We study the transmission through single and double ferromagnetic barriers on the surface of a topological insulator. By adjusting the gate voltage and magnetization oreintation, the ferromagnetic barrier can be tuned into various transmission regions, where the wavevector-dependent tunnelings are quite different. We find that the Klein tunneling can be manipulated or even be turned off. These special properties offer the possibility to control electron beams on the "topological metal". Various novel devices, such as electronic collimation, wavevector filter, magnetic and electric switchs, and wavevector-based spin valve, may be constructed based on our observed phenomena.
The paper addresses inelastic spin-flip tunneling accompanied by surface spin excitations (magnons) in ferromagnetic junctions. The inelastic tunneling current is proportional to the magnon density of states which is energy-independent for the surface waves and, for this reason, cannot account for the bias-voltage dependence of the observed inelastic tunneling spectra. This paper shows that the bias-voltage dependence of the tunneling spectra can arise from the tunneling matrix elements of the electron-magnon interaction. These matrix elements are derived from the Coulomb exchange interaction …
A new quantum approach is presented that can account for the description of small ferromagnetic particles magnetization tunneling. An estimate of the saturation value of an external applied magnetic field along the easy axis is obtained. An analytic expression for the tunneling factor in the absence of an external magnetic field is deduced from the present approach that also allows to obtain the crossover temperature characterizing the regime where tunneling is dominated by the quantum effects.
We study transport through a ferromagnetic single-electron transistor. The resistance is represented as a path integral, so that systems where the tunnel resistances are smaller than the quantum resistance can be investigated. Beyond the low order sequential tunneling and co-tunneling regimes, a large magnetoresistance ratio at sufficiently low temperatures is found. In the opposite limit, when the thermal energy is larger than the charging energy, the magnetoresistance ratio is only slightly enhanced.
We measure electron tunneling via discrete energy levels in ferromagnetic cobalt particles less than 4 nm in diameter, using non-magnetic electrodes. Due to magnetic anisotropy, the energy of each tunneling resonance shifts as an applied magnetic field rotates the particle's magnetic moment. We see both spin-increasing and decreasing tunneling transitions, but we do not observe the spin degeneracy at small magnetic fields seen previously in non-magnetic materials. The tunneling spectrum is denser than predicted for independent electrons, possibly due to spin-wave excitations.
Quantum resonant tunneling behaviors of double-barrier structures on graphene are investigated under the tight-binding approximation. The Klein tunneling and resonant tunneling are demonstrated for the quasiparticles with energy close to the Dirac points. The Klein tunneling vanishes by increasing the height of the potential barriers to more than 300 meV. The Dirac transport properties continuously change to the Schrodinger ones. It is found that the peaks of resonant tunneling approximate to the eigen-levels of graphene nanoribbons under appropriate boundary conditions. A comparison between t…
At finite temperature we study the quantum tunneling of magnetization for a small ferromagnetic particle with the biaxial symmetry placed in a magnetic field at an arbitrary angle. We present numerical WKB exponent below the crossover temperature in which the quantum tunneling is affected by the thermal activation, and the approximate form of the WKB exponent around the crossover region. The effect of quantum fluctuations on the thermal activation rate beyond the crossover regime are discussed.
We consider spin-dependent tunneling through a gallium arsenide barrier, a material which has no inversion symmetry. We are dealing with free electrons, with one effective mass and a spin-splitting in the barrier material. When we take into account both the spin-orbit interaction and the absence of the inversion symmetry, the evanescent states in the barrier are spin split and the tunneling process can become rather involved. Along some crystallographic directions, the incident wave experiences spin filtering during the tunneling. These results open stimulating perspectives for spin manipulati…
We fabricate ferromagnetic nanowires with constrictions whose cross section can be reduced gradually from 100 nm to the atomic scale and eventually to the tunneling regime by means of electromigration. These devices are mechanically stable against magnetostriction and magnetostatic effects. We measure magnetoresistances ~ 0.3% for 100*30 nm^2 constrictions, increasing to a maximum of 80% for atomic-scale widths. These results are consistent with a geometrically-constrained domain wall trapped at the constriction. For the devices in the tunneling regime we observe large fluctuations in MR, betw…
We explore the characteristics of equilibrium tunneling of electrons from a 3D electrode into a high mobility 2D electron system. For most 2D Landau level filling factors, we find that tunneling can be characterized by a single, well-defined tunneling rate. However, for spin-polarized quantum Hall states (nu = 1, 3 and 1/3) tunneling occurs at two distinct rates that differ by up to 2 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.
We have utilized the finite-difference approach to explore electron-tunneling properties in gapped graphene through various electrostatic-potential barriers changing from Gaussian to a triangular envelope function in comparison with a square potential barrier. Transmission coefficient is calculated numerically for each case and applied to corresponding tunneling conductance. It is well known that Klein tunneling in graphene will be greatly reduced in a gapped graphene. Our results further demonstrate that such a decrease of transmission can be significantly enhanced for spatially-modulated pot…
We study the tunneling magnetoresistance in the ensembles of ferromagnetic granules with random easy axes of magnetic anisotropy taking into account the exchange interaction between granules. It is shown that due to the exchange interaction magnetoresistance is effectively decoupled from magnetization, i.e. the strongest negative magnetoresistance can be observed at the field where magnetization is almost saturated. Under some conditions, the sign of magnetoresistance can be reversed and tunneling magnetoresistance can become positive at certain magnetic fields. Our theory agrees with measurem…
We have investigated the spin current polarization without the external magnetic field in the resonant tunneling diode with the emitter and quantum well layers made from the ferromagnetic GaMnN. For this purpose we have applied the self-consistent Wigner-Poisson method and studied the spin-polarizing effect of the parallel and antiparallel alignment of the magnetization in the ferromagnetic layers. The results of our calculations show that the antiparallel magnetization is much more advantageous for the spin filter operation and leads to the full spin current polarization at low temperatures a…
The recently suggested mechanism [Y. Song and H. Dery, Phys. Rev. Lett. 113, 047205 (2014)] of the three-terminal spin transport is based on the resonant tunneling of electrons between ferromagnetic and normal electrodes via an impurity. The sensitivity of current to a weak external magnetic field stems from a spin blockade, which, in turn, is enabled by strong on-site repulsion. We demonstrate that this sensitivity exists even in the absence of repulsion when a single-particle description applies. Within this description, we calculate exactly the resonant-tunneling current between the electro…
The role of spin polarized reservoirs in quantum tunneling of magnetization and relaxation processes in a single molecular magnet (SMM) is investigated theoretically. The SMM is exchange-coupled to the reservoirs and also subjected to a magnetic field varying in time, which enables the quantum tunneling of magnetization (QTM). The spin relaxation times are calculated from the Fermi golden rule. The exchange interaction with tunneling electrons is shown to affect the spin reversal due to QTM. Furthermore, it is shown that the switching is associated with transfer of a certain charge between the…
We study the interconversion between photons and phonons coupled via radiation pressure in artificial Dirac materials realized by a honeycomb array of optomechanical cells. In particular we analyze the chiral tunneling of (photon-phonon) polaritons through an oscillating planar barrier. While a static barrier accommodates constructively interfering optical or mechanical waves leading to photon or phonon transmission, an oscillating barrier allows for inelastic scattering that causes sideband excitations and interference effects which, in turn, may suppress or revive the light-sound interconver…
We study the lateral tunneling through the gate-voltage-controlled barrier, which arises as a result of partial elimination of the donor layer of a heterostructure along a fine strip using an atomic force microscope, between edge channels at the depletion-induced edges of a gated two-dimensional electron system. For a sufficiently high barrier a typical current-voltage characteristic is found to be strongly asymmetric and include, apart from a positive tunneling branch, the negative branch that corresponds to the current overflowing the barrier. We establish the barrier height depends linearly…
Quantum tunneling of domain walls out of an impurity potential in a mesoscopic ferromagnetic sample is investigated. Using improved expressions for the domain wall mass and for the pinning potential, we find that the cross-over temperature between thermal activation and quantum tunneling is of a different functional form than found previously. In materials like Ni or YIG, the crossover temperatures are around 5 mK. We also find that the WKB exponent is typically two orders of magnitude larger than current estimates. The sources for these discrepancies are discussed, and precise estimates for t…
We present a theory of the low-energy excitations of a ferromagnetic metal nanoparticle. In addition to the particle-hole excitations, which occur in a paramagnetic metal nanoparticle, we predict a branch of excitations involving the magnetization-orientation collective coordinate. Tunneling matrix elements are in general sizable for several different collective states associated with the same band configuration. We point out that the average change in ground state spin per added electron differs from non-interacting quasiparticle expectations, and that the change in the spin-polarization, due…
Graphene electrons feature a pair of massless Dirac cones of opposite pseudospin chirality at two valleys. Klein tunneling refers to the intriguing capability of these chiral electrons to penetrate through high and wide potential barrier. The two valleys have been treated independently in the literature, where time reversal symmetry dictates that neither the normal incidence transmission nor the angle-averaged one can have any valley polarization. Here we show that, when intervalley scattering by barrier is accounted, graphene electrons normally incident at a superlattice barrier can experienc…
The large tunneling anisotropic magneto-resistance of a single $p^{++}$-(Ga,Mn)As/$n^{+}$-GaAs Zener-Esaki diode is evidenced in a perpendicular magnetic field over a large temperature and voltage range. Under an applied bias, the tunnel junction transparency is modified, allowing to continuously tune anisotropic transport properties between the tunneling and the ohmic regimes. Furthermore, an asymmetric bias-dependence of the anisotropic tunneling magneto-resistance is also observed: a reverse bias highlights the full (Ga,Mn)As valence band states contribution, whereas a forward bias only pro…
We theoretically investigate the effects of strain-induced pseudomagnetic fields on the transmission probability and the ballistic conductance for Dirac fermion transport in suspended graphene. We show that resonant tunneling through double magnetic barriers can be tuned by strain in the suspended region. The valley-resolved transmission peaks are apparently distinguishable owing to the sharpness of the resonant tunneling. With the specific strain, the resonant tunneling is completely suppressed for Dirac fermions occupying the one valley, but the resonant tunneling exists for the other valley…
The phenomenon of resonant tunneling transport through polar double-barrier heterostructures is systematically investigated using a combined experimental and theoretical approach. On the experimental side, GaN/AlN RTDs are grown by MBE. In-situ electron diffraction is employed to monitor the number of monolayers incorporated into each tunneling barrier. Using this precise epitaxial control at the monolayer level, we demonstrate exponential modulation of the resonant tunneling current as a function of barrier thickness. Both the peak voltage and characteristic threshold bias exhibit a dependenc…
Photon-assisted charge transport through a double barrier structure under a time periodic field in graphene is studied. Within the framework of the Floquet formalism and using the transfer matrix method, the transmission probabilities for the central band and sidebands are calculated. A critical phase difference between the harmonic potentials at the barriers, which cancels transmission through the inelastic sidebands due to quantum interference is found. This phenomenon could be of help to design graphene based filters and high-frequency radiation detectors. Quenching of resonant tunneling by…
A vertical resonant tunneling diode (RTD) based on the paramagnetic Zn1-x-yMnyCdxSe system has been fabricated with a pillar diameter down to ~ 6 micron. The diode exhibits high quality resonant tunneling characteristics through the electron sub-band of the quantum well at a temperature of 4.2K, where a clear phonon replica was observable in addition to the primary peak. Both peaks show a giant Zeeman splitting in an applied magnetic field. Employing a self-consistent real-time Green's function method, the current-voltage characteristic was simulated, showing good agreement with the measured r…
Spin-dependent tunneling through a symmetric semiconductor barrier is studied including the k^3 Dresselhaus effect. The spin-dependent transmission of electron can be obtained analytically. By comparing with previous work(Phys. Rev. B 67. R201304 (2003) and Phys. Rev. Lett. 93. 056601 (2004)), it is shown that the spin polarization and interface current are changed significantly by including the off-diagonal elements in the current operator, and can be enhanced considerably by the Dresselhaus effect in the contact regions.
Periodic arrays of antidots, i.e. nanoscale perforations, in graphene enable tight confinement of carriers and efficient transport barriers. Such barriers evade the Klein tunneling mechanism by being of the mass rather than electrostatic type. While all graphene antidot lattices (GALs) may support directional barriers, we show, however, that a full transport gap exists only for certain orientations of the GAL. Moreover, we assess the applicability of gapped graphene and the Dirac continuum approach as simplified models of various antidot structures showing that, in particular, the former is an…
We measure the low-temperature resistance of permalloy break junctions as a function of contact size and the magnetic field angle, in applied fields large enough to saturate the magnetization. For both nanometer-scale metallic contacts and tunneling devices we observe large changes in resistance with angle, as large as 25% in the tunneling regime. The pattern of magnetoresistance is sensitive to changes in bias on a scale of a few mV. We interpret the effect as a consequence of conductance fluctuations due to quantum interference.
We have found experimentally that the shot noise in InAlAs-InGaAs-InAlAs Triple-Barrier Resonant-Tunneling Diodes (TBRTD) is reduced over the 2eI Poissonian value whenever their differential conductance is positive, and is enhanced over 2eI when the differential conductance is negative. This behavior, although qualitatively similar to that found in double-barrier diodes, differs from it in important details. In TBRTDs the noise reduction is considerably larger than predicted by a semi-classical model, and the enhancement does not correlate with the strength of the negative differential conduct…
We investigate the tunneling of the quasiparticles arising in multi-Weyl semimetals through a barrier consisting of both electrostatic and vector potentials, existing uniformly in a finite region along the transmission axis. The dispersion of a multi-Weyl semimetal is linear in one direction (say, $k_z$), and proportional to $k_\perp^J$ in the plane perpendicular to it (where $k_\perp =\sqrt{k_x^2+k_y^2}$). Hence, we study the cases when the barrier is perpendicular to $k_z$ and $k_x$, respectively. For comparison, we also state the corresponding results for the Weyl semimetal.
The two apparently disparate phenomena, viz. the Klein tunneling and the electric field driven topological phase transition(TPT), exhibited by the silicene converge on the issue of the no change in the pseudo-spin. An ensuing possibility is that the former, in the case of a normal/magnetic/normal silicene junction, may be considered theoretically as a probe to ascertain the onset of the latter. In this communication, we explore this option and calculate the total transmission probability(TTP). We find that TPT is characterized by a cusp in a plot of TTP as a function of the electric field.
The effect of an in-plane magnetic field on resonant tunneling in a symmetric GaAs/AlYGa1-YAs triple-barrier resonant tunneling TBRT structure is presented. The splitting of the resonant lines (and hence the coupling energy vs. magnetic induction) for the ground and the first excited resonant doublet shifts up in energy by increasing the magnetic induction. Each of branches in the resonant dispersion relations shows a parabolic behavior with the location of the cyclotron orbit center. It is expected that, at very high fields, the interaction with confined phonons be enhanced, due to phonon cou…
A current due to a tunneling event that involves three times the charge of an electron was observed in the current - voltage characteristics of a superconducting single-electron tunneling transistor. In this tunnel event, a Cooper pair tunnels through one tunnel barrier simultaneously with a quasiparticle that tunnels through a second tunnel barrier which is about 0.5 microns distant from the first tunnel barrier. This current was observed in a bias regime where current flow due to sequential quasiparticle tunneling is forbidden due to the Coulomb blockade.
We study resonant tunneling through a superconducting double barrier structure in graphene as a function of the system parameters. At each barrier, due to the proximity effect, an incident electron can either reflect as an electron or a hole (specular as well as retro Andreev reflection in graphene). Similarly, transport across the barriers can occur via electrons as well as via the crossed (specular and/or retro) Andreev channel, where a hole is transmitted nonlocally to the other lead. In this geometry, in the subgap regime, we find resonant suppression of Andreev reflection at certain energ…
We present a self-consistent calculation, based on the global coherent tunnelling model, and show that structural asymmetry of double barrier resonant tunnelling structures significantly modifies the current-voltage characteristics compared to the symmetric structures. In particular, a suitably designed asymmetric structure can produce much larger peak current and absolute value of the negative differential conductivity than its commonly used symmetric counterpart.
We report on the realization of a double barrier resonant tunneling diode for cavity polaritons, by lateral patterning of a one-dimensional cavity. Sharp transmission resonances are demonstrated when sending a polariton flow onto the device. We use a non-resonant beam can be used as an optical gate and control the device transmission. Finally we evidence distortion of the transmission profile when going to the high density regime, signature of polariton-polariton interactions.
Tunneling, though a physical reality, is shrouded in mystery. Wave packets cannot be constructed under the barrier and group velocity cannot be defined. The tunneling particle can be observed on either sides of the barrier but its properties under the barrier has never been probed due to several problems related to quantum measurement. We show that there are ways to bypass these problems in mesoscopic systems and one can even derive an expression for the quantum mechanical current under the barrier. A general scheme is developed to derive this expression for any arbitrary system. One can use m…
The Hamiltonian of electrons interacting with interface phonons in three-barrier resonant tunneling structure is established using the first principles within the models of effective mass and polarization continuum. Using the Green's functions method, the temperature shifts and decay rates of operating electron states are calculated depending on geometric design of three-barrier nano-structure GaAs/Al$_{x}$Ga$_{1-x}$As which is an active region of quantum cascade detector. It is established that independently of the temperature, the energy of quantum transition during the process of electromag…
We theoretically investigate the effect of the negative differential conductance of a ferromagnetic barrier on the surface of a topological insulator. Due to the changes of the shape and position of the Fermi surfaces in the ferromagnetic barrier, the transport processes can be divided into three kinds: the total, partial and blockade transmission mechanisms. The bias voltage can give rise to the transition of the transport processes from partial to blockade transmission mechanisms, which results in a giant effect of negative differential conductance. With appropriate structural parameters, th…
The non-equilibrium spin accumulation in ferromagnetic double barrier junctions is shown to govern the transport in small structures. Transport properties of such systems are described by a generalization of the theory of the Coulomb blockade. The spin accumulation enhances the magnetoresistance. The transient non-linear transport properties are predicted to provide a unique experimental evidence of the spin-accumulation in the form of a reversed current on time scales of the order of the spin-flip relaxation time.
We investigate electronic transport in epitaxial Fe(100)/MgO/Fe/MgO/Fe double magnetic tunnel junctions with soft barrier breakdown (hot spots). Specificity of these junctions are continious middle layer and Nitrogen doping of the MgO barriers which provides soft breakdown at biases about 0.5V. In the junctions with hot spots we observe quasi-periodic changes in the resistance as a function of bias voltage which point out formation of quantum well states in the middle Fe continuous free layer. The room-temperature oscillations have been observed in both parallel and antiparallel magnetic confi…
Chiral tunneling through a harmonically driven potential barrier in graphene monolayer is considered in this work. Since the quasiparticles in this system are chiral in nature, tunneling is highly anisotropic, we determine the transmission probabilities for the central and sidebands as the incident angle of the electron beam is changed . Furthermore, we investigate how the transmission probabilities change as the width, amplitude and frequency of the oscillating barrier is changed. An interesting result of our study is that perfect transmission for normal incidence that has been reported for a…
We review studies on spin-dependent tunneling phenomena in systems containing ferromagnetic nanoparticles. We discuss preparation methods of assembling nanoparticles as well as the mechanisms and results of spin-dependent transport properties. The emphasis of this review is on characteristic spin-dependent tunneling phenomena such as enhanced tunnel magnetoresistance (TMR) due to co-tunneling in the Coulomb blockade regime and sign changes of the TMR due to spin accumulation in nanoparticles.
Tunneling of fractionally charged quasi-particles (QPs) through a barrier is considered in the context of a multiply connected geometry. In this geometry global constraints do not prohibit such a tunneling process. The tunneling amplitude is evaluated and the crossover from mesoscopic QP-dominated to electron-dominated tunneling as the system's size is increased is found. The presence of disorder enhances both electron and QP tunneling rates.
We predict bistability in the Curie temperature-voltage characteristic of double barrier resonant-tunneling structures with dilute ferromagnetic semiconductor quantum wells. Our conclusions are based on simulations of electrostatics and ballistic quantum transport combined with a mean-field theory description of ferromagnetism in dilute magnetic semiconductors.
A model for dealing with energy and momentum exchanges between ballistic electrons in a vacuum barrier in a tunneling probe used as an electromechanical transducer is studied and its physical significance in devices of size comparable to the mean free path of the tunneling electrons is discussed
Frequency dependent current noise in ferromagnetic double junctions with Coulomb blockade is studied theoretically in the limit of sequential tunneling. Two different relaxation processes are found in the correlations between spin polarized tunneling currents; low frequency spin fluctuations and high frequency charge fluctuations. Spin accumulation in strongly asymmetric junctions is shown to lead to a negative differential resistance. We also show that large spin noise activated in the range of negative differential resistance gives rise to a significant enhancement of the current noise.
Recently, it has been shown that magnetic tunnel junctions with thin MgO tunnel barriers exhibit extraordinarily high tunneling magnetoresistance (TMR) values at room temperature1, 2. However, the physics of spin dependent tunneling through MgO barriers is only beginning to be unravelled. Using planar magnetic tunnel junctions in which ultra-thin layers of magnetic metals are deposited in the middle of a MgO tunnel barrier here we demonstrate that the TMR is strongly modified when these layers are discontinuous and composed of small pancake shaped nanodots. At low temperatures, in the Coulomb …
We propose a ferromagnetic spintronic system, which consists of two serial connected resonant tunneling diodes. One diode is nonmagnetic whereas the other comprises a ferromagnetic emitter and quantum well. Using a selfconsistent coherent transport model we show that the current-voltage characteristic of the ferromagnetic diode can be strongly modulated by changing the relative orientation of the magnetizations in the emitter and quantum well, respectively. By a continuous change of the relative magnetization angle the total resistance exhibits a discrete jump realizing digital magneto resista…
A theory of resonant spin-dependent tunneling has been developed for symmetrical double-barrier structures grown of non-centrosymmetrical semiconductors. The dependence of the tunneling transparency on the spin orientation and the wave vector of electrons leads to (i) spin polarization of the transmitted carriers in an in-plane electric field, (ii) generation of an in-plane electric current under tunneling of spin-polarized carriers. These effects originated from spin-orbit coupling-induced splitting of the resonant level have been considered for double-barrier tunneling structures.
We studied the proximity effect between a superconductor (Nb) and a diluted ferromagnetic alloy (CuNi) in a bilayer geometry. We measured the local density of states on top of the ferromagnetic layer, which thickness varies on each sample, with a very low temperature Scanning Tunneling Microscope. The measured spectra display a very high homogeneity. The analysis of the experimental data shows the need to take into account an additional scattering mechanism. By including in the Usadel equations the effect of the spin relaxation in the ferromagnetic alloy, we obtain a good description of the ex…
Spin dependent single electron tunneling in a ferromagnetic double junction is investigated theoretically in the limit of incoherent sequential tunneling. The junction consists of a small nonmagnetic metallic grain with discrete energy levels, which is connected to two ferromagnetic electrodes. We have developed a new theoretical model taking into account charge as well as spin degrees of freedom. The model allows us to investigate new phenomena such as spin accumulation and spin fluctuations.
The effect of the barrier on the proximity effect in normal-superconductor junction is analyzed. A general criterion for the barrier, though large, to be effectively transparent, is given. This criterion is applied to both the conductance of a disordered NS junction (reflectionless tunneling) and the density of states across it, showing that both phenomena stem from the same physical effect.
We analyze distinct sources of spin-dependent energy level shifts and their impact on the tunneling magnetoresistance (TMR) of interacting quantum dots coupled to collinearly polarized ferromagnetic leads. Level shifts due to virtual charge fluctuations can be quantitatively evaluated within a diagrammatic representation of our transport theory. The theory is valid for multilevel quantum dot systems and we exemplarily apply it to carbon nanotube quantum dots, where we show that the presence of many levels can qualitatively influence the TMR effect.
We experimentally explore the phenomenon of electron tunneling across a modulated tunneling barrier which is created between an STM tip and an Au film deposited on a vibrating piezo surface. Measurements of the time series of the quantum mechanical tunneling current across the modulating barrier show large fluctuations. Analysis of the average work done in establishing tunneling current in finite time interval shows a distribution of both positive and negative work events. The negative work events suggest tunneling against the bias voltage direction. We show that these distributions obey the G…
We calculate the widths, migration barriers, effective masses, and quantum tunneling rates of kinks and jogs in extended screw dislocations in copper, using an effective medium theory interatomic potential. The energy barriers and effective masses for moving a unit jog one lattice constant are close to typical atomic energies and masses: tunneling will be rare. The energy barriers and effective masses for the motion of kinks are unexpectedly small due to the spreading of the kinks over a large number of atoms. The effective masses of the kinks are so small that quantum fluctuations will be imp…
Within the Büttiker dephasing model, the backscattering in the dephasing process is eliminated by setting a proper boundary condition. Explicit expression is carried out for the effective total tunneling probability in the presence of multiple pure dephasing scatterers with partial coherence. The derived formula is illustrated analytically by various limiting cases, and numerically for its application in tunneling through multi-barrier systems.
We predict that the Curie temperature of a ferromagnetic resonant tunneling diode will decrease abruptly, by approximately a factor of two, when the downstream chemical potential falls below the quantum well resonance energy. This property follows from elementary quantum transport theory notions combined with a mean field description of diluted magnetic semiconductor ferromagnetism. We illustrate this effect by solving coupled non-equilibrium Green's function, magnetic mean-field, and electrostatic Poisson equations self-consistently to predict the bias voltage and temperature dependence of th…
