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.     

Acoustic tunneling through artificial structures: From phononic crystals to acoustic metamaterials

We present a comparative study on the acoustic tunneling through artificial periodical composites, from phononic crystals to acoustic metamaterials. We find that the features of the acoustic tunneling are closely related with the origins of band gaps. In particular, the band gap associated with the negative effective material parameter in the metamaterial results in a better analog of the tunneling effect to the quantum system.     

Fano-type spin-flip mesoscopic transport through an Aharonov-Bohm interferometer

We have investigated the mesoscopic transport properties of a quantum dot embedded Aharonov-Bohm (AB) interferometer applied with a rotating magnetic field. The spin-flip effect is induced by the rotating magnetic field, and the tunneling current is sensitive to the spin-flip effect. The spin-flipped electrons tunneling from the direct channel and the resonant channel interfere with each other to form spin-polarized tunneling current components. The non-resonant tunneling (direct transmission) strength and the AB phase φ play important roles. When the non-resonant tunneling (background transmission) exists, the spin and charge currents form asymmetric peaks and valleys, which exhibit Fano-type line shapes by varying the source-drain bias voltage, or gate voltage. The AB oscillations of the spin and charge currents exhibit distinct dependence on the magnetic flux and direct tunneling strength.     

Influence of phonon-associated tunneling rate on transport through a single-molecule transistor

We study the electronic transport through a single-molecule transistor (SMT) by considering the phonon-associated tunneling rate. We find that the electron-phonon interaction (EPI) changes the constant conductivities of the leads into a multi-channel structure of single vibration frequency. This interference of the multi-channel tunneling process results in a bias-dependent tunneling rate and obscures the conductance peaks at large bias voltage. The bias-dependent tunneling rate further causes a remarkable conductivity gap between the chemical potential of the leads (n=0) and the first phonon sideband (n=1). These anomalies are consistent with the experimental observations in transport experiments.     

Interference and dispersion effects on tunneling time

We study the interplay between pulse width, interference and tunneling for a wave packet incident upon a barrier and, within the context of tunneling time, we offer a complementary insight into the origin of the Hartman effect. We find that interference together with momentum spread lower (increase) the transmission (reflection) tunneling time thereby `breaking the symmetry between transmission and reflection times'. But, within the limits of our method, we are unable to confirm that negative tunneling time can be obtained.     

High-resolution magnetic imaging by local tunneling magnetoresistance

We give an overview over our recent efforts of high-resolution magnetic imaging using scanning tunneling microscopy with a ferromagnetic tip. Magnetic sensitivity is obtained on the basis of local tunneling magnetoresistance between a soft magnetic tip and the sample. The magnetisation of the tip is switched periodically with a small coil, leading to variations of the tunneling current due to the tunneling magnetoresistance effect. These variations are detected with a lock-in amplifier to separate spin-dependent parts from the topographic parts of the tunneling current such that the topography and the magnetic structure of the sample can be recorded simultaneously. Crucial for this method is to avoid mechanical vibrations of the tip, that may also lead to variations in the tunneling current. Exemplary studies of polycrystalline Ni and the closure domain pattern of Co(0001) are presented, showing high contrast at acquisition times as low as 3 ms/pixel and a lateral resolution of the order of 1 nm. Further it is demonstrated that besides topography and magnetisation, also local information about the magnetic susceptibility can be obtained. Received: 28 April 2000 / Accepted: 15 May 2000 / Published online: 7 March 2001     

The temperature in Hawking radiation as tunneling

The quasi-classical method of deriving Hawking radiation under the consideration of canonical invariance is investigated. We find that the horizon should be regarded as a two-way barrier and the ingoing amplitude should be calculated according to the negative energy particles tunneling into the black hole because of the whole space–time interchange and thus the standard Hawking temperature is recovered. We also discuss the advantage of the Painlevé coordinates in Hawking radiation as tunneling.     

Tunneling spectroscopy of voltage tunable quantum wires

Resonant tunneling spectroscopy is used to investigate the tuning range for the one-dimensional subband spacing of side-gated quantum wires. We introduce a simplified selective depletion scheme for the implementation of a resonant tunneling device. From the analysis of the differential tunneling conductance obtained for a single-wire device we conclude that the energetic spacing for the one-dimensional subbands can be varied from effectively 0 to about 6 meV. Measurements in magnetic fields directed parallel and perpendicular to the tunnel current confirm the one-dimensional nature of the tunneling processes as well as the order of magnitude of the subband spacing by comparison of the tunneling characteristics with a model calculation that assumes a parabolic confinement.     

Quantum ratchets and quantum heat pumps

Quantum ratchets are Brownian motors in which the quantum dynamics of particles induces qualitatively new behavior. We review a series of experiments in which asymmetric semiconductor devices of sub-micron dimensions are used to study quantum ratchets for electrons. In rocked quantum-dot ratchets electron-wave interference is used to create a non-linear voltage response, leading to a ratchet effect. The direction of the net ratchet current in this type of device can be sensitively controlled by changing one of the following experimental variables: a small external magnetic field, the amplitude of the rocking force, or the Fermi energy. We also describe a tunneling ratchet in which the current direction depends on temperature. In our discussion of the tunneling ratchet we distinguish between three contributions to the non-linear current–voltage characteristics that lead to the ratchet effect: thermal excitation over energy barriers, tunneling through barriers, and wave reflection from barriers. Finally, we discuss the operation of adiabatically rocked tunneling ratchets as heat pumps. Received: 8 February 2002 / Accepted: 11 February 2002 / Published online: 22 April 2002     

Intradot spin-flip Andreev reflection tunneling through a ferromagnet-quantum dot-superconductor system with ac field

We investigate Andreev reflection (AR) tunneling through a ferromagnet-quantum dot-superconductor (F-QD-S) system in the presence of an external ac field. The intradot spin-flip scattering in the QD is involved. Using the nonequilibrium Green function and BCS quasiparticle spectrum for superconductor, time-averaged AR conductance is formulated. The competition between the intradot spin-flip scattering and photon-assisted tunneling dominates the resonant behaviors of the time-averaged AR conductance. For weak intradot spin-flip scattering strengths, the AR conductance shows a series of equal interval resonant levels. However, the single-peak at main resonant level develops into a well-resolved double-peak resonance at a strong intradot spin-flip scattering strength. Remarkable, multiple-photon-assisted tunneling that generates photonic sideband peaks with a variable interval has been found. In addition, the AR conductance-bias voltage characteristic shows a transition between the single-peak to double-peak resonance as the ratio of the two tunneling strengths varies.     

Low-temperature STM/STS studies on boron-doped (1 1 1) diamond films

We have performed scanning tunneling microscopy/spectroscopy (STM/STS) experiments on (1 1 1)-oriented epitaxial films of heavily boron-doped diamond (T_c∼5.4 K). We present that tunneling conductance spectra show temperature-dependent spatial variations. In the low-temperature region (T=0.47 K), the tunneling spectra do not show strong spatial dependence and a superconducting energy gap is observed independent of the surface morphology. In the high-temperature region (T=4.2 K), on the other hand, the tunneling conductance spectra show significant spatial dependence, indicating the inhomogeneous distribution of the superconducting property due to the distribution of boron atoms.     

Tunneling in 2-D quantum dots via quantum adiabatic switching route

We explore the phenomenon of tunneling in single carrier 2-D quantum dot by quantum adiabatic switching route. The confinement in the y-direction is kept harmonic which ensures that tunneling is allowed only along the x-direction. The harmonic confinement potential is kept fixed and a constant external magnetic field is applied along the z-direction. The growth of probability density in the classically forbidden zones and tunneling current are monitored critically which reveals how tunneling significantly depends on the barrier parameters. The efficacy of the switching function in enforcing adiabaticity of the evolution is demonstrated. The effective mass, barrier width, and height emerge as important control parameters.     

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.     

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     

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     

The effect of non-constant effective tunneling mass and asymmetry for resonant tunneling in double-barrier structures

We discuss the transmission coefficient τ_d in non-repetitive, one-dimensional, rectangular double-barrier structures without simplifications such as strongly attenuating barriers, strong localization, or overall constant effective tunneling mass of the electron. For resonance τ_d=1, we obtain two non-approximative conditions which require different resonance energies of the tunneling electron than previously reported in the literature. In fact, the resonance peaks are shifted to higher energy levels in the order of the width of the peaks due to the effect of non-constant tunneling mass. We investigate the dependence of the resonance condition and the shape of the resonance peaks in regard to perturbation of the electron energy, the gap width as well as the barrier width and height. Resonance is stable for variation of the barrier width but sensitive for variation of the barrier height and the gap width. Received: 9 December 1998 / Accepted: 5 January 1999 / Published online: 31 March 1999     

Carrier-envelope phase-dependent electron tunneling in a coupled double-quantum-dot system driven by a few-cycle laser pulse

We theoretically investigate the dependence of the electron tunneling on the carrier-envelope phase of a few-cycle laser pulse in a coupled double-quantum-dot system, and we show that the electron tunneling between coupled quantum dots is very sensitive to the carrier-envelope phase under a change of the parameters of the system. This in turn provides an additional means to measure the carrier-envelope phase of a laser pulse at lower laser intensity regime in the solid-state nanostructure.     

Numerical analysis of gate leakage current in AlGaN Schottky diodes

We studied theoretically the influence of the tunneling current on the leakage current in AlGaN Schottky diodes. It is shown that the most important conductance mechanism in these structures is the tunneling. The thermionic emission has lower influence on the total current practically throughout the whole reverse bias range and doping concentrations studied. For high doping concentrations we found very slow temperature dependence of the diode current.     

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     

Next-nearest-neighbor-tunneling-induced symmetry breaking of Hofstadter's butterfly spectrum for ultracold atoms on the honeycomb lattice

We study the spectrum of ultracold atoms on the honeycomb lattice under a constant effective magnetic field. In the tight-binding approximation, we derived the generalized Harper's equations and numerically calculate the spectrum, which has a fractal structure. For the cases with and without the next-nearest-neighbor tunneling, the graphs of spectra have different symmetries. Comparing the symmetries of the graphs of spectra, we find that next-nearest-neighbor tunneling induces symmetry breaking of the graph of spectrum.