Single electron tunneling at large conductance: The semiclassical approach

We study the linear conductance of single electron devices showing Coulomb blockade phenomena. Our approach is based on a formally exact path integral representation describing electron tunneling nonperturbatively. The electromagnetic environment of the device is treated in terms of the Caldeira-Leggett model. We obtain the linear conductance from the Kubo formula leading to a formally exact expression which is evaluated in the semiclassical limit. Specifically we consider three models. First, the influence of an electromagnetic environment of arbitrary impedance on a single tunnel junction is studied focusing on the limits of large tunneling conductance and high to moderately low temperatures. The predictions are compared with recent experimental data. Second, the conductance of an array of N tunnel junctions is determined in dependence on the length N of the array and the environmental impedance. Finally, we consider a single electron transistor and compare our results for large tunneling conductance with experimental findings. Received 2 February 2000     

Imaging and tunneling spectroscopy of gold nanocrystals and nanocrystal arrays

Scanning tunneling microscopy (STM) and spectroscopy (STS) have been used to determine the structural and electronic properties of thiol-passivated 29000 amu gold nanocrystals, both individually and in spontaneously formed quasi-two-dimensional arrays. Experiments were performed at temperatures of 300 K, 77 K, and 8 K. Even at room temperature, tunneling through these 1.7 nm nanocrystals is shown to give rise to a Coulomb blockade. At cryogenic temperatures, the spectroscopy of the nanocrystals in arrays and in isolation shows an incremental charging effect (the Coulomb staircase) and evidence is found for quantization of the electronic states. Received: 10 September 1998 / Received in final form: 16 February 1999     

Velocity fluctuations of a column of water streaming down a wire: the possibility of one-dimensional turbulence

In this paper we study the influence of the magneto-coupling effect between the longitudinal motion component and the transverse Landau orbits of an electron on transmission features in single barrier structures. Within the parabolic conduction-band approach, a modified one-dimensional effective-mass Schr?dinger equation, including the magneto-coupling effect generated from the position-dependent effective mass of the electron, is strictly derived. Numerical calculations for single barrier structures show that the magneto-coupling effect brings about a series of the important changes for the transmission probability, the above-barrier quasi-bound states, and the tunneling time. Through examining the variation of the above-barrier resonant-transmission spectrum with the barrier width and observing the well-defined Lorentzian line-shape of the above-barrier resonant peaks, we convincingly show that the above-barrier resonant transmission in single barrier structures is delivered by the above-barrier quasibound states in the barrier region, just as the below-barrier resonant tunneling in double barrier structures is mediated by the below-barrier quasi-bound states in the well. Furthermore, we come to the conclusion that the magneto-coupling effect brings about not only the splitting of the above-barrier quasi-bound levels but also the striking reduction of the level-width of the quasi-bound states, correspondingly, the substantial increase of the density of the quasi-bound states. We suggest that magneto-coupling effects may be observed by the measurements of the optical absorption spectrum associated with the above-barrier quasi-bound states in the single barrier structures. Received: 26 September 1997 / Revised: 26 November 1997 / Accepted: 15 December 1997     

Affine turbulence

We present a generalization of the multiplicative model for velocity increments involving an affine process. The consequences on the shape of the probability distribution functions for the velocity increments are explored, and shown to be better compatible with the existence of a scale variation of the skewness. Received 29 March 1999 and Received in final form 14 September 1999     

Tunneling of two interacting electrons in a quantum wire

A model calculation is reported for the tunneling probability of one as well as two interacting electrons from a quantum well within a narrow channel. We discuss the cases when the two electrons are spin polarized or unpolarized by transforming the system to a noninteracting one with the use of quantal density functional theory to obtain an effective single-particle confining potential. A semiclassical approach is used to obtain the tunneling probability from this effective potential. The calculation is motivated by recent measurements of the conductance of an electron gas in a narrow channel but is not meant to explain the anomalous behavior that has been reported since, for example, we deal with a simplified two-level system. Numerical results for the tunneling probability are presented.     

Cavitation in superfluid helium-4 at low temperature

We have studied the nucleation of bubbles in pure superfluid helium-4 at temperatures down to 65 mK. We have found that the nucleation is a stochastic process, and that at temperatures below 600 mK the nucleation rate is independent of temperature. These results are consistent with the assumption that the nucleation takes place via quantum tunneling. Received: 15 November 1997 / Received in final form: 19 December 1997 / Accepted: 22 January 1998     

Plateau transitions in fractional quantum Hall liquids

Effects of backward scattering between fractional quantum Hall (FQH) edge modes are studied. Based on the edge-state picture for hierarchical FQH liquids, we discuss the possibility of the transitions between different plateaux of the tunneling conductance G. We find a selection rule for the sequence which begins with a conductance (m: integer, p: even integer) in units of e ²/h. The shot-noise spectrum as well as the scaling behavior of the tunneling current is calculated explicitly. Received 5 October 1999 and Received in final form 19 November 1999     

Topological phase interference effects in resonant quantum tunneling of the Néel vector between nonequivalent magnetic wells in mesoscopic single-domain antiferromagnets

Resonant quantum tunneling of the Néel vector between nonequivalent magnetic wells is investigated theoretically for a nanometer-scale single-domain antiferromagnet with biaxial crystal symmetry in the presence of an external magnetic field applied along the easy anisotropy axis, based on the two-sublattice model. Both the Wentzel-Kramers-Brillouin exponent and the preexponential factors are evaluated in the instanton contribution to the tunneling rate for finite and zero magnetic fields by applying the instanton technique in the spin-coherent-state path-integral representation, respectively. The quantum interference or spin-parity effects induced by the topological phase term in the Euclidean action are discussed in the rate of quantum tunneling of the Néel vector. In the absence of an external applied magnetic field, the effect of destructive phase interference or topological quenching on resonant quantum tunneling of the Néel vector is evident for the half-integer excess spin antiferromagnetic nanoparticle. In the weak field limit, the tunneling rates are found to oscillate with the external applied magnetic field for both integer and half-integer excess spins. We discuss the experimental condition on the applied magnetic field which may allow one to observe the topological quenching effect for nanometer-scale single-domain antiferromagnets with half-integer excess spins. Tunneling behavior in resonant quantum tunneling of the magnetization vector between nonequivalent magnetic wells is also studied for a nanometer-scale single-domain ferromagnet by applying the similar technique, but in the large noncompensation limit. Received 4 June 1999     

Coherent resonant transport through a mesoscopic system with quantum ac microwave field

The time-dependent transport through an ultrasmall quantum dot coupling to two electron reservoirs is investigated. The quantum dot is perturbed by a quantum microwave field (QMF) through gate. The tunneling current formulae are obtained by taking expectation values over coherent state (CS), and SU(1,1) CS. We derive the transport formulae at low temperature by employing the nonequilibrium Green function technique. The currents exhibit coherent behaviors which are strongly associated with the applied QMF. The time-dependent currents appear compound effects of resonant tunneling and time-oscillating evolution. The time-averaged current and differential conductance are calculated, which manifest photon-assisted behaviors. Numerical calculations reveal the similar properties as those in classical microwave field (CMF) perturbed system for the situations concerning CS and squeezed vacuum SU(1,1) CS. But for other squeezed SU(1,1) CS, the tunneling behavior is quite different from the system perturbed by a single CMF through gate. Due to the quantum signal perturbation, the measurable quantities fluctuate fiercely. Received 28 May 1998     

Electron-phonon scattering in an asymmetric double barrier resonant tunneling structure

We calculate the electron-phonon scattering rate for an asymmetric double barrier resonant tunneling structure based on dielectric continuum theory, including all phonon modes, and show that interface phonons contribute much more to the scattering rate than do bulk-like LO phonons for incident energies which are approximately within an order of magnitude of the Fermi energy. The maximum scattering rate occurs for incident electron energies near the quantum well resonance. Subband nonparabolicity has a significant influence on electron-phonon scattering in these structures. We show that the relaxation time is comparable to the dwell time of electrons in the quantum well for a typical resonant tunneling structure. Received: 23 December 1997 / Revised: 24 March 1998 / Accepted: 9 March 1998     

Comparison of tunneling through molecules with Mott-Hubbard and with dimerization gaps

In order to study the tunneling of electrons through an interacting, 1D, dimerized molecule connected to leads, we consider the persistent current in a ring embedding this molecule. We find numerically that, for spinless fermions, a molecule with a gap mostly due to interactions, i.e. a Mott-Hubbard gap, gives rise to a larger persistent current than a molecule with the same gap, but due only to the dimerization. In both cases, the tunneling current decreases exponentially with the size of the molecule, but more slowly in the interacting case. Implications for molecular electronic are briefly discussed. Received: 17 November 1997 / Revised: 16 January 1998 / Accepted: 16 January 1998     

Thermodynamic properties of small amorphous and crystalline Silica particles at low temperatures

We have measured the low-temperature (K) specific heat and heat release of small amorphous and crystalline SiO₂ particles embedded in Teflon and of Vycor. The temperature and time dependence of these properties have been interpreted in terms of the tunneling model. We found that the particle size influences the density of states of tunneling systems of the composite. The smaller the size of the particles the larger is the density of states of tunneling systems P₀. Quartz grains with dimensions in the micrometer range show similar glass-like properties as vitreous silica. In comparison with bulk vitreous silica, Vycor shows a much larger P₀ in agreement with the behavior we found for small SiO₂ particles. We discuss the implication of our results on the origin of the universal low-temperature properties of glasses. Received 9 April 1998     

The interplay between the surface band structure and possible surface reconstructions of Mo(112)

The experimental band structure of Mo(112) and the effects by temperature and adsorbate are presented. A surface resonance, identified as crossing the Fermi level at about 1/3 from to of surface Brillouin zone, was observed to be very sensitive to both contamination and temperature. We find evidence of adsorbate and temperature induced reconstruction of the Mo(112) surface. Examination of low-energy electron diffraction (LEED) and scanning tunneling microscopy (STM) data provides evidence for an adsorbate induced reconstruction of the Mo(112) surface with periodicities consistent with the Fermi level crossing of the surface resonance. The reconstruction is found to occur at coverages as low as 0.03 Langmuirs of oxygen or carbon. The reconstruction and/or adsorbate affects the density of states and bands near the Fermi level of a ₁ symmetry. Received 3 March 1999 and Received in final form 1 October 1999     

Transport through cavities with tunnel barriers: a semiclassical analysis

We study the influence of a tunnel barrier on the quantum transport through a circular cavity. Our analysis in terms of classical trajectories shows that the semiclassical approaches developed for ballistic transport can be adapted to deal with the case where tunneling is present. Peaks in the Fourier transform of the energy-dependent transmission and reflection spectra exhibit a nonmonotonic behaviour as a function of the barrier height in the quantum mechanical numerical calculations. Semiclassical analysis provides a simple qualitative explanation of this behaviour, as well as a quantitative agreement with the exact calculations. The experimental relevance of the classical trajectories in mesoscopic and microwave systems is discussed. Received: 23 October 1997 / Received in final form and Accepted: 11 March 1998     

Tunneling time in magnetic barrier structures

We adopt the group velocity approach to the issue of tunneling time in two configurations of magnetic barrier structures, which are arranged with identical or unidentical building blocks. The effects of an external electric field are also taken into account. The tunneling time in magnetic barrier structures is found to be strongly dependent on the magnetic configuration, the applied bias, the incident energy as well as the longitudinal wave vector. The results indicate that for electrons with equal energy but different incident angles, the tunneling processes are significantly separated in time within the same magnetic barrier structure. In the configuration arranged with unidentical building blocks, there exists obvious asymmetry of tunneling time in two opposite tunneling directions. Such a discrepancy of the tunneling time varies distinctly with the longitudinal wave vector and the applied bias. Received 4 March 2002 / Received in final form 22 May 2002 Published online 17 September 2002     

Low frequency elastic properties of neutron-irradiated quartz. Comparison with glasses

Neutron-irradiated quartz is a promising model system to learn more about the low-energy excitations (tunneling states) in vitreous silica and in similar glasses. We present the first systematic study of the elastic properties of neutron-irradiated quartz at low frequencies and very low temperatures. Using the vibrating reed technique at frequencies of several kHz we have measured the sound velocity and internal friction of six quartz crystals irradiated with different neutron doses over a wide range of temperatures (7 mK-300 K). The results are analyzed using the tunneling model and several extensions of this theory. Comparisons are made with recent low-frequency measurements on normal and compacted vitreous silica and with ultrasound experiments on neutron-irradiated quartz. Received 23 October 1998     

Rapid communicationPhotoelectron emission in femtosecond laser assisted scanning tunneling microscopy

Direct illumination of the tunneling gap in an ultrahigh vacuum scanning tunneling microscope with ultrashort pump-probe laser pulses may offer ultimate spatial and temporal resolution in surface experiments. The electronic bandwidth of the tunneling gap ( 1 THz) does not limit the time resolution. Our experiments show that multiphoton photoelectron emission from the sample limits the application of this detection scheme at high laser fluence. However, a substrate specific pump-probe effect in the photoelectron yield with femtosecond transients is observed on Tantalum and on GaAs(110) surfaces. Received: 5 November 1996     

Asymmetry and separation of spin tunneling time in ZnSe/Zn1-xMnxSe multilayers

We investigate characteristics of spin tunneling time in ZnSe/Ze_1-xMn_xSe multilayers under the influence of both an electric field and a magnetic field. The results indicate that the tunneling time shows complicated oscillations and significant spin separation for electrons with different spin orientations traversing semimagnetic semiconductor heterostructures. It is also shown that the tunneling time exhibits obvious asymmetry in opposite tunneling directions for electrons tunneling through asymmetric heterostructures, which mainly occurs in resonant regions. The degree of the asymmetry of the tunneling time is not only spin-polarization dependent but also external-field induced. Received 10 July 2001     

The Penna model for biological ageing on a lattice: spatial consequences of child-care

We introduce a square lattice into the Penna bit-string model for biological ageing and study the evolution of the spatial distribution of the population considering different strategies of child-care. Two of the strategies are related to the movements of a whole family on the lattice: in one case the mother cannot move if she has any child younger than a given age, and in the other case if she moves, she brings these young children with her. A stronger condition has also been added to the second case, considering that young children die with a higher probability if their mothers die, this probability decreasing with age. We show that a highly non uniform occupation can be obtained when child-care is considered, even for an uniform initial occupation per site. We also compare the standard survival rate of the model with that obtained when the spacial lattice is considered (without any kind of child-care). Received 30 October 1998 and Received in final form 27 November 1998     

On the probability distributions of relaxation times in glasses

The scale of relaxation times in glasses has led to generalizations of the Drude model of the dielectric function in terms of an integral, containing a Drude kernel and a probability distribution. This integral equation is solved by a Mellin or a Stieltjes transform. Beyond known results, we obtain the probability distribution of the Havriliak-Negami dielectric function. Even more general classes of dielectric models can be dealt with, using Mellin's transform. They may serve as checks for numerical procedures applied to the underlying ill-posed problem, if experimental data for the dielectric function are used. Received: 2 February 1998 / Accepted: 17 March 1998