Spin-polarized tunneling in a ferromagnetic graphene junction: Interplay between the exchange interaction and the orbital effect of the magnetic field

The influence of magnetic vector potential barrier (MVPB) on the spin-polarized transport of massless Dirac particles in ferromagnetic graphene is studied theoretically. The phenomenon of Klein tunneling of relativistic particles across a rectangular potential barrier prevents any of the massless fermions from being confined but they can be electrically confined by quantum dots with integrable dynamics (Bardarson et al., 2009) [36]. Utilization of only the in-plane exchange splitting in the ferromagnetic graphene cannot produce 100% spin polarization. This tunneling can be confined using the magnetic vector potential barrier, which leads to high degree of spin polarization. By combining the orbital effect and the Zeeman interaction in graphene junction, it is found that the junction mimics behavior of half-metallic tunneling junction, in which it acts as a metal to particles of one spin orientation but as an insulator or a semiconductor to those of the opposite orientation. The idea of the half-metallic tunneling junction can provide a source of ∼100% spin-polarized current, which is potentially very useful. Adjustment of the position of the Fermi level in ferromagnetic layer by placing a gate voltage on top of the ferromagnetic layer shows that reverse of the orientation of the completely spin-polarized current passing through the junction is controlled by adjusting the gate voltage. These interesting characteristics should lead to a practical gate voltage controlled spin filtering and spin-polarized switching devices as a perfect spin-polarized electron source for graphene-based spintronics.     

Tunneling conductance on surface of topological insulator ferromagnet/insulator/(s- or d-wave) superconductor junction: Effect of magnetically-induced relativistic mass

We investigate the tunneling conductance on the surface of topological insulator ferromagnet (F)/insulator (I)/superconductor (S) junction where superconducting type is either s- or d-wave paring. Topological insulators (TI) are insulating in bulk but conducting on the surface with the Dirac-fermion-like carriers. In contrast to the Dirac fermions in graphene, relativistic mass of the Dirac fermions in TI can be easily caused by applying magnetic field perpendicular to its surface. In this work, we emphatically focus on the effect of the magnetically-induced relativistic mass on the tunneling conductance of a TI-based F/I/S junction. We find that, due to the effect of spinless fermions as carriers in TI, the behavior of the tunneling conductance in a TI-based NIS junction resembles that in a nonmagnetic graphene-based NIS junction. In case of the d-wave paring F/I/S junction, increasing magnetically-induced relativistic mass changes the zero bias conductance dip (peak) to a zero bias conductance peak (dip). This behavior cannot be observed in a graphene-based F/I/S junction.     

Josephson Effect in Graphene： Comparison of Real and Pseudo Vector Potential Barriers

The Josephson currents through real vector potential （RVP） and pseudo vector potential （PVP） barriers in graphene are investigated. In graphene, the pseudo vector potential may be caused by a local strain. The comparison of supercurrents induced by the two type-barriers is focused. As a result, we find that not only will the RVP induce a transition Josephson current from the 0→π state but also causes the difference in the phases of the order parameters of the two superconducting graphene layers to shift from φ→2φ. The critical current is PVP-independent around the neutrality point while it strongly depends on the RVP. The vector potential dependence of critical current is found to be perfectly linear for both PVP and RVP barriers.     

Quantum modulation effect in a graphene-based magnetic tunnel junction

The electronic (quantum) transport in a NG/F_B/FG tunnel junction (where NG, F_B and FG are a normal graphene layer, a ferromagnetic barrier connected to a gate and a ferromagnetic graphene layer, respectively) is investigated. The motions of the electrons in the graphene layers are taken to be governed by the Dirac Equation. Parallel (P) and antiparallel alignment (AP) of the magnetizations in the barrier and in the ferromagnetic graphene are considered. Our work focuses on the oscillation of the electrical conductance (Gq), of the spin conductance (Gs) and of the tunneling magneto resistance (TMR) of this magnetic tunnel junction. We find that, the quantum modulation due to the effect of the exchange field in F_B will be seen in the plots the conductance and of the TMR as functions of the thickness of ferromagnetic barrier (L). The period of two multiplied sinusoidal terms of the modulation are seen to be controlled by varying the gate potential and the exchange field of the F_B layer. The phenomenon, a quantum beating, is built up with two oscillating spin conductance components which have different periods of oscillation related to the splitting of Dirac's energies in the F_B region. The amplitudes of oscillations of Gq, Gs and TMR are not seen to decrease as the thickness increases. The decaying behaviors seen in the conventional transport through an insulator do not appear.     

Tunneling conductance in a gapped graphene-based superconducting structure: Case of massive Dirac electrons

The tunneling conductance in a NG/SG graphene junction in which the graphene was grown on a SiC substrate is simulated. The carriers in the normal graphene (NG) and the superconducting graphene (SG) are treated as massive relativistic particles. It is assumed that the Fermi energy in the NG and SG are E_FN400 meV and E_FS400 meV+U, respectively. Here U is the electrostatic potential from the superconducting gate electrode. It is seen that the Klein tunneling disappears in the case where a gap exist in the energy spectrum. As U→∞, the zero bias normalized conductance becomes persistent at a minimal value of G/G₀1.2. The normalized conductance G/G₀ is found to depend linearly on U with constant slope of , where is the size of the gap Δ opening up in the energy spectrum of the graphene grown on the SiC substrate. It is found that G/G₀2+αU for potentials in the range −270 meV<U<0 meV and G=0 for potentials U<−270 meV. As α→∞, the conductance for eV=Δ (V is the bias voltage placed across the NG/SG junction) can be approximated by a unit step function G(eV=Δ,U)/G₀2Θ(U). This last behavior indicates that a NG/SG junction made with gapped graphene could be used as a nano switch having excellent characteristics.