Transport measurements across a tunable potential barrier in graphene

The peculiar nature of electron scattering in graphene is among many exciting theoretical predictions for the physical properties of this material. To investigate electron scattering properties in a graphene plane, we have created a gate-tunable potential barrier within a single-layer graphene sheet. We report measurements of electrical transport across this structure as the tunable barrier potential is swept through a range of heights. When the barrier is sufficiently strong to form a bipolar junction (n-p-n or p-n-p) within the graphene sheet, the resistance across the barrier sharply increases. We compare these results to predictions for both diffusive and ballistic transport, as the barrier rises on a length scale comparable to the mean free path. Finally, we show how a magnetic field modifies transport across the barrier.     

Tunnelling states in a potential of hexagonal symmetry

The tunnel splitting of the ground state multiplet in a potential of the form V₀cos 6φ is calculated both in the weak perturbation and in the high barrier limit. In the latter limit a true variational calculation is performed and this gives better results than obtained by previous methods.     

Tunnelling time of a gaussian wave packet through two potential barriers

The resonant and non-resonant dynamies of a Gaussian quantum wave packet travelling through a double barrier system is studied as a function of the initial characteristics of the spectrum and of the parameters of the potential. The behaviour of the tunnelling time shows that there are situations where the Hartman effect occurs, while, when the resonances are dominant, and in particular for b>π/Δk (b being the inter-barrier distance and Δk the spectrum width), the tunnelling time becomes very large and the Hartman effect does not take place.     

Impurity-assisted interlayer exchange coupling across a tunnel barrier

Localized impurity or defect states in the insulating barrier layer separating two ferromagnetic films affect dramatically the interlayer exchange coupling (IEC), making it significantly stronger compared to perfect barriers. We demonstrate that the impurity-assisted IEC becomes antiferromagnetic if the energy of the impurity states matches the Fermi energy and that the coupling strength decreases with temperature. These results explain available experimental data on the IEC across tunnel barriers.     

Tunneling through a disordered potential barrier

Tunnelling through a weakly disordered potential barrier is studied analytically. A perturbative approach is developed to calculate all statistical moments of the tunnelling transmission coefficient, and its probability distribution function. It is shown that on average disorder enhances the tunnelling conductance, resistance, and the coherent component of the transmitted field.On leave from the Institute of Low-Temperature Physics and Engineering, Kharkov 310164, Ukraine.     

Resonance-like tunneling across a barrier with adjacent wells

We examine the behavior of transmission coefficient T across the rectangular barrier when attractive potential well is present on one or both sides and also the same is studied for a smoother barrier with smooth adjacent wells having Woods-Saxon shape. We find that presence of well with suitable width and depth can substantially alter T at energies below the barrier height leading to resonant-like structures. In a sense, this work is complementary to the resonant tunneling of particles across two rectangular barriers, which is being studied in detail in recent years with possible applications in mind. We interpret our results as due to resonant-like positive energy states generated by the adjacent wells. We describe in detail the possible potential application of these results in electronic devices using n-type oxygen-doped gallium arsenide and silicon dioxide. It is envisaged that these results will have applications in the design of tunneling devices.     

Escape by diffusion from a square well across a square barrier

The problem of escape of a particle by diffusion from a square potential well across a square barrier is studied on the basis of the one-dimensional Smoluchowski equation for the space- and time-dependent probability distribution. For the model potential the Smoluchowski equation is solved exactly by a Laplace transform with respect to time. In the limit of a high barrier the rate of escape is given by an asymptotic result similar to that derived by Kramers for a curved well and a curved barrier. An approximate analytic formula is derived for the outward time-dependent probability current in terms of the width and depth of the well and the width and height of the barrier. A similar expression holds for the complete probability distribution.     

Scattering and pair production by a potential barrier

Physics of Atomic Nuclei - Scattering and electron-positron pair production by a one-dimensional electric barrier is considered in the framework of the S-matrix formalism. The solutions of the...     

Tunneling time of electrons through a potential barrier

We investigate the problem of the average time spent by a tunneling electron in the classically forbidden region. We propose a natural method of generalizing the classical transit time concept to the quantum mechanical case and apply it to the problem of tunneling through a one-dimensional potential barrier. Considering the transmitted and reflected particles separately yields complex parameters which represent the tunneling times of reflected and transmitted particles. We investigate the connection of these parameters to the angles of rotation of electron spins in a magnetic field localized in the barrier region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 26–29, March, 1987.     

The potential barrier height for a Jahn-Teller center

The EPR spectrum of the Cu²⁺ ion in a ZnSiF₆·6H₂O crystal is studied in the temperature range T=5?300K. It is shown that the EPR spectrum can be represented in the form of a superposition of three contributions with essentially different properties. The first contribution is characterized by the maximal intensity at low temperatures and is described by a spin Hamiltonian with a large anisotropy of parameters. The second contribution has the maximal intensity at high temperatures and is described by a spin Hamiltonian with a low anisotropy of parameters. The third contribution cannot be described by a spin Hamiltonian and has the form of a partly orientationally averaged EPR spectrum. The reason for the emergence of these contributions is substantiated along with the form of the temperature dependence of their intensities on the basis of variation of the populations of vibronic states upon a change in temperature. The height (E₀=4±1cm_?1) of the potential barrier separating three equivalent Jahn-Teller potential wells of the Cu²⁺ ion is determined from analysis of the temperature dependence of the integrated intensity of the EPR spectrum. The obtained value of the barrier height substantially differs from the estimate (100 cm^?1) obtained earlier [2, 3] for the Cu²⁺ ion in ZnSiF₆·6H₂O on the basis of the tunneling model. It is shown that the forms of the temperature dependences of the linewidth of the low-and high-temperature EPR spectra are essentially different. This difference indicates that the contributions of the low-and high-temperature EPR spectra are associated with quantum-mechanical transitions between these states. It is proposed that the low-and high temperature contributions to the EPR spectrum are associated with the filling of under-the-barrier and above-the-barrier vibronic states, respectively.     

Traversal time for Dirac particles through a potential barrier

A traversal time that has no problem of superluminality was advanced for particles to tunnel through potential barriers in the non‐relativistic quantum theory in a previous paper by C.‐F. Li and Q. Wang, Physica B 296 (2001) 356. This time is generalized in this paper to Dirac's relativistic quantum theory. Both evanescent and propagating cases are considered. It is shown that the traversal time in the evanescent case has much the same properties as in the non‐relativistic quantum theory and thus has no problem of superluminality. It also gets rid of the problem of superluminality in the propagating case. Comparisons with the dwell time, the group delay, and the velocity of monochromatic front are also made.     

Simulation of transmission coefficient through a triangular potential barrier

An analytical expression of the transmission coefficient for the electron transport through a triangular potential barrier has been modified for solution using the method of numerical simulation. The triangular potential barrier has been modelled as a staircase function. The performance of this numerical simulation method is briefly described. The simulation has been developed for personal computer IBM PC AT.     

Tunnelling and hot electron effects in single barrier (AlGa)AsGaAs heterostructure devices

Experimental investigations of the effect of hydrostatic pressure (up to 15 kilobar) and magnetic field (up to 11 T) on the low temperature J(V) characteristics of single barrier n⁺GaAs/(AlGa)As/n⁻GaAs/n⁺GaAs tunnelling structures are reported. The pressure dependence is accurately described by the effective mass/WKB model up to 10 kilobar. At higher pressure the observed breakdown of the model indicates the onset of band structure effects associated with the higher conduction band minima. The reduction of the tunnelling current in an applied magnetic field is discussed in terms of the effect of the diamagnetic energy in increasing the effective height of the barrier. The paper reviews recent models that have been proposed to explain the origin of the oscillatory structure of period ΔV = ↔hω_L/e observed in the low temperature reverse bias J(V) characteristics.     

Effect of a modified potential barrier in field emission

The use of a modified surface potential barrier, which includes not only classical image force and the external force but also the exchange and correlation forces on the field emission has been investigated for tungsten. The theoretical calculations of the emitted current density and total energy distribution are obtained. A comparison of the experimental results with the theoretical predictions has been made. The agreement between them is good.     

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.