“Angular confinement and direction-dependent transmission in graphene nanostructures with magnetic barriers”. Masir MR, Vasilopoulos P, Matulis A, Peeters FM, AIP conference proceedings 1199, 363 (2009). http://doi.org/10.1063/1.3295453
Abstract: We evaluate the transmission through magnetic barriers in graphene-based nanostructures. Several particular cases are considered: a magnetic step, single and double barriers, delta -function barriers as well as barrier structures with inhomogeneous magnetic field profiles but with average magnetic field equal to zero. The transmission exhibits a strong dependence on the direction of the incident wave vector. In general the resonant structure of the transmission is significantly more pronounced for (Dirac) electrons with linear spectrum compared to that for electrons with a parabolic one.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
DOI: 10.1063/1.3295453
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Masir MR (2012) Electronic properties of graphene in inhomogeneous magnetic fields. Antwerpen
Keywords: Doctoral thesis; Condensed Matter Theory (CMT)
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“Magnetic Kronig-Penney model for Dirac electrons in single-layer graphene”. Masir MR, Vasilopoulos P, Peeters FM, New journal of physics 11, 095009 (2009). http://doi.org/10.1088/1367-2630/11/9/095009
Abstract: he properties of Dirac electrons in a magnetic superlattice (SL) on graphene consisting of very high and thin (δ-function) barriers are investigated. We obtain the energy spectrum analytically and study the transmission through a finite number of barriers. The results are contrasted with those for electrons described by the Schrödinger equation. In addition, a collimation of an incident beam of electrons is obtained along the direction perpendicular to that of the SL. We also highlight an analogy with optical media in which the refractive index varies in space.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.786
Times cited: 89
DOI: 10.1088/1367-2630/11/9/095009
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“Pseudo magnetic field in strained graphene : revisited”. Masir MR, Moldovan D, Peeters FM, Solid state communications 175, 76 (2013). http://doi.org/10.1016/j.ssc.2013.04.001
Abstract: We revisit the theory of the pseudo magnetic field as induced by strain in graphene using the tight- binding approach. A systematic expansion of the hopping parameter and the deformation of the lattice vectors is presented from which we obtain an expression for the pseudo magnetic field for low energy electrons. We generalize and discuss previous results and propose a novel effective Hamiltonian. The contributions of the different terms to the pseudo field expression are investigated for a model triaxial strain profile and are compared with the full solution. Our work suggests that the previous proposed pseudo magnetic field expression is valid up to reasonably high strain (15%) and there is no K-dependent pseudo-magnetic field.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.554
Times cited: 57
DOI: 10.1016/j.ssc.2013.04.001
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“Magnetic field dependence of the atomic collapse state in graphene”. Moldovan D, Masir MR, Peeters FM, 2D materials 5, 015017 (2018). http://doi.org/10.1088/2053-1583/AA9647
Abstract: <script type='text/javascript'>document.write(unpmarked('Quantum electrodynamics predicts that heavy atoms (Z \u003E Z(c) approximate to 170) will undergo the process of atomic collapse where electrons sink into the positron continuum and a new family of so-called collapsing states emerges. The relativistic electrons in graphene exhibit the same physics but at a much lower critical charge (Z(c) approximate to 1) which has made it possible to confirm this phenomenon experimentally. However, there exist conflicting predictions on the effect of a magnetic field on atomic collapse. These theoretical predictions are based on the continuum Dirac-Weyl equation, which does not have an exact analytical solution for the interplay of a supercritical Coulomb potential and the magnetic field. Approximative solutions have been proposed, but because the two effects compete on similar energy scales, the theoretical treatment varies depending on the regime which is being considered. These limitations are overcome here by starting from a tight-binding approach and computing exact numerical results. By avoiding special limit cases, we found a smooth evolution between the different regimes. We predict that the atomic collapse effect persists even after the magnetic field is activated and that the critical charge remains unchanged. We show that the atomic collapse regime is characterized: (1) by a series of Landau level anticrossings and (2) by the absence of root B scaling of the Landau levels with regard to magnetic field strength.'));
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 6.937
Times cited: 13
DOI: 10.1088/2053-1583/AA9647
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“Application of optical beams to electrons in graphene”. Matulis A, Masir MR, Peeters FM, Physical review : B : condensed matter and materials physics 83, 115458 (2011). http://doi.org/10.1103/PhysRevB.83.115458
Abstract: The technique of beam optics is applied to the description of the wave function of Dirac electrons. This approach is illustrated by considering electron transmission through simple nonhomogeneous structures, such as flat and bent p-n junctions and superlattices. We found that a convex p-n junction compresses the beam waist, while a concave interface widens it without loosing its focusing properties. At a flat p-n junction the waist of the transmitted Gaussian beam can be narrowed or widened, depending on the angle of incidence. A general condition is derived for the occurrence of beam collimation in a superlattice which is less stringent than previous discussed.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 13
DOI: 10.1103/PhysRevB.83.115458
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“Bilayer graphene Hall bar with a pn-junction”. Milovanovic SP, Masir MR, Peeters FM, Journal of applied physics 114, 113706 (2013). http://doi.org/10.1063/1.4821264
Abstract: We investigate the magnetic field dependence of the Hall and the bend resistances for a ballistic Hall bar structure containing a pn-junction sculptured from a bilayer of graphene. The electric response is obtained using the billiard model, and we investigate the cases of bilayer graphene with and without a band gap. Two different conduction regimes are possible: (i) both sides of the junction have the same carrier type and (ii) one side of the junction is n-type while the other one is p-type. The first case shows Hall plateau-like features in the Hall resistance that fade away as the band gap opens. The second case exhibits a bend resistance that is asymmetric in magnetic field as a consequence of snake states along the pn-interface, where the maximum is shifted away from zero magnetic field.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.068
Times cited: 3
DOI: 10.1063/1.4821264
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“Effect of spin-orbit couplings in graphene with and without potential modulation”. Shakouri K, Masir MR, Jellal A, Choubabi EB, Peeters FM, Physical review : B : condensed matter and materials physics 88, 115408 (2013). http://doi.org/10.1103/PhysRevB.88.115408
Abstract: We investigate the effect of Rashba and intrinsic spin-orbit couplings on the electronic properties and spin configurations of Dirac fermions confined in: (i) a flat graphene sheet, (ii) a graphene wire with p-n-p structure, and (iii) a superlattice of graphene wires. The interplay between the spin-orbit interaction mechanisms breaks the electron-hole symmetry and the spin configuration induced by Rashba spin-orbit coupling lacks inversion symmetry in k space. We show that the Rashba spin-orbit interaction doubles the Fabry-Perot resonant modes in the transmission spectrum of a graphene wire and opens new channels for the electron transmission. Moreover, it leads to the appearance of spin split extra Dirac cones in the energy spectrum of a graphene superlattice. It is shown that the spin of the electrons and holes confined in a flat graphene sheet is always perpendicular to their motion while this is not the case for the other nanostructures.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 36
DOI: 10.1103/PhysRevB.88.115408
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“Fabry-Pérot resonances in graphene microstructures: influence of a magnetic field”. Masir MR, Vasilopoulos P, Peeters FM, Physical review : B : condensed matter and materials physics 82, 115417 (2010). http://doi.org/10.1103/PhysRevB.82.115417
Abstract: Fabry-Pérot resonances in the transmission through single and double, graphene-based barriers (of height V) and wells are investigated and their dependence on an applied perpendicular magnetic field. For rectangular barriers the conductance decreases with increasing magnetic field while the resonances weaken (become more pronounced) with increasing magnetic field for EF<V (EF>V). The position of the resonances exhibit a linear shift with magnetic field which move to lower (higher) energy for EF<V (EF>V). Compared to semielliptic- or Gaussian-shaped barriers they show a smaller number of resonances in the absence of a magnetic field and an overall lower conductance but the resonant structure is more pronounced. The conductance of asymmetric double barriers show two major regions of resonances while the symmetric ones show one, that of three asymmetric barriers three, and so on.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 74
DOI: 10.1103/PhysRevB.82.115417
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“Resonant valley filtering of massive Dirac electrons”. Moldovan D, Masir MR, Covaci L, Peeters FM, Physical review : B : condensed matter and materials physics 86, 115431 (2012). http://doi.org/10.1103/PhysRevB.86.115431
Abstract: Electrons in graphene, in addition to their spin, have two pseudospin degrees of freedom: sublattice and valley pseudospin. Valleytronics uses the valley degree of freedom as a carrier of information similarly to the way spintronics uses electron spin. We show how a double-barrier structure consisting of electric and vector potentials can be used to filter massive Dirac electrons based on their valley index. We study the resonant transmission through a finite number of barriers and we obtain the energy spectrum of a superlattice consisting of electric and vector potentials. When a mass term is included, the energy bands and energy gaps at the K and K′ points are different and they can be tuned by changing the potential.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 55
DOI: 10.1103/PhysRevB.86.115431
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“Tuning a circular p-n junction in graphene from quantum confinement to optical guiding”. Jiang Y, Mao J, Moldovan D, Masir MR, Li G, Watanabe K, Taniguchi T, Peeters FM, Andrei EY, Nature nanotechnology 12, 1045 (2017). http://doi.org/10.1038/NNANO.2017.181
Abstract: <script type='text/javascript'>document.write(unpmarked('The photon-like propagation of the Dirac electrons in graphene, together with its record-high electronic mobility(1-3), can lead to applications based on ultrafast electronic response and low dissipation(4-6). However, the chiral nature of the charge carriers that is responsible for the high mobility also makes it difficult to control their motion and prevents electronic switching. Here, we show how to manipulate the charge carriers by using a circular p-n junction whose size can be continuously tuned from the nanometre to the micrometre scale(7,8). The junction size is controlled with a dual-gate device consisting of a planar back gate and a point-like top gate made by decorating a scanning tunnelling microscope tip with a gold nanowire. The nanometre-scale junction is defined by a deep potential well created by the tip-induced charge. It traps the Dirac electrons in quantum-confined states, which are the graphene equivalent of the atomic collapse states (ACSs) predicted to occur at supercritically charged nuclei(9-13). As the junction size increases, the transition to the optical regime is signalled by the emergence of whispering-gallery modes(14-16), similar to those observed at the perimeter of acoustic or optical resonators, and by the appearance of a Fabry-Perot interference pattern(17-20) for junctions close to a boundary.'));
Keywords: A1 Journal article; Engineering sciences. Technology; Condensed Matter Theory (CMT)
Impact Factor: 38.986
Times cited: 65
DOI: 10.1038/NNANO.2017.181
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“Interplay between snake and quantum edge states in a graphene Hall bar with a pn-junction”. Milovanović, SP, Masir MR, Peeters FM, Applied physics letters 105, 123507 (2014). http://doi.org/10.1063/1.4896769
Abstract: The magneto- and Hall resistance of a locally gated cross shaped graphene Hall bar is calculated. The edge of the top gate is placed diagonally across the center of the Hall cross. Four-probe resistance is calculated using the Landauer-Büttiker formalism, while the transmission coefficients are obtained using the non-equilibrium Green's function approach. The interplay between transport due to edge channels and snake states is investigated. When two edge channels are occupied, we predict oscillations in the Hall and the bend resistance as function of the magnetic field, which are a consequence of quantum interference between the occupied snake states.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.411
Times cited: 18
DOI: 10.1063/1.4896769
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“Realization of a tunable artificial atom at a supercritically charged vacancy in graphene”. Mao J, Jiang Y, Moldovan D, Li G, Watanabe K, Taniguchi T, Masir MR, Peeters FM, Andrei EY, Nature physics 12, 545 (2016). http://doi.org/10.1038/nphys3665
Abstract: Graphene’s remarkable electronic properties have fuelled the vision of a graphene-based platform for lighter, faster and smarter electronics and computing applications. One of the challenges is to devise ways to tailor graphene’s electronic properties and to control its charge carriers. Here we show that a single-atom vacancy in graphene can stably host a local charge and that this charge can be gradually built up by applying voltage pulses with the tip of a scanning tunnelling microscope. The response of the conduction electrons in graphene to the local charge is monitored with scanning tunnelling and Landau level spectroscopy, and compared to numerical simulations. As the charge is increased, its interaction with the conduction electrons undergoes a transition into a supercritical regime where itinerant electrons are trapped in a sequence of quasi-bound states which resemble an artificial atom. The quasi-bound electron states are detected by a strong enhancement of the density of states within a disc centred on the vacancy site which is surrounded by halo of hole states. We further show that the quasi-bound states at the vacancy site are gate tunable and that the trapping mechanism can be turned on and off, providing a mechanism to control and guide electrons in graphene.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 22.806
Times cited: 93
DOI: 10.1038/nphys3665
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“Quasibound states of Schrödinger and Dirac electrons in a magnetic quantum dot”. Masir MR, Matulis A, Peeters FM, Physical review : B : solid state 79, 155451 (2009). http://doi.org/10.1103/PhysRevB.79.155451
Abstract: The properties of a two-dimensional electron are investigated in the presence of a circular step magnetic-field profile. Both electrons with parabolic dispersion as well as Dirac electrons with linear dispersion are studied. We found that in such a magnetic quantum dot no electrons can be confined. Nevertheless close to the Landau levels quasibound states can exist with a rather long lifetime.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 55
DOI: 10.1103/PhysRevB.79.155451
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“Graphene hall bar with an asymmetric pn-junction”. Milovanovic SP, Masir MR, Peeters FM, Journal of applied physics 113, 193701 (2013). http://doi.org/10.1063/1.4805350
Abstract: We investigated the magnetic field dependence of the Hall and the bend resistances in the ballistic regime for a single layer graphene Hall bar structure containing a pn-junction. When both regions are n-type the Hall resistance dominates and Hall type of plateaus are formed. These plateaus occur as a consequence of the restriction on the angle imposed by Snell's law allowing only electrons with a certain initial angles to transmit though the potential step. The size of the plateau and its position is determined by the position of the potential interface as well as the value of the applied potential. When the second region is p-type, the bend resistance dominates, which is asymmetric in field due to the presence of snake states. Changing the position of the pn-interface in the Hall bar strongly affects these states and therefore the bend resistance is also changed. Changing the applied potential, we observe that the bend resistance exhibits a peak around the charge-neutrality point (CNP), which is independent of the position of the pn-interface, while the Hall resistance shows a sign reversal when the CNP is crossed, which is in very good agreement with a recent experiment [J. R. Williams and C. M. Marcus, Phys. Rev. Lett. 107, 046602 (2011)].
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.068
Times cited: 7
DOI: 10.1063/1.4805350
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“Scattering of a Dirac electron on a mass barrier”. Matulis A, Masir MR, Peeters FM, Physical review : A : atomic, molecular and optical physics 86, 022101 (2012). http://doi.org/10.1103/PhysRevA.86.022101
Abstract: The interaction of a wave packet (and in particular the wave front) with a mass barrier is investigated in one dimension. We discuss the main features of the wave packet that are inherent to two-dimensional wave packets, such as compression during reflection, penetration in the case when the energy is lower than the height of the barrier, waving tails, precursors, and the retardation of the reflected and penetrated wave packets. These features depend on the wave-packet envelope function which we demonstrate by considering the case of a rectangular wave packet with sharp front and trailing edges and a smooth Gaussian wave packet. The method of Fourier integral for obtaining the nonstationary solutions is used.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.925
Times cited: 9
DOI: 10.1103/PhysRevA.86.022101
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“Scattering of Dirac electrons by a random array of magnetic flux tubes”. Masir MR, Peeters FM, Journal of computational electronics 12, 115 (2013). http://doi.org/10.1007/s10825-013-0440-4
Abstract: The scattering of two-dimensional (2D) massless electrons as presented in graphene in the presence of a random array of circular magnetic flux tubes is investigated. The momentum relaxation time and the Hall factor are obtained using optical theorem techniques for scattering. Electrons with energy close to those of the Landau levels of the flux tubes exhibit resonant scattering and have a long life-time to reside inside the magnetic flux tube. These resonances appear as sharp structures in the Hall factor and the magneto-resistance.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 1.526
Times cited: 2
DOI: 10.1007/s10825-013-0440-4
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“Direction-dependent tunneling through nanostructured magnetic barriers in graphene”. Masir MR, Vasilopoulos P, Matulis A, Peeters FM, Physical review : B : condensed matter and materials physics 77, 235443 (2008). http://doi.org/10.1103/PhysRevB.77.235443
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 212
DOI: 10.1103/PhysRevB.77.235443
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“Spectroscopy of snake states using a graphene Hall bar”. Milovanović, SP, Masir MR, Peeters FM, Applied physics letters 103, 233502 (2013). http://doi.org/10.1063/1.4838557
Abstract: An approach to observe snake states in a graphene Hall bar containing a pn-junction is proposed. The magnetic field dependence of the bend resistance in a ballistic graphene Hall bar structure containing a tilted pn-junction oscillates as a function of applied magnetic field. We show that each oscillation is due to a specific snake state that moves along the pn-interface. Furthermore, depending on the value of the magnetic field and applied potential, we can control the lead in which the electrons will end up and hence control the response of the system.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.411
Times cited: 15
DOI: 10.1063/1.4838557
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“Scattering of Dirac electrons by circular mass barriers : valley filter and resonant scattering”. Masir MR, Matulis A, Peeters FM, Physical review : B : condensed matter and materials physics 84, 245413 (2011). http://doi.org/10.1103/PhysRevB.84.245413
Abstract: The scattering of two-dimensional (2D) massless Dirac electrons is investigated in the presence of a random array of circular mass barriers. The inverse momentum relaxation time and the Hall factor are calculated and used to obtain parallel and perpendicular resistivity components within linear transport theory. We found a nonzero perpendicular resistivity component which has opposite sign for electrons in the different K and K′ valleys. This property can be used for valley filter purposes. The total cross section for scattering on penetrable barriers exhibits resonances due to the presence of quasibound states in the barriers that show up as sharp gaps in the cross section while for Schrödinger electrons they appear as peaks.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 32
DOI: 10.1103/PhysRevB.84.245413
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“Wavevector filtering through single-layer and bilayer graphene with magnetic barrier structures”. Masir MR, Vasilopoulos P, Peeters FM, Applied physics letters 93, 242103 (2008). http://doi.org/10.1063/1.3049600
Abstract: 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 structures 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.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.411
Times cited: 91
DOI: 10.1063/1.3049600
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“Electronic states in a graphene flake strained by a Gaussian bump”. Moldovan D, Masir MR, Peeters FM, Physical review : B : condensed matter and materials physics 88, 035446 (2013). http://doi.org/10.1103/PhysRevB.88.035446
Abstract: The effect of strain in graphene is usually modeled by a pseudomagnetic vector potential which is, however, derived in the limit of small strain. In realistic cases deviations are expected in view of graphene's very high strain tolerance, which can be up to 25%. Here we investigate the pseudomagnetic field generated by a Gaussian bump and we show that it exhibits significant differences with numerical tight-binding results. Furthermore, we calculate the electronic states in the strained region for a hexagon shaped flake with armchair edges. We find that the sixfold symmetry of the wave functions inside the Gaussian bump is directly related to the different effects of strain along the fundamental directions of graphene: zigzag and armchair. Low energy electrons are strongly confined in the armchair directions and are localized on the carbon atoms of a single sublattice.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 50
DOI: 10.1103/PhysRevB.88.035446
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“Tunneling, conductance, and wavevector filtering through magnetic barriers in bilayer graphene”. Masir MR, Vasilopoulos P, Peeters FM, Physical review : B : solid state 79, 035409 (2009). http://doi.org/10.1103/PhysRevB.79.035409
Abstract: We evaluate the transmission and conductance through magnetic barrier structures in bilayer graphene. In particular we consider a magnetic step, single and double barriers, -function barriers, as well as barrier structures that have average magnetic field equal to zero. The transmission depends strongly on the direction of the incident electron or hole wavevector and gives the possibility to construct a direction-dependent wavevector filter. The results contrast sharply with previous results on single-layer graphene. In general, the angular range of perfect transmission becomes drastically wider and the gaps narrower. This perfect transmission range decreases with the number of barriers, the barrier width, and the magnetic field. Depending on the structure, a variety of transmission resonances occur that are reflected in the conductance through the structure.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 3.836
Times cited: 80
DOI: 10.1103/PhysRevB.79.035409
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“Graphene in inhomogeneous magnetic fields : bound, quasi-bound and scattering states”. Masir MR, Vasilopoulos P, Peeters FM, Journal of physics : condensed matter 23, 315301 (2011). http://doi.org/10.1088/0953-8984/23/31/315301
Abstract: The electron states in graphene-based magnetic dot and magnetic ring structures and combinations of both are investigated. The corresponding spectra are studied as a function of the radii, the strengths of the inhomogeneous magnetic field and of a uniform background field, the strength of an electrostatic barrier and the angular momentum quantum number. In the absence of an external magnetic field we have only long-lived quasi-bound and scattering states and we assess their influence on the density of states. In addition, we consider elastic electron scattering by a magnetic dot, whose average B vanishes, and show that the Hall and longitudinal resistivities, as a function of the Fermi energy, exhibit a pronounced oscillatory structure due to the presence of quasi-bound states. Depending on the dot parameters this oscillatory structure differs substantially for energies below and above the first Landau level.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.649
Times cited: 38
DOI: 10.1088/0953-8984/23/31/315301
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“Magnetic electron focusing and tuning of the electron current with a pn-junction”. Milovanović, SP, Masir MR, Peeters FM, Journal of applied physics 115, 043719 (2014). http://doi.org/10.1063/1.4863403
Abstract: Transverse magnetic focusing properties of graphene using a ballistic four terminal structure are investigated. The electric response is obtained using the semiclassical billiard model. The transmission exhibits pronounced peaks as a consequence of skipping orbits at the edge of the structure. When we add a pn-junction between the two probes, snake states along the pn-interface appear. Injected electrons are guided by the pn-interface to one of the leads depending on the value of the applied magnetic field. Oscillations in the resistance are found depending on the amount of particles that end up in each lead.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.068
Times cited: 21
DOI: 10.1063/1.4863403
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“Kronig-Penney model of scalar and vector potentials in graphene”. Masir MR, Vasilopoulos P, Peeters FM, Journal of physics : condensed matter 22, 465302 (2010). http://doi.org/10.1088/0953-8984/22/46/465302
Abstract: We consider a one-dimensional (1D) superlattice (SL) on graphene consisting of very high and very thin (δ-function) magnetic and potential barriers with zero average potential and zero magnetic field. We calculate the energy spectrum analytically, study it in different limiting cases, and determine the condition under which an electron beam incident on an SL is highly collimated along its direction. In the absence of the magnetic SL the collimation is very sensitive to the value of W/Ws and is optimal for W/Ws = 1, where W is the distance between the positive and negative barriers and L = W + Ws is the size of the unit cell. In the presence of only the magnetic SL the collimation decreases and the symmetry of the spectrum around ky is broken for W/Ws\neq 1 . In addition, a gap opens which depends on the strength of the magnetic field. We also investigate the effect of spatially separated potential and magnetic δ-function barriers and predict a better collimation in specific cases.
Keywords: A1 Journal article; Condensed Matter Theory (CMT)
Impact Factor: 2.649
Times cited: 41
DOI: 10.1088/0953-8984/22/46/465302
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