Topological surface states are a class of novel electronic states that are of potential interest in quantum computing or spintronic applications. Unlike conventional two-dimensional electron states, these surface states are expected to be immune to localization and to overcome barriers caused by material imperfection. Previous experiments have demonstrated that topological surface states do not backscatter between equal and opposite momentum states, owing to their chiral spin texture. However, so far there is no evidence that these states in fact transmit through naturally occurring surface defects. Here we use a scanning tunnelling microscope to measure the transmission and reflection probabilities of topological surface states of antimony through naturally occurring crystalline steps separating atomic terraces. In contrast to nontopological surface states of common metals (copper, silver and gold), which are either reflected or absorbed by atomic steps, we show that topological surface states of antimony penetrate such barriers with high probability. This demonstration of the extended nature of antimony's topological surface states suggests that such states may be useful for high current transmission even in the presence of atomic scale irregularities-an electronic feature sought to efficiently interconnect nanoscale devices.
We discuss electron scattering in a one-dimensional delta barrier potential with either time-dependent coupling constant (classical model) or a coupling constant that is linear in a boson coordinate (quantum model). We find an exact continued fraction solution and Fano like resonances in the transmission coefficient. In the quantum model, energies for perfect transmission exist below the first sideband threshold.
The list of textbook tunneling formulas is extended by deriving exact expressions for the transmission coefficient in graphene ribbons with armchair edges and the step-like and barrier-like profiles of site energies along the ribbon. These expressions are obtained by matching wave functions at the interfaces between the regions, where quasiparticles have constant but different potential energies. It is shown that for an $U_0$ high barrier and low-energy electrons and holes, the mode transmission of charge carriers in this type of ribbons is described by the textbook formula, where the constant…
The kinetic transport of electrons through graphene magnetic barriers is studied theoretically in presence of an external time harmonic scalar potential. The transmission coefficients are calculated in the framework of the non-perturbative Floquet theory using transfer matrix method. The time dependent scalar potential is found to suppress the usual Fabry-Perot oscillations occurring in the transmission through a constant vector potential barrier (corresponding to two oppositely directed delta-function magnetic barriers). Two types of asymmetric Fano resonances (FR) are noted and are discussed…
We investigate transmission properties of triple barrier parabolic double quantum well structure using the non-equilibrium Green's function method. In particular, we examine the effect of system parameters on transmission coefficient. The properties of the electronic state are also studied as a function of the system parameters (such as the well and barrier widths) and electric field bias. We also tested energy electronic state with calculating the density of states. It has been found that the first resonant peaks shift towards the lower energy region as the middle barrier width increases. New…
We study the electronic transmission through a graphene bilayer in the presence of an applied bias between layers. We consider different geometries involving interfaces between both a monolayer and a bilayer and between two bilayers. The applied bias opens a sizable gap in the spectrum inside the bilayer barrier region, thus leading to large changes in the transmission probability and electronic conductance that are controlled by the applied bias.
We investigate theoretically the transmission of electrons through a pair of δ- function magnetic barriers in graphene in presence of external monochromatic, linearly polarised and CW laser field. The transmission coefficients are calculated in the framework of non-perturbative Floquet theory using the transfer matrix method. It is noted that the usual Fabry-Perot oscillations in transmission through the graphene magnetic barriers with larger inter barrier separation takes the shape of beating oscillations in presence of the external laser field. The laser assisted transmission spectra are als…
Strong magnetic barriers are defined in two-dimensional electron gases by magnetizing dysprosium ferromagnetic platelets on top of a Ga[Al]As heterostructure. A small resistance across the barrier is observed even deep inside the closed regime. We have used semiclassical simulations to explain this behavior quantitatively in terms of a combined effect of elastic electron scattering inside the barrier region and E x B drift at the intersection of the magnetic barrier with the edge of the Hall bar.
In this contribution, we calculate in a self-consistent way the ballistic transmission as a function of energy of one Fe/MgO (001) single-barrier and one double-barrier tunnel junction, relating them to their electronic structure. The transmission spectra of each kind of junction is calculated at different applied bias voltages. We focus on the impact that bias has on the resonant tunneling mediated by surface and quantum well states. The calculations are done in the coherent regime, using a combination of density functional theory and non-equilibrium Green's functions, as implemented in the {…
We derive the local density of states from itinerant and boundary states around transport barriers and edges in graphene and show that the itinerant states lead to mesoscale undulations that could be used to probe their scattering properties in equilibrium without the need for lateral transport measurements. This finding will facilitate vetting of extended structural defects such as grain boundaries or line defects as transport barriers for switchable graphene resonant tunneling transistors. We also show that barriers could exhibit double minima and that the charge density away from highly ref…
We show that the transmission through single and double δ-function potential barriers of strength P in bilayer graphene is periodic in P with period π. For a certain range of P values we find states that are bound to the potential barrier and that run along the potential barrier. Similar periodic behaviour is found for the conductance. The spectrum of a periodic succession of δ-function barriers (Kronig-Penney model) in bilayer graphene is periodic in P with period 2π. For P smaller than a critical value, the spectrum exhibits two Dirac points while for P larger than this value an energy gap o…
We present two approaches for studying the uniformity of a tunnel barrier. The first approach is based on measuring single-electron and two-electron tunneling in a hybrid single-electron transistor. Our measurements indicate that the effective area of a conduction channel is about one order of magnitude larger than predicted by theoretical calculations. With the second method, transmission electron microscopy, we demonstrate that variations in the barrier thickness are a plausible explanation for the larger effective area and an enhancement of higher order tunneling processes.
The transmission T and conductance G through one or multiple one-dimensional, delta-function barriers of two-dimensional fermions with a linear energy spectrum are studied. T and G are periodic functions of the strength P of the delta-function barrier V(x,y) / hbar v_F = P delta(x). The dispersion relation of a Kronig-Penney (KP) model of a superlattice is also a periodic function of P and causes collimation of an incident electron beam for P = 2 pi n and n integer. For a KP superlattice with alternating sign of the height of the barriers the Dirac point becomes a Dirac line for P = (n + 1/2) …
The anisotropy in resonant tunneling transport through an electrostatic barrier in mono layer black phosphorus either in presence or in absence of an oscillating potential is studied. Non-perturbative Floquet theory is applied to solve the time dependent problem and the results obtained are discussed thoroughly. The resonance spectra in field free transmission are Lorentzian in nature although the width of the resonance for the barrier along the zigzag direction is too thinner than that for the armchair one. Resonant transmission is suppressed for both the cases by the application of oscillati…
We investigate the transport properties of charge carriers in AB bilayer graphene through a triple electrostatic barrier. We calculate the transmission and reflection using the continuity conditions at the interfaces of the triple barrier together with the transfer matrix method. First, we consider the case where the energy is less than the interlayer coupling $γ_1$ and show that, at normal incidence, transmission is completely suppressed in the gap for a large barrier width while it appears in the gap for a small barrier width. For energies greater than $γ_1$, we show that in the absence of a…
We show that the presence of a side-attached state strongly modifies the transmission through a one-dimensional double-barrier system in the window of wavevectors around the Fano antiresonance. Specifically, the interplay between the Fano interference and the size quantization inside the structure gives rise to narrow resonant peaks in the transmission coefficient. The height of the peaks may become close to unity (perfect transmission) even for an asymmetric setup with strong barriers, where the transmission coefficient in the absence of the Fano state is strongly suppressed at all other wave…
We evaluate the electronic transmission and conductance in bilayer graphene through a finite number of potential barriers. Further, we evaluate the dispersion relation in a bilayer graphene superlattice with a periodic potential applied to both layers. As a model we use the tight-binding Hamiltonian in the continuum approxi- mation. For zero bias the dispersion relation shows a finite gap for carriers with zero momentum in the direction parallel to the barriers. This is in contrast to single-layer graphene where no such gap was found. A gap also appears for a finite bias. Numerical results for…
We address the problem of barrier tunneling in the two-dimensional T_3 lattice (dice lattice). In particular we focus on the low-energy, long-wavelength approximation for the Hamiltonian of the system, where the lattice can be described by a Dirac-like Hamiltonian associated with a pseudospin one. The enlarged pseudospin S = 1 (instead of S = 1/2 as for graphene) leads to an enhanced "super" Klein tunneling through rectangular electrostatic barriers. Our results are confirmed via numerical investigation of the tight-binding model of the lattice. For a uniform magnetic field, we discuss the Lan…
Charge transport through a rectangular vector potential barrier modulated by a continuum laser in monolayer phosphorene is studied theoretically in the ballistic regime along the line of Floquet formalism. Laser free transmission profile displays strong directional behavior exhibiting collimation depending on the incident energy and width of the barrier. However, the application of laser, polarized along the zig-zag direction, creates a sharp anti-resonance in the transmission spectrum and reveals a strong light matter interaction due to broken symmetry in presence of the magnetic vector poten…
We investigate the tunneling of pseudospin-1 and pseudospin-3/2 quasiparticles through a barrier consisting of both electrostatic and vector potentials, existing uniformly in a finite region along the transmission axis. First, we find the tunneling coefficients, conductivities, and Fano factors in the absence of the vector potential. Then we repeat the calculations by switching on the relevant magnetic fields. The features show clear distinctions, which can be used to identify the type of semimetals, although both of them exhibit linear band-crossing points.
The relativistic nature of charge carriers in graphene is expected to lead to an angle- dependent transmission through a potential barrier, where Klein tunneling involves annihilation of an electron and a hole at the edges of the barrier. The signatures of Klein tunneling have been observed in gated graphene devices, but the angle dependence of the transmission probability has not been directly observed. Here we show measurements of the angle-dependent transmission through quasi-ballistic graphene heterojunctions with straight and angled leads, in which the barrier height is controlled by a sh…
For potential barriers with scalar and vector coupling, we show that a Dirac particle could experience nearly full transmission within a wide sub-barrier energy band. Moreover, for certain potential configurations, including pseudo-spin symmetry where the scalar potential is the negative of the vector, full transmission occurs for arbitrarily small momentum.
We investigate near-equilibrium ballistic transport through a quantum point contact (QPC) along a GaAs/AlGaAs heterojunction with a transfer matrix technique, as a function of temperature and the shape of the potential barrier in the QPC. Our analysis is based on a three-dimensional (3D) quantum-mechanical variational model within the Hartree-Fock approximation that takes into account the vertical depletion potential from ionized acceptors in GaAs and the gate-induced transverse confinement potential that reduce to an effective slowly-varying one-dimensional (1D) potential along the narrow con…
We find that the total spectrum of electron states in a bounded 2D electron gas with spin-orbit interaction contains two types of evanescent states lying in different energy ranges. The first-type states fill in a gap, which opens in the band of propagating spin-splitted states if tangential momentum is nonzero. They are described by a pure imaginary wavevector. The states of second type lie in the forbidden band. They are described by a complex wavevector. These states give rise to unusual features of the electron transmission through a lateral potential barrier with spin-orbit interaction, s…
We studied the transport properties of electrons in graphene as they are scattered by a double barrier potential in the presence of an inhomogeneous magnetic field. We computed the transmission coefficient and Goos-Hänchen like shifts for our system and noticed that transmission is not allowed for certain range of energies. In particular, we found that, in contrast to the electrostatic barriers, the magnetic barriers are able to confine Dirac fermions. We also established some correlation between the electronic transmission properties of Dirac fermions with the Goos-Hänchen like shifts, as ref…
We study the transmission probability of Dirac fermions in graphene scattered by a triangular double barrier potential in the presence of an external magnetic field. Our system made of two triangular potential barrier regions separated by a well region characterized by an energy gap $G_p$. Solving our Dirac-like equation and matching the solutions at the boundaries we express our transmission and reflection coefficients in terms of transfer matrix. We show in particular that the transmission exhibits oscillation resonances that are manifestation of the Klein tunneling effect.
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.
We show that the angular range of the transmission through magnetic barrier structures can be efficiently controlled in single-layer and bilayer graphenes and this renders the structure's efficient wavevector filters. As the number of magnetic barriers increases, this range shrinks, the gaps in the transmission versus energy become wider, and the conductance oscillates with the Fermi energy.
We investigate the Goos-Hänchen-like shifts for Dirac fermions in transmission through a monolayer graphene barrier. The lateral shifts, as the functions of the barrier's width and the incidence angle, can be negative and positive in Klein tunneling and classical motion, respectively. Due to their relations to the transmission gap, the lateral shifts can be enhanced by the transmission resonances when the incidence angle is less than the critical angle for total reflection, while their magnitudes become only the order of Fermi wavelength when the incidence angle is larger than the critical ang…
Transmission of electrons across a rectangular barrier of IV-VI semiconductor compounds is considered. Conduction electrons arrive at the barrier and are reflected or transmitted through it depending on the relative values of the barrier potential $V_b$ and the electron energy $E$. The theory, in close analogy to the Dirac four component spinors, accounts for the boundary conditions on both sides of the barrier. The calculated transmission coefficient $T_C$ is an oscillatory function of the barrier voltage varying between zero (for full electron reflection) and unity (for full electron transmi…
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…
It is shown that potential barriers in bilayer graphene (BLG) and monolayer transition metal dichalcogenides (TMDs) can split a valley unpolarized incident current into reflected and transmitted currents with opposite valley polarization. Valley asymmetric transmission inevitably occurs because of the low symmetry of the total Hamiltonian and when total external reflection occurs the transmission is 100% valley polarized in BLG and 100% spin and valley polarized in TMDs, except for exponentially small corrections. By adjusting the potential, 100% polarization can be obtained regardless of the …
Transmission probabilities of Dirac fermions in graphene under linear barrier potential oscillating in time are investigated. Solving Dirac equation we end up with the solutions of the energy spectrum depending on several modes coming from the oscillations. These will be used to obtain a transfer matrix that allows to determine transmission amplitudes of all modes. Due to numerical difficulties in truncating the resulting coupled channel equations, we limit ourselves to low quantum channels, i.e. $l = 0, \pm1$, and study the three corresponding transmission probabilities.
Controlling the transmission of electrical current using a quantum point contact constriction paved a way to a large variety of experiments in mesoscopic physics. The increasing interest in heat transfer in such systems fosters questions about possible manipulations of quantum heat modes that do not carry net charge(neutral modes). Here, we study the transmission of upstream neutral modes through a quantum point contact in fractional hole-conjugate quantum Hall states. Employing two different measurement techniques, we were able to render the relative spatial distribution of these chargeless m…
We have investigated the transmission in monolayer graphene barrier at nonzero angle of incidence. Taking the influence of parallel wave vector into account, the transmission as the function of incidence energy has a gap due to the evanescent waves in two cases of Klein tunneling and classical motion. The modulation of the transmission gap by the incidence angle, the height, and width of potential barrier may lead to potential applications in graphene-based electronic devices.
Electron tunneling through a single magnetic barrier in a HgTe topological insulator has been theoretically investigated. We find that the perpendicular magnetic field would not lead to spin-flip of the edge states due to the conservation of the angular moment. By tuning the magnetic field and Fermi energy, the edge channels can be transited from switch-on states to switch-off states and the current can be transmitted from unpolarized states to totally spin polarized states. These features offer us and efficient way to control the topological edge state transport, and pave a way to construct t…
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 ballistic edge-channel transport in quantum wires with a magnetic quantum dot, which is formed by two different magnetic fields B^* and B_0 inside and outside the dot, respectively. We find that the electron states located near the dot and the scattering of edge channels by the dot strongly depend on whether B^* is parallel or antiparallel to B_0. For parallel fields, two-terminal conductance as a function of channel energy is quantized except for resonances, while, for antiparallel fields, it is not quantized and all channels can be completely reflected in some energy ranges. All…
A scheme is proposed to electrically measure the spin-momentum coupling in the topological insulator surface state by injection of spin polarized electrons from silicon. As a first approach, devices were fabricated consisting of thin (<100nm) exfoliated crystals of Bi2Se3 on n-type silicon with independent electrical contacts to silicon and Bi2Se3. Analysis of the temperature dependence of thermionic emission in reverse bias indicates a barrier height of 0.34 eV at the Si-Bi2Se3 interface. This robust Schottky barrier opens the possibility of novel device designs based on sub-band gap internal…
We study the transport properties of Dirac electrons across a two-dimensional normal metal-barrier-normal metal (NBN) interfaces in monolayer borophane. We analyse the transmission probability with variation of the width of the barrier region, the incidence energy and transverse momentum. We demonstrate that a gap exists in the transmission probability spectrum and the position, width of transmission gap can be tuned by the barrier strength and transverse momentum respectively. We point out the variation of the ballistic tunneling conductance as a function of the width of the barrier region an…
We report the direct measurement of the topological skyrmion energy barrier through a hysteresis of the skyrmion lattice in the chiral magnet MnSi. Measurements were made using small-angle neutron scattering with a custom-built resistive coil to allow for high-precision minor hysteresis loops. The experimental data was analyzed using an adapted Preisach model to quantify the energy barrier for skyrmion formation and corroborated by the minimum-energy path analysis based on atomistic spin simulations. We reveal that the skyrmion lattice in MnSi forms from the conical phase progressively in smal…
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…
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…
We theoretically investigate the barrier tunneling in the three-dimensional model of the hyperhoneycomb lattice, which is a nodal-line semimetal with a Dirac loop at zero energy. In the presence of a rectangular potential, the scattering amplitudes for different injecting states around the nodal loop are calculated, by using analytical treatments of the effective model, as well as numerical simulations of the tight binding model. In the low energy regime, states with remarkable transmissions are only concentrated in a small range around the loop plane. When the momentum of the injecting electr…
Resonant electronic transmission through graphene-based double barriers (wells) is studied as a function of the incident wave vector, the widths and heights (depths) of the barriers (wells), and the separation between them. Resonant features in the transmission result from resonant electron states in the wells or hole states in the barriers and strongly influence the ballistic conductance of the structures.
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…
The electron spin effects on the surface of a nanotube have been considered through the spin-orbit interaction (SOI), arising from the electron confinement on the surface of the nanotube. This is of the same nature as the Rashba-Bychkov SOI at a semiconductor heterojunction. We estimate the effect of disorder within a potential barrier on the transmission probability. Using a continuum model, we obtained analytic expressions for the spin-split energy bands for electrons on the surface of nanotubes in the presence of SOI. First we calculate analytically the scattering amplitudes from a potentia…
We study transport across a time-dependent magnetic barrier present on the surface of a three-dimensional topological insulator. We show that such a barrier can be implemented for Dirac electrons on the surface of a three-dimensional topological insulator by a combination of a proximate magnetic material and linearly polarized external radiation. We find that the conductance of the system can be tuned by varying the frequency and amplitude of the radiation and the energy of an electron incident on the barrier providing us optical control on the conductance of such junctions. We first study a $…
