductance (dI/dV) of this point contact tunnel junction becomes almost identical to that of a conventional barrier type tunnel junction and both show a linear dI/dV —V curve. The observation implies that at high resistance a point contact junction behaves in the same way as a barrier type tunnel junction. We suggested that the almost linear tunneling conductance obtained in both the cases most likely arises due to an intrinsic characteristic of the surface of the crystal comprising of a mosaic of superconducting regions of the order of a few nanometers. We also conclude that the barrierless (N-S) point contact obtained by piercing the surface oxide layer of the crystal shows Andreev reflection which we suggest as the origin of the zero bias anomaly often observed in point contact junctions.     

Coulomb blockade in single tunnel-junctions: Quantum mechanical effects of the electromagnetic environment

We discuss the interaction of a tunneling electron with its equilibrium electromagnetic environment. The environment of an isolated tunnel junction is modeled by a set of harmonic oscillators that are suddenly displaced when an electron tunnels across the junction. We treat these displaced oscillators quantum mechanically, predicting behavior that is very different than that predicted by a semiclassical treatment. In particular, the shape of the zero-bias anomaly caused by the Coulomb blockade (a single-electron charging effect), is found to be strongly dependent on the impedance,Z (), of the leads connected to the junction. Comparison with three recent experiments demonstrates that the quantum mechanical treatment of this model correctly describes the essential physics in these systems.     

Andreev reflection in a quantum dot coupled to ferromagnetic and superconductor leads under magnetic fields

By employing the nonequilibrium Green's function, we investigate the spin-dependent linear Andreev reflection (AR) resonant tunneling through a quantum dot connected to a ferromagnetic lead and a superconducting lead, where the magnetization direction in the ferromagnetic lead can be tuned by one. We focus our attention on the effects of the magnetic fields on the AR conductance. One high conductance peak and one low conductance peak are developed in the linear AR conductance when a stronger magnetic field is considered. The interplay between the spin-flip scattering and the magnetic fields on the AR conductance are also studied.     

Resonance split of ballistic conductance peaks in electric and magnetic superlattices

Resonant peak splitting for ballistic conductance in finite electric superlattices (ES) and magnetic superlattices (MS) was investigated theoretically. It is shown that, for electron tunneling through the ES (MS) of identical n electric (magnetic) barriers, the resonance split of the conductance peak is (n–1)-fold; while for electron tunneling through the ES (MS) made of two different barriers, one resonant window of the former splits into two subwindows, within each of which the resonance split is (m–1)-fold, where m is the number of the renormalized building blocks consisting of two different barriers of the latter. Received 15 February 2000     

Coulomb blockade of proximity effect at large conductance

We consider the proximity effect in a normal dot coupled to a bulk superconducting reservoir by the tunnel contact with large normal conductance. Coulomb interaction in the dot suppresses the proximity minigap induced in the normal part of the system. We find exact expressions for the thermodynamic and tunneling minigaps as functions of the junction's capacitance. The tunneling minigap interpolates between its proximity-induced value in the regime of weak Coulomb interaction to the Coulomb gap in the regime of strong interaction. In the intermediate case a nonuniversal two-step structure of the tunneling density of states is predicted. The charge quantization in the dot is also studied.     

Evidence for direct and indirect gap in FeSi from electron tunneling spectroscopy

We report electron tunneling spectroscopy studies on single crystalline FeSi sample performed for the case of homogeneous tunnel junction (TJ) contacts and for the case of counter electrodes made from Pt-Rh alloy. Our results reveal that while the tunneling spectroscopy in the configuration with Pt-Rh tip is preferably sensitive to the d-partial density of states (DOS) and to the indirect energy gap, the FeSi-FeSi type of TJ yields spectroscopic information on the c-partial DOS and on the direct gap in FeSi.     

Transmission resonances in magnetic-barrier structures

Quantum transport properties of electrons in simple magnetic-barrier (MB) structures and in finite MB superlattices are investigated in detail. It is shown that there exists a transition of transmission resonances, i.e., from incomplete transmission resonances in simple MB structures consisting of unidentical blocks, to complete transmission resonances in comparatively complex MB structures (, n is the number of barriers). In simple unidentical block arrangements in double- and triple-MB structures we can also obtain complete transmission by properly adjusting parameters of the building blocks according to k_y-value (k_y is the wave vector in y direction). Strong suppression of the transmission and of the conductance is found in MB superlattices which are periodic arrangements of two different blocks. The resonance splitting effect in finite MB superlattices is examined. It is confirmed that the rule (i.e., for n-barrier tunneling the splitting would be (n-1)-fold) obtained in periodic electric superlattices can be extended to periodically arranged MB superlattices of identical blocks through which electrons with tunnel, and it is no longer proper for electrons with k _y <0 to tunnel. Received: 18 August 1997 / Revised: 20 September 1997 / Accepted: 13 October 1997     

c-axis tunneling on YBCO films

We have measured I(V) characteristics of c-axis planar tunnel junctions on Y₁Ba₂Cu₃O _{7 - δ} films. Our results and their analysis provide experimental support for the importance of the two-dimensional character of the YBCO band structure, and a method to measure the ratio between the Fermi energy of YBCO and the barrier height. The analysis is based on the relation between the linear conductance background, related to the inelastic tunneling component, and the zero bias conductance, related to the elastic one. Received 24 September 2000 and Received in final form 15 November 2000     

Single Cooper pair pump

We have operated a Cooper pair pump, a linear array of superconducting tunnel junctions in which single Cooper pairs are moved under the influence of ac signals applied to two gate electrodes. The pump is based on the Coulomb blockade of charge tunneling. Because of the small junction capacitance precisely one Cooper pair is transferred per ac cycle. The current-voltage characteristics of this device show current plateaus close to 2ef, wheref is the frequency of the ac voltages. Deviations are explained in terms of Zener tunneling, Cooper pair co-tunneling, and sporadic quasiparticle tunneling.     

Effect of the electromagnetic environment on the single electron transistor

The influence of envirommental impedances on tunneling rates in a single electron transistor circuit is investigated. Effects of the finite gate capacitance and of stray capacitances at the tunnel junctions are considered. For the case of a low impedance environment the electron tunneling rates reduce to the so-called global rule rate while for a high impedance environment a modification of the so-called local rule rate arises from the stray capacitances. Special emphasis is given to the dependence of the current on the gate voltage which determines the sensitivity of electrometers based on the transistor setup. It is found that a higher sensitivity of the electrometer can be achieved by means of asymmetric transistors.