The polaron state of a crystal

The quantum mechanics of an electron-nuclear system with strong electron-phonon coupling is considered. First, a two-site model is treated in the adiabatic approximation. As the coupling constant increases, electron transfer undergoes qualitative changes; more specifically, a potential barrier forms in the adiabatic potential, the electron transfer becomes associated with the tunneling of nuclei through the barrier, and the level splitting in the system falls off exponentially. The properties of a similar crystal model are discussed. It is shown that electron transfer in a crystal in the case of strong coupling is likewise associated with the tunneling of nuclei through barriers in the deformation space. Strong coupling modifies the electron-electron interaction terms. The Hamiltonian (exchange) terms, which are not associated with electron transfer, are only weakly modified. At the same time, the terms involving transfer (the band terms) undergo exponential reduction and vanish in the limit as M → ∞ (M is the ion mass) and the carriers become small polarons. This reduction provides a basis for the natural mechanism of enhancement of the isotope effect.     

栅极电势对强光场下石墨烯场效应管中电子隧穿的影响

利用时域有限差分方法研究了强光场下石墨烯场效应管中栅极电势对电子隧穿的影响. 在强光场下由于光学stark效应,石墨烯场效应管的完美手征透射被抑制.这种抑制除了 可以利用光场来调控外,也可以通过改变栅极电势的宽度、势垒高度等来调控. 研究了非方势垒中电子的隧穿. 研究发现,当电势的倾斜较小时,电子隧穿概率变化不大.而当电势倾斜很大时,电子隧穿概率急剧改变.     

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.     

Tunnel magnetoresistance oscillations in a ferromagnet-insulator-ferromagnet system

A model of spin-dependent transport of electrons through a ferromagnet-insulator-ferromagnet structure is developed. It takes into account the image forces, tunnel barrier parameters, and effective masses of an electron tunneling in the barrier and in the ferromagnetic electrode in the free electron approximation. Calculations for an iron-aluminum oxide-iron structure show that, with an increase in the bias voltage, the tunnel magnetoresistance decreases monotonically and then breaks into damped oscillations caused by the interference of the electrons’ wave functions in the conduction region of the potential barrier. The image forces increase the tunnel magnetoresistance by two or three times.     

Momentum and spin filtering of electrons on the surface of a topological insulator

We study theoretically electron tunneling through planar magnetic barrier arrays on the surface of a three-dimensional topological insulator. Interestingly, the transmission displays a collimation behavior at some specific incident angles. This feature provides us a new way to construct a momentum and spin filter in topological insulators.     

Entangled electron current through finite size normal-superconductor tunneling structures

We investigate theoretically the simultaneous tunneling of two electrons from a superconductor into a normal metal at low temperatures and voltages. Such an emission process is shown to be equivalent to the Andreev reflection of an incident hole. We obtain a local tunneling Hamiltonian that permits to investigate transport through interfaces of arbitrary geometry and potential barrier shapes. We prove that the bilinear momentum dependence of the low-energy tunneling matrix element translates into a real space Hamiltonian involving the normal derivatives of the electron fields in each electrode. The angular distribution of the electron current as it is emitted into the normal metal is analyzed for various experimental setups. We show that, in a full three-dimensional problem, the neglect of the momentum dependence of tunneling causes a violation of unitarity and leads to the wrong thermodynamic (broad interface) limit. More importantly for current research on quantum information devices, in the case of an interface made of two narrow tunneling contacts separated by a distance r, the assumption of momentum-independent hopping yields a nonlocally entangled electron current that decays with a prefactor proportional to r ^-2 instead of the correct r ^-4.Received: 14 June 2004, Published online: 24 September 2004PACS: 74.45. + c Proximity effects; Andreev effect; SN and SNS junctions - 74.50. + r Tunneling phenomena; point contacts, weak links, Josephson effects     

Transmission times of wave packets tunneling through barriers

The transmission of wave packets through barriers by tunneling is studied in detail by the method of quantum molecular dynamics. The distribution of the arrival times of a tunneling packet in front of and behind a barrier and the momentum distribution function of the packet are calculated. The average position and average momentum of the packet and their spread are investigated. It is found that below the barrier a part of the packet is reflected, and a Gaussian barrier increases the average momentum of the transmitted packet and its spread in momentum space. Zh. éksp. Teor. Fiz. 115, 1872–1889 (May 1999)     

Secondary ion emission processes of sputtered alkali ions from alkali/Si(100) and Si(111)

The secondary alkali ion yield vs. the work function change (Δφ) of Na, K and Cs/Si(100) and Si(111) was measured to discuss the details of secondary ion emission processes. In the case of alkali/metal systems, the secondary ion emission is explained by the electron tunneling model. In this model, the ionization of the ejected atom occurs as a result of electron resonant tunneling through the potential barrier separating an atom and a metal, and the secondary ion yield depends on exponentially the work function change of metal surface. For alkali/Si(100) systems, the secondary ion emission processes are explained in terms of the electron tunneling model since the secondary alkali ion yield vs. the work function change (Δφ) follows the exponential manner. However, it is not easy to apply the simple electron tunneling model to our experimental results for alkali/Si(111) systems. There is the essential difference in surface structures between Si(100) and Si(111). Therefore, it is suggested that the local electronic environment around the adsorbates might be taken into consideration for alkali/Si(111) systems.     

Properties of photon tunneling through single-negative materials

The photon tunneling phenomena in the composite barriers of single-negative materials were analyzed. It was found that the tunneling through such a barrier shifts TE- and TM-polarization light waves laterally (parallel to the material interface) in two opposite directions, causing them to be divided into two waves after tunneling. This property could not be obtained with double-positive and (or) double-negative materials.     

Electron tunneling in single layer graphene with an energy gap

When a single layer graphene is epitaxially grown on silicon carbide,it will exhibit a finite energy gap like a conventional semiconductor,and its energy dispersion is no longer linear in momentum in the low energy regime.In this paper,we have investigated the tunneling characteristics through a two-dimensional barrier in a single layer graphene with an energy gap.It is found that when the electron is at a zero angle of incidence,the transmission probability as a function of incidence energy has a gap.Away from the gap the transmission coefficient oscillates with incidence energy which is analogous to that of a conventional semiconductor.The conductance under zero temperature has a gap.The properties of electron transmission may be useful for developing graphene-based nano-electronics.     

Interference in the collective electron momentum in double photoionization of H2

We investigate single-photon double ionization of H(2) by 130 to 240 eV circularly polarized photons. We find a double slitlike interference pattern in the sum momentum of both electrons in the molecular frame which survives integration over all other degrees of freedom. The difference momentum and the individual electron momentum distributions do not show such a robust interference pattern. We show that this interference results from a non-Heitler-London fraction of the H(2) ground state where both electrons are at the same atomic center.     

Investigation of HfO<Subscript>2</Subscript>/SiO<Subscript>2</Subscript>/<Emphasis Type="Italic">n</Emphasis>-Si(001)-based MOS structures via ballistic electron emission microscopy

(Au, Pt)/HfO₂/SiO₂/n-Si(001) metal-oxide-semiconductor structures with a thin (≈0.5 nm) SiO₂ layer, which is formed between HfO₂ and Si during atomic layer deposition of oxide layers, have been investigated via ballistic electron emission spectroscopy. The potential barrier heights at the (Au, Pt)/HfO₂ interfaces have been determined experimentally. The peculiarities observed in the curves of dependence of the collector current on the voltage between a scanning tunneling microscope probe and a metallic electrode are related to electron transport through the vacancy defect region of HfO₂ and the quantum-mechanical interference of electron waves arising from multiple reflections at the interfaces of the two-layer dielectric and at the interfaces of dielectric with a substrate and a metallic electrode.     

Multiple Internal Reflections During Particle and Photon Tunneling

We discuss the time analysis of multiple internal reflections during one-dimensional tunneling of non-relativistic particles and photons with sub-barrier energies through potential barriers. The approach exploited is a simple analytic continuation from real (over-barrier) wave numbers to imaginary (sub-barrier) wave numbers. It is shown in particular that not only the general effective tunneling velocity, but also every effective transmission (tunneling) velocity for at least the first intermediate stage between successive internal reflections is superluminal. An interpretation of this seemingly strange fact is given in terms of an effective deformation of spacetime inside the barrier. The results obtained are interpreted with the help of the Fourier expansion over the virtual momentum space. A comparison with the instanton approach is also made.     

Coherent Resonant Tunneling Model in Double-Barrier Nanostructures

We propose a coherent resonant tunneling model in double-barrier nanostructutes in which besides an interference effect originated from coherent tunneling of single electron through two barriers, the effects of one-electron charging, discrete energy spectrum and electron interactions between barriers are also important. The interference effect, like that for light in Fabry-Perot cavity, will occur no matter whether a magnetic field exists or not, and is shown to have significant effect on the systems' tunneling current. Our model agrees
surprisingly well with all the main experimental features of the phenomenon discovered by Scott Thomas et al.     

How do electronic carriers cross Si-bound alkyl monolayers?

Electron transport through Si-C bound alkyl chains, sandwiched between and Hg, is characterized by two distinct types of barriers, each dominating in a different voltage range. At low voltage, the current depends strongly on temperature but not on molecular length, suggesting transport by thermionic emission over a barrier in the Si. At higher voltage, the current decreases exponentially with molecular length, suggesting transport limited by tunneling through the molecules. The tunnel barrier is estimated, from transport and photoemission data, to be approximately 1.5 eV with a 0.25m(e) effective mass.     

Tunneling by an electron packet with an initially sharp wavefront

We have studied the time behavior of electron wavepackets traversing one-dimensional potentials. These packets are described as plane wave states that have been cut off to give a sharp initial wavefront. We find that the shift, or delay time, of the main part of the pulse is comparable to that of a Gaussian wavepacket with the same momentum, and that both kinds of pulses have the same broad-pulse (sharp-momentum) limit. This is shown to hold for a general class of potentials. We show explicitly that the steepest descents calculation described by Stevens does not lead to a finite tunneling velocity. An exact expression is given for the packet transmitted through a delta-function barrier, which suggests a new interpretation of the tunneling velocity that has been obtained in other calculations.     

Quasiparticle tunneling through a barrier in the fractional quantum hall regime

Tunneling of fractionally charged quasiparticles (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.     

Enhancement of tunneling from a correlated 2D electron system by a many-electron Mössbauer-type recoil in a magnetic field

We consider the effect of electron correlations on tunneling from a 2D electron layer in a magnetic field parallel to the layer. A tunneling electron can exchange its momentum with other electrons, which leads to an exponential increase of the tunneling rate compared to the single-electron approximation. The effect depends on the interrelation between the dynamics of tunneling and momentum exchange. The results explain and provide a no-parameter fit to the data on electrons on helium. We also discuss tunneling in semiconductor heterostructures.