Magneto transport on the surface of a topological insulator spin valve

The effects of the magnetization on the transport properties of a ferromagnet/barrier/ferromagnet spin valve fabricated with a topological insulator are studied. We consider two types of junctions, (i) an F₁/normal barrier (NB)/F₂ junction and (ii) an F₁/magnetic barrier (FB)/F₂ junction. The junctions in both cases lie in the xy-plane with the magnetizations in both ferromagnetic regions, F₁ and F₂ aligned in the z-direction. The charge carriers in the topological insulator have a Dirac like energy spectrum of a massive relativistic particle with the magnetization M playing the role of the mass. The gap opening is a special magneto feature of topological insulators. In an anti parallel alignment of the two magnetizations, the mass of the carriers is negative in the region where M is in the negative direction. The negative mass leads the behaviors of the magneto transport properties and the tunneling magneto resistance of these junctions to be quite different from those of graphene-based spin values.     

Magnetic gap effect on the tunneling conductance in a topological insulator ferromagnet/superconductor junction

The tunneling conductance on the surface of a topological-insulator-based ferromagnet/superconductor (F/S) structure is studied where S is an s-wave superconductor with superconducting order parameter ∼Δ. The conductance is calculated based on the BTK formalism. The magnetization in F is applied along the z-direction () in order to induce the energy-mass gaps (m) for the Dirac electrons in the F-region. In this work, the influence of energy gap due to the magnetic field in the F-region on the conductance is emphasized. The Fermi energy mismatch between F (EFF=EF) and S (EFS=EF+U), where the gate potential U is applied to the electrode on top of S, is also considered. As a result, a biased voltage V can cause the conductance switch at eV=Δ, depending on the value of the magnetic field. The conductance is found to be linearly dependent on either m or U. The slope of the curve can also be adjusted. This linear behavior in a topological-insulator-based F/S structure may be valuable for electronic applications of the linear-control-current devices. The tunneling conductances of the quasi-Dirac-particle in a topological-insulator-based F/S junction are quite different from those of a graphene-based F/S junction.     

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.     

Strain-induced switching of magnetoresistance and perfect spin-valley filtering in graphene

We study spin-dependent valley currents and magnetoresistance (TMR) in double magnetic layer graphene-based N/F₁/St/F₂/N junction where N, F_1,2 and St are normal, ferromagnetic and strain-engineered graphene, respectively. Local strain in the St region causes a pseudo-vector potential with the same magnitude for the K- and K′-valleys but different sign, leading to valley polarization when applying real vector potential into the junction. The F layers cause the Zeeman field for controlling spin current and can be orientated either parallel (P) or anti parallel (AP). As an effect of the interplay of the Zeeman field and the strain field, the current in the junction is split into four current groups, I_k↑, I_k↓, I_k′↑ and I_k′↓, called spin-valley currents. We find that, the interplay of the Zeeman and strain field causes a perfect spin-valley filtering in the angular space only for the P configuration. Large TMR and switching of TMR triggered by a very small strain are also predicted. Our work reveals the potential of the interplay of the Zeeman and the strain field for application of spin-valley-based nanoelectronics and the switching effect induced by a very small strain should be applicable for strain sensor device.     

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.