Quantum nature of proton transferring across one-dimensional potential fields

Proton transfer plays a key role in the applications of advanced energy materials as well as in the functionalities of biological systems.In this work,based on the transfer matrix method,we study the quantum effects of proton transfer in a series of one-dimensional(1 D) model potentials and numerically calculate the quantum probability of transferring across single and double barriers(wells).In the case of single barriers,when the incident energies of protons are above the barrier height,the quantum oscillations in the transmission coefficients depend on the geometric shape of the barriers.It is found that atomic resonant tunneling(ART) not only presents in the rectangular single well and rectangular double barriers as expected,but also exists in the other types of potential wells and double barriers.For hetero-structured double barriers,there is no resonant tunneling in the classical forbidden zone,i.e.,in the case when the incident energy(E_i) is lower than the barrier height(E_b).Furthermore,we have provided generalized analysis on the characteristics of transmission coefficients of hetero-structured rectangular double barriers.     

N重方势垒结构共振隧道效应研究

本文从理论上研究了N重方势垒结构的共振隧道效应,推导出透射系数及共振隧道条件的解析表达式,结果发现,由于多势垒结构(n≥3)量子阱间的耦合,共振能级不同于量子阱的本征值。此外,由透射系数表示式证实了多势垒结构电子透射谱在共振能级附近为Lorentzian型。所得结果对于分析透射系数随能量的变化关系,估计共振能级以及制造共振隧道器件都具有十分重要的意义。 关键词：     

Dynamics of electrons in gradient nanostructures (exactly solvable model)

A flexible multi-parameter exactly solvable model of potential profile, containing an arbitrary number of continuous smoothly shaped barriers and wells, both equal or unequal, characterized by finite values and continuous profiles of the potential and of its gradient, is presented. We demonstrate an influence of both gradient and curvature of these potentials on the electron transport and spectra of symmetric and asymmetric double-well (DW) potentials. The use of this model is simplified due to one to one correspondence between the algorithms of calculation of the transmittance of convex barriers and energy spectra of concave wells. We have shown that the resonant contrast between maximum and minimum in over-barrier reflectivity of curvilinear barrier exceeds significantly the analogous effect for rectangular barrier with the same height and width. Reflectionless tunneling of electrons below the bottom of gradient nanostructures forming concave potential barriers is considered. The analogy between dynamics of electrons in gradient fields and gradient optics of heterogeneous photonic barriers is illustrated.     

Spin-polarized tunneling in a ferromagnetic graphene junction: Interplay between the exchange interaction and the orbital effect of the magnetic field

The influence of magnetic vector potential barrier (MVPB) on the spin-polarized transport of massless Dirac particles in ferromagnetic graphene is studied theoretically. The phenomenon of Klein tunneling of relativistic particles across a rectangular potential barrier prevents any of the massless fermions from being confined but they can be electrically confined by quantum dots with integrable dynamics (Bardarson et al., 2009) [36]. Utilization of only the in-plane exchange splitting in the ferromagnetic graphene cannot produce 100% spin polarization. This tunneling can be confined using the magnetic vector potential barrier, which leads to high degree of spin polarization. By combining the orbital effect and the Zeeman interaction in graphene junction, it is found that the junction mimics behavior of half-metallic tunneling junction, in which it acts as a metal to particles of one spin orientation but as an insulator or a semiconductor to those of the opposite orientation. The idea of the half-metallic tunneling junction can provide a source of ∼100% spin-polarized current, which is potentially very useful. Adjustment of the position of the Fermi level in ferromagnetic layer by placing a gate voltage on top of the ferromagnetic layer shows that reverse of the orientation of the completely spin-polarized current passing through the junction is controlled by adjusting the gate voltage. These interesting characteristics should lead to a practical gate voltage controlled spin filtering and spin-polarized switching devices as a perfect spin-polarized electron source for graphene-based spintronics.     

Particle tunneling and scattering in a three-dimensional potential with a barrier

The particle tunneling through a 3-D rectangular potential barrier has been studied. The simplest model for multiple internal reflections has been assumed. The explicit expression for all the transmission and reflection probability amplitudes have been derived, as well as the tunneling and reflection phase times.      

Generalization of Büttiker-Landauer characteristic barrier interaction times to an arbitrary point within a barrier

Using a variety of approaches, Büttiker and Landauer have derived characteristic barrier interaction times for the transmission of particles completely across a rectangular potential barrier. We propose a generalization of these characteristic times to any point within an arbitrary barrier and present calculated results for a rectangular barrier with and without a multiple image potential correction.     

压缩应变载荷下氮化镓隧道结微观压电特性及其巨压电电阻效应

电子器件可控性研究在日益追求器件智能化和可控化的当今社会至关重要. 基于第一性原理和量子输运计算, 本文研究了压缩应变载荷对氮化镓(GaN)隧道结基态电学性质和电流输运的影响, 在原子尺度上窥视了氮化镓隧道结的微观压电性, 验证了其内在的巨压电电阻(GPR)效应. 计算结果表明, 压缩应变载荷可以调节隧道结内氮化镓势垒层的电势能降、内建电场、电荷密度和极化强度, 进而实现对隧道结电流输运和隧穿电阻的调控. 在-1.0 V的偏置电压下, -5%的压缩应变载荷将使氮化镓隧道结的隧穿电阻增至4倍. 本研究展现了氮化镓隧道结在可控电子器件中的应用潜力, 也展现了应变工程在调控电子器件性能方面的光明前景.     

Quantum scattering in one-dimensional systems satisfying the minimal length uncertainty relation

In quantum gravity theories, when the scattering energy is comparable to the Planck energy the Heisenberg uncertainty principle breaks down and is replaced by the minimal length uncertainty relation. In this paper, the consequences of the minimal length uncertainty relation on one-dimensional quantum scattering are studied using an approach involving a recently proposed second-order differential equation. An exact analytical expression for the tunneling probability through a locally-periodic rectangular potential barrier system is obtained. Results show that the existence of a non-zero minimal length uncertainty tends to shift the resonant tunneling energies to the positive direction. Scattering through a locally-periodic potential composed of double-rectangular potential barriers shows that the first band of resonant tunneling energies widens for minimal length cases when the double-rectangular potential barrier is symmetric but narrows down when the double-rectangular potential barrier is asymmetric. A numerical solution which exploits the use of Wronskians is used to calculate the transmission probabilities through the Pöschl–Teller well, Gaussian barrier, and double-Gaussian barrier. Results show that the probability of passage through the Pöschl–Teller well and Gaussian barrier is smaller in the minimal length cases compared to the non-minimal length case. For the double-Gaussian barrier, the probability of passage for energies that are more positive than the resonant tunneling energy is larger in the minimal length cases compared to the non-minimal length case. The approach is exact and applicable to many types of scattering potential.     

Magnetic-field-dependent excitation transfer in quantum wells of diluted magnetic semiconductor

We studied the excitation transfer in double quantum wells of a diluted magnetic semiconductor using a scanning near-field optical microscope at 7 K in external magnetic fields up to 9 T. In each quantum well, local energy minima are generated by local fluctuation of layer thickness and doping concentration of magnetic components. Excitons relax into the local energy minima and transfer between the minima via near-field optical interactions even across quantum wells toward stable sites at which to localize. We measured the intensity maps of near-field photoluminescence with spatial resolution estimated to be 30 nm under varying external magnetic fields. The measurement position reproducibility was confirmed by scanning tunneling microscope images. Analysis of the maps derived the magnetic-field dependence of the typical size of exciton-localization sites for each quantum well. Based on these results, we investigated the excitation transfer between the two quantum wells lying in different layers of the double quantum well system, and showed that the exciton transfer takes place at the two specific applied magnetic-field intensities that result in the crossing of Zeeman-split energy levels of the two different wells. We concluded that both the localization and the inter-quantum-well transfer of excitons are able to be controlled by an external magnetic field. This provides the basis for functional devices operating without any wiring.     

Tunneling of electrons in quantum wells with indirect gap semiconductor barriers

One of the features peculiar to GaAs-Ga_1−xAl_x As quantum wells with x ⩾0.43 are barriers formed by an indirect gap semiconductor. We make use of a simple one-dimensional tight-binding model to study the tunneling properties of such a system. Wave-functions and probabilities associated with an electron in each spatial region as a function of time are computed and compared with the results of a simple square barrier model. It is shown that the states related to the indirect conduction band minima of the barrier act as a new channel and increase the tunneling current between the wells. We suggest that these states are the origin of an unexplained structure observed in photoemission from a double quantum well. The effect of an external electric field is analyzed as well.     

Effective classical stochastic theory for quantum tunneling

The ensemble mean equations for a classical particle moving stochastically obtain the form of fluid equations. When applying the Madelung transformation to write the Schrödinger equation in a fluid-like form we find that the equations are equivalent to the classical ensemble mean equations if an additional force is added to the equations. The latter can be expressed as a pressure gradient force of a fluctuating pressure with zero mean. Here we analyze the mechanism of quantum tunneling through a rectangular potential barrier from this perspective. We find that despite of the vanishing of the mean of the pressure fluctuations their local non zero gradients enable the tunneling by balancing the counter external potential gradients at the two sides of the potential barrier. Consequently, for stationary solutions, the ensemble mean kinetic energy remains unchanged across the boundaries of the barrier.     

About some optical properties of AlxGa1−xN /GaN quantum wells grown by molecular beam epitaxy

Wurtzitic nitride quantum wells grown along the (0001) axis experience a large Stark effect induced by the differences of spontaneous and piezoelectric polarizations between the well and barrier materials. In Al_xGa_1−xN/GaN quantum wells, due to the adverse actions of quantum confinement, that blue-shifts transition energies, and of the Stark field, that red-shifts them, the transition energies are nearly independent of barrier compositions at a particular well thickness (L₀2.6 nm), at least for x≤0.3. The effect of alloy fluctuations is then minimal, as reflected by a minimum in the quantum well luminescence linewidth when LL₀ for wells grown by molecular beam epitaxy on silicon or sapphire substrates. We use this effect to estimate the average variances of well widths and alloy composition fluctuations. Both results are in good agreement with, respectively, a scanning tunneling microscopy study of GaN (0001) surfaces, and estimates based on the lateral extent of the quantum well excitons.We then discuss the optical properties of the Al_xGa_1−xN barrier material, with particular emphasis on the symmetry of the valence band maximum (Γ₉ or Γ₇). We show that it may play an important role in the apparent barrier luminescence efficiency. We analyse the possible consequences of the barrier Γ₉–Γ₇ crossover on the Al_xGa_1−xN/GaN quantum well properties.     

Quantum conductance through a uniform scatterer in a narrow-wire semiconductor

The quantum conductance for electrons scattering from a uniform scatterer in a narrow-wire semiconductor is calculated. Instead of getting the conductance directly from the calculation of transmission coefficient, we calculate the reflection coefficient instead. The transmission coefficient is then calculated by using the conservation law, T=I−R. This alternative method can avoid the instability of the conductance obtained by including more evanescent modes for a finite-range scatterer in a narrow-wire semiconductor. This method is applied to a semi-infinite strip potential barrier and a rectangular potential barrier in a narrow wire. The quantum stepwise conductance is obtained in both cases. For a repulsive rectangular potential barrier, there are oscillations in each stepwise conductance. For an attractive rectangular potential barrier, there exist multiple quasi-bound states below the sub-band energies which can cause the drop of the quantum conductance. The effect of the continuum quasi-bound states diminishes as the energy of the incident electron increases, but the influence of the discrete quasi-bound states still persists.     

Tunneling through a time-dependent barrier — a numerical study

We present a numerical investigation of quantum mechanical tunneling process in a double well potential with fluctuating barrier. The tunneling probability and rate are calculated for two cases in which (i) the height of the barrier is undergoing harmonic oscillation with frequency θ and (ii) the height of the barrier is undergoing random fluctuation with frequency θ. It is observed that in both cases, the quantum mechanical tunneling probability and rate exhibit a maximum as a function of the fluctuation frequency. The optimal frequency i.e. the frequency at which rate exhibits a maximum shows a strong isotopic mass effect.     

Total transparency in quantum tunneling of counterpropagating waves

The problem of quantum tunneling is considered for matter waves which are impinging on the potential barrier from both sides. Possibility of the total transmission of one of incident waves at the simultaneous total reflection of the other one is studied. The analysis is carried out for two essentially different, rectangular and bell-shaped, forms of the potential barrier.     

Resonance tunneling in double-well billiards with a point-like scatterer

Coherent tunneling is investigated in rectangular billiards divided into two domains by a classically unclimbable potential barrier. We show that by placing a point-like scatterer inside the billiard, we can control the occurrence and the resonance tunneling rate. The key role of the avoided crossing is stressed.     

Electron tunneling effects on radiative recombination in modulation n-doped ZnSe/BeTe type-II quantum wells

We have studied the cyclotron-resonance absorption and photoluminescence properties of the modulation n-doped ZnSe/BeTe/ZnSe type-II quantum wells.It is shown that only the doped sample shows electron cyclotron-resonance absorption.Also,the undoped sample shows two distinctive peaks in the spatially indirect photoluminescence spectra,and the doped one shows only one peak.The results reveal that the high concentration electrons accumulated in ZnSe quantum well layers from n-doped layers can tunnel through BeTe barrier from one well layer to the other.The electron concentration difference between these two well layers originating from the tunneling results in a new additional electric field,and can cancel out a built-in electric field as observed in the undoped structures.     

Bistable charge states in a photoexcited quasi-two-dimensional electron-hole system

The luminescence spectra of GaAs/AlGaAs quantum wells (QWs) with low-density quasi-two-dimensional electron and hole channels were studied. It was demonstrated that, at temperatures below some critical value (T _c ～30 K) and for an excitation power lying in a certain temperature-dependent range, two metastable charge states with two-dimensional charge densities differing in both magnitude and sign can occur in the system under the same conditions. The obtained experimental data agree well with the mathematical model allowing for the transfer of photoexcited carriers to the barrier followed by their tunneling into QW.     

Picosecond luminescence of AlxGa1-xAs and GaAs double quantum well structures under high pressure

Abstract

The time-resolved luminescence of an electron-hole plasma in Al_0.36Ga_0.64As was studied as a function of pressure. Application of hydrostatic pressure varies the energy separation between the conduction band minima at Г and X. The dependence of the intensity ratio of the zero-phonon line and the two phonon replicas on this energy separation shows that scattering from X to Г by alloy disorder is as effective as scattering by phonons. We have further studied the tunneling of electrons between two GaAs quantum wells (QW) of different thicknesses through an Al_0.35Ga_0.65As barrier. The lifetime of electrons in the narrow QW, which is limitd by electron tunneling into the wider QW, stays constant from 0 to 2.4 GPa, where it drops within 0.1 GPa from 140 ps to less than 7 ps. At this pressure the X-point energy of the barrier coincides with the electron level in the wider QW. We infer that tunneling occurs only via the Г states in the barrier and that X states become effective only when real-state transfer is possible.     

Ballistic transmission through quasi-periodic shape barrier resonant tunneling structures

A theoretical model is proposed to study the ballistic electron transport for a quasi-periodic multibarrier structure where two different barrier shapes are arranged according to the Thue–Morse sequence. Important tunneling features are revealed form such arrangements. It is noted that the tunneling band spectrum could be fragmented by tailoring the shape of the barriers in the structure. Results for the transmission coefficients and the current densities are compared with the corresponding periodic and single shape barrier arrangements. The quasi-periodic structure consisting of the rectangular and triangular barrier shapes is suggested to be more suitable for the electronic and opto-electronic devices due to its high negative differential conducting effect.