Tunneling and reflection of an exciton incident upon a quantum heterostructure barrier

We investigate, in one spatial dimension, the quantum mechanical tunneling of an exciton incident upon a heterostructure barrier. We model the relative motion eigenstates of the exciton using a form of the one-dimensional hydrogen atom which avoids difficulties previously associated with 1D hydrogenic states. We obtain probabilities of reflection and transmission using the method of variable transmission and reflection amplitudes. Our calculations may be broadly divided into two sets. In the first set, we consider general qualitative aspects of exciton tunneling, such as the effect of different effective masses for electrons and holes and a relative difference in electron and hole barrier strengths. The second set models the tunneling of an exciton in a GaAs/Al(x)Ga(1-x)As heterostructure. In these calculations we find that, for energies such that the two lowest exciton states are coupled, the probability spectrum for transition from the ground state to the first excited state is identical to that for transition from the first excited state to the ground state. In addition, narrow peaks in the probability spectrum for transition are observed across this energy range for low dopant concentration x. Other interesting phenomena correlated with these peaks in the transition probability are reported.     

Time and energy dependent dynamics of the STM tip — graphene system

Probability current and probability density of wave packets was calculated by solving the three dimensional time-dependent Schrödinger equation for a local potential model of the scanning tunneling microscope (STM) tip — graphene system. Geometrical and electronic structure effects of the three dimensional tunneling process are identified by studying three models of increasing complexity: a jellium half space, a narrow jellium sheet, and a local one electron pseudopotential. It was found that some of the key characteristics of the STM tip — graphene tunneling process are already present at the simple jellium models. In the STM tip — jellium half space system the direction of the momentum does not change during the tunneling event, hence this setup is characterised by introducing an effective distance. For the STM tip — narrow jellium sheet system the direction of the momentum is changed from vertical to horizontal during the tunneling event. The wave packet preferentially tunnels into the bound state of the jellium sheet. For the atomistic model of the graphene sheet an anisotropic spreading of the wave packet was found for hot electrons. This may open new opportunities to build carbon based nanoelectronic devices.     

Elastic and inelastic tunneling of photoelectrons from the dimensional quantization band at a p +-GaAs-(Cs,O) interface into vacuum

The photoemission of electrons from a p ⁺-GaAs surface with negative electron affinity was studied experimentally at 4.2 K. A narrow peak and its phonon replicas were observed in the distribution of emitted electrons over the energies of longitudinal motion. These replicas are caused by elastic and inelastic electron tunneling from the bottom of the dimensional quantization band in the near-surface spatial-charge region through the potential barrier of the (Cs,O) activating coverage with emission of LO phonons. The measured position of the peak corresponding to elastically tunneling electrons is close to the calculated one.     

The geometric potential of a double-frequency corrugated surface

For an electron confined to a surface reconstructed by double-frequency corrugations, we give the effective Hamiltonian by the formula of geometric influences, obtain an additive scalar potential induced by curvature that consists of attractive wells with different depth. The difference is generated by the multiple frequency of the double-frequency corrugation. Subsequently, we investigate the effects of geometric potential on the transmission probability, and find the resonant tunneling peaks becoming rapidly sharper and the transmission gaps being substantially widened with increasing the multiple frequency. As a potential application, double-frequency corrugations can be employed to select electrons with particular incident energy, as an electronic switch, which are more effective than a single-frequency ones.     

A theoretical calculation of tunneling spectroscopy of an electron waveguide with or without a scatterer

A theoretical study on the tunneling spectroscopy of an electron waveguide recently observed by Eugster and del Alamo is presented. A narrow electron waveguide coupled with another much wider one by a thin barrier between them is taken as a theoretical model for the leaky electron waveguide implemented by Eugster et al., and the transport properties of electrons are studied comprehensively through the wavefunction of the system. The results demonstrate that the conductance for the current tunneling out the barrier oscillates strongly with the width of the narrow electron waveguide, in line with its conductance steps. The theory is in good agreement with the experiments and confirm that the oscillations of the tunneling current can be considered as a spectroscopy of the 1D DOS (one dimensional electron density of states) in the electron waveguide as proposed by Eugster et al. In order to study the effects of scatterers on the transport properties of the leaky electron waveguide, a δ-function is used to simulate the scattering potential The results show that the presence of even a single scatterer located in the waveguide will lead to obvious distortion of the shape of conductance steps, and will greatly influence the oscillations of the tunneling current observed in clean waveguides. However the effects of scatterers located outside the tunneling barrier on either the conductance steps or the oscillations of the tunneling current are negligible.     

The effects of two-dimensional bifurcations and quantum beats in a system of combined atomic force and scanning tunneling microscopes with quantum dots

The field and temperature dependence of the probability of two-dimensional dissipative tunneling is studied in the framework of one-instanton approximation for a model double-well oscillator potential in an external electric field at finite temperature with account for the influence of two local phonon modes for quantum dots in a system of a combined atomic force and a scanning tunneling microscope. It is demonstrated that in the mode of synchronous parallel transfer of tunneling particles from the cantilever tip to the quantum dot the two local phonon modes result in the occurrence of two stable peaks in the curve of the 2D dissipative tunneling probability as a function of the field. Qualitative comparison of the theoretical curve in the limit of weak dissociation and the experimental current–voltage characteristic for quantum dots that grow from colloidal gold under a cantilever tip at the initial stage of quantum-dot formation when the quantum dot size does not exceed 10 nm is performed. It is established that one of the two stable peaks that correspond to interaction of tunneling particles with two local phonon modes in the temperature dependence of the 2D dissipative tunneling probability can be split in two, which corresponds to the tunneling channel interference mechanism. It is found that the theoretically predicted and experimentally observed mode of quantum beats occurs near the bifurcation point.     

Controlled dephasing of a quantum dot: from coherent to sequential tunneling

Resonant tunneling through two identical potential barriers renders them transparent, as particle trajectories interfere coherently. Here we realize resonant tunneling in a quantum dot (QD), and show that detection of electron trajectories renders the dot nearly insulating. Measurements were made in the integer quantum Hall regime, with the tunneling electrons in an inner edge channel coupled to detector electrons in a neighboring outer channel, which was partitioned. Quantitative analysis indicates that just a few detector electrons completely dephase the QD.     

Resonant tunneling condition and transmission coefficient in a symmetrical one-dimensional rectangular double-barrier system

The resonant tunneling condition and transmission coefficient are derived theoretically for a symmetrical one-dimensional rectangular double-barrier structure under the assumption of the tunneling effective mass. They are given in analytical form, which has been overlooked. The energy variation of the transmission coefficient of electrons is shown for an ABABA-type and an ABCBA-type potential cases.     

Theoretical aspects of electron transport in modulated structures

In the theory of transport in modulated structures we have studied both transport perpendicular and parallel to the heterojunction interfaces. In perpendicular transport we have investigated models for tunneling through double barriers and find that resonant tunneling and sequential tunneling lead to the same expression for the current as long as the width of the energy distribution of the injected electrons is larger than the width of the resonant level in the diode. We present results for phonon assisted tunneling between two wells in a model which remains valid even when the barrier shrinks and the tunneling probability becomes very high. In parallel transport we show that very satisfactory agreement with extensive measurements of the mobility in modulation doped structures in the whole temperature range from 4 K to 300 K can be obtained if one takes into account the complete quasi-two-dimensional subband structure and all the relevant scattering mechanisms. Having established this we apply this program to systems with more complicated double channel structures, and show how one can tailor the conductivity of a channel in which perpendicular resonant tunneling affects parallel transport.     

CdSe/ZnSe复合结构非对称量子阱的发光特性

利用MOCVD技术在GaAs衬底上外延生长了非对称量子阱结构CdSe/ZnSe材料,通过对其稳态变温光谱及变激发功率光谱,研究了其发光特性。稳态光谱表明:在82～141K时,观测到的两个发光峰来源于不同阱层厚度的量子阱激子发光,用对比实验验证了高能侧发光的来源。宽阱发光强度先增加后减小,将其归结为激子隧穿与激子热离化相互竞争的结果。通过Arrhenius拟合,对宽阱激子热激活能进行了计算。82K时变激发功率PL光谱表明:由于激子隧穿的存在,使得窄阱发光峰位不随激发功率变化而变化,宽阱发光峰位随激发功率增加发生了蓝移,并对激子隧穿进行了实验验证。     

Spin-valley-dependent transport and giant tunneling magnetoresistance in silicene with periodic electromagnetic modulations

The transport property of electrons tunneling through arrays of magnetic and electric barriers is studied in silicene.In the tunneling transmission spectrum, the spin-valley-dependent filtered states can be achieved in an incident energy range which can be controlled by the electric gate voltage. For the parallel magnetization configuration, the transmission is asymmetric with respect to the incident angle θ, and electrons with a very large negative incident angle can always transmit in propagating modes for one of the spin-valley filtered states under a certain electromagnetic condition. But for the antiparallel configuration, the transmission is symmetric about θ and there is no such transmission channel. The difference of the transmission between the two configurations leads to a giant tunneling magnetoresistance(TMR) effect.The TMR can reach to 100% in a certain Fermi energy interval around the electrostatic potential. This energy interval can be adjusted significantly by the magnetic field and/or electric gate voltage. The results obtained may be useful for future valleytronic and spintronic applications, as well as magnetoresistance device based on silicene.     

The variably spaced superlattice energy filter

A new superlattice device concept which provides for high energy injection of electrons into a semiconductor layer is presented. The device is based on resonant tunneling of electrons between adjacent aligned quantum well levels in a variably spaced superlattice structure. By a judicial choice of well and barrier widths the energy levels under reverse bias become aligned such that resonant tunneling of electrons through the structure can occur. Thus, electrons are injected into a semiconductor layer at an energy corresponding to the energy of the first subband in the last quantum well. This structure has significant advantages over the conventional method of producing hot electrons in that a nearly monoenergetic high-energy electron distribution is created at low reverse bias and with high efficiency, since energy loss to phonons is inhibited as a consequence of the channeling of electrons through a narrow band of quantum states. Applications of the VSSEF structure to avalanche photodiodes, IMPATT diodes and electroluminescent devices are discussed.     

Effects of periodic modulation on the nonlinear Landau--Zener tunneling

We study the Landau-Zener tunneling of a nonlinear two-level system by applying a periodic modulation on its energy bias. We find that the two levels are splitting at the zero points of the zero order Bessel function for high-frequency modulation. Moreover, we obtain the effective coupling constant between two levels at the zero points of the zero order Bessel function by calculating the final tunneling probability at these points. It seems that the effective coupling constant can be regarded as the approximation of the higher order Bessel function at these points. For the low-frequency modulation, we find that the final tunneling probability is a function of the interaction strength. For the weak inter-level coupling case, we find that the final tunneling probability is more disordered as the interaction strength becomes larger.     

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.     

Klein tunneling in graphene: optics with massless electrons

This article provides a pedagogical review on Klein tunneling in graphene, i.e. the peculiar tunneling properties of two-dimensional massless Dirac electrons. We consider two simple situations in detail: a massless Dirac electron incident either on a potential step or on a potential barrier and use elementary quantum wave mechanics to obtain the transmission probability. We emphasize the connection to related phenomena in optics, such as the Snell-Descartes law of refraction, total internal reflection, Fabry-Pérot resonances, negative refraction index materials (the so called meta-materials), etc. We also stress that Klein tunneling is not a genuine quantum tunneling effect as it does not necessarily involve passing through a classically forbidden region via evanescent waves. A crucial role in Klein tunneling is played by the conservation of (sublattice) pseudo-spin, which is discussed in detail. A major consequence is the absence of backscattering at normal incidence, of which we give a new shorten proof. The current experimental status is also thoroughly reviewed. The Appendix contains the discussion of a one-dimensional toy model that clearly illustrates the difference in Klein tunneling between mono- and bi-layer graphene.     

对称双势垒量子阱中自旋极化输运的时间特性

电子的隧穿时间是描述量子器件动态工作范围的重要指标. 本文考虑k³ Dresselhaus 自旋轨道耦合效应对系统哈密顿量的修正, 结合转移矩阵方法和龙格-库塔法来解含时薛定谔方程, 进而讨论了电子在非磁半导体对称双势垒结构中的透射系数及隧穿寿命等问题. 研究结果发现:由于k³ Dresselhaus 自旋轨道耦合效应使自旋简并消除, 并在时间域内得到了表达, 导致自旋向上和自旋向下电子的透射峰发生了自旋劈裂; 不同自旋取向的电子构建时间和隧穿寿命不同, 这是导致自旋极化的原因之一; 电子的自旋极化在时间上趋于稳定. 关键词： 自旋极化输运 透射系数 隧穿寿命 自旋极化率     

苯基分子器件 量子相干输运第一性原理研究

摘要：分子器件在纳米尺度下,电子的相干性将对体系的电导产生重大影响。本文基于第一性原理计算研究了苯分子连接于一维金属电极下的电荷输运性质。发现一维金电极连接下,不同的连接方式（para与meta）体系下的电导将会有显著差别,而一维铂电极连接下,体系的电导差别不大。我们通过计算电极的能带,发现金电极与铂电极在费米面处的散射态数目有差别。 当量子相干效应导致散射态局域化发生改变时,由于铂电极的通道数较多,电子依然可以通过扩展的通道输运,因此不同连接方式下的电导变化不明显。     

Dynamical tunneling of bound systems through a potential barrier: Complex way to the top

A semiclassical method of complex trajectories for the calculation of the tunneling exponent n systems with many degrees of freedom is further developed. It is supplemented with an easily implemented technique that enables one to single out the physically relevant trajectory from the whole set of complex classical trajectories. The method is applied to semiclassical transitions of a bound system through a potential barrier. We find that the properties of physically relevant complex trajectories are qualitatively different in the cases of potential tunneling at low energy and dynamical tunneling at energies exceeding the barrier height. Namely, in the case of high energies, the physically relevant complex trajectories describe tunneling via creation of a state close to the top of the barrier. The method is checked against exact solutions of the Schrödinger equation in a quantum-mechanical system of two degrees of freedom.     

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.     

Zeeman splitting of single semiconductor impurities in resonant tunneling heterostructures

Zeeman splitting of the ground state of single impurities in the quantum wells of resonant tunneling heterostructures is reported. We determine the absolute magnitude of the effective magnetic spin splitting factorg* for a single impurity in a 44 Å Al_0.27Ga_0.73As/GaAs/Al_0.27Ga_0.73As quantum well to be 0.28±0.02. This system also allows for independent measurement of the electron tunneling rates through the two potential barriers and estimation of the occupation probability of the impurity state in the quantum well.