Fingerprint of parity anomaly for localized magnetic states in quantum anomalous Hall systems.

We investigate the local magnetic states of impurities in quantum anomalous Hall (QAH) systems and observe that with an increasing band gap, the magnetic region of impurities expands in the QAH phase, while it contracts in the ordinary insulator (OI) phase. During the transition between the QAH and the OI phase, the magnetization area undergoes a significant transformation from a broad region to a narrow strip, which serves as a distinctive characteristic of the parity anomaly in the localized magnetic states. Furthermore, the presence of the parity anomaly leads to notable alterations in the dependence of the magnetic moment and magnetic susceptibility on the Fermi energy. Additionally, we analyze the spectral function of the magnetic impurity as a function of Fermi energy for both the QAH and OI phases.

Suppression of impurity magnetization by the saddle points.

We study the localized magnetic states of an impurity in the semi-Dirac-like system where the saddle point (SP) is present. It is found that with increasing the saddle point energy (SPE), the impurity magnetization region diminishes greatly, and reaches a minimum at the SPE equal to the impurity energy. When continuing to increase the SPE, the impurity magnetization region rapidly becomes large. Correspondingly, an explicit decrease with the SPE close to the impurity energy is also observed in the magnetic moment of the impurity. This suppression behavior for the magnetization of the impurity can be understood from the SP induced mitigation of asymmetry on the density of state at impurity energy. In contrast, when the SP vanishes, due to the opening of the gap, the magnetic region exhibits a monotonous decay when the conduction band edge goes up through the impurity energy. The combined effect of the SP and the Coulomb interaction at the impurity on the local magnetization is also investigated.

Laser-assisted spin-polarized transport in graphene tunnel junctions.

The Keldysh nonequilibrium Green's function method is utilized to theoretically study spin-polarized transport through a graphene spin valve irradiated by a monochromatic laser field. It is found that the bias dependence of the differential conductance exhibits successive peaks corresponding to the resonant tunneling through the photon-assisted sidebands. The multi-photon processes originate from the combined effects of the radiation field and the graphene tunneling properties, and are shown to be substantially suppressed in a graphene spin valve which results in a decrease of the differential conductance for a high bias voltage. We also discuss the appearance of a dynamical gap around zero bias due to the radiation field. The gap width can be tuned by changing the radiation electric field strength and the frequency. This leads to a shift of the resonant peaks in the differential conductance. We also demonstrate numerically the dependences of the radiation and spin valve effects on the parameters of the external fields and those of the electrodes. We find that the combined effects of the radiation field, the graphene and the spin valve properties bring about an oscillatory behavior in the tunnel magnetoresistance, and this oscillatory amplitude can be changed by scanning the radiation field strength and/or the frequency.

Spin-dependent transport for armchair-edge graphene nanoribbons between ferromagnetic leads.

We theoretically investigate the spin-dependent transport for the system of an armchair-edge graphene nanoribbon (AGNR) between two ferromagnetic (FM) leads with arbitrary polarization directions at low temperatures, where a magnetic insulator is deposited on the AGNR to induce an exchange splitting between spin-up and -down carriers. By using the standard nonequilibrium Green's function (NGF) technique, it is demonstrated that the spin-resolved transport property for the system depends sensitively on both the width of AGNR and the polarization strength of FM leads. The tunneling magnetoresistance (TMR) around zero bias voltage possesses a pronounced plateau structure for a system with semiconducting 7-AGNR or metallic 8-AGNR in the absence of exchange splitting, but this plateau structure for the 8-AGNR system is remarkably broader than that for the 7-AGNR one. Interestingly, an increase of the exchange splitting Δ suppresses the amplitude of the structure for the 7-AGNR system. However, the TMR is much enhanced for the 8-AGNR system under a bias amplitude comparable to the splitting strength. Further, the current-induced spin-transfer torque (STT) for the 7-AGNR system is systematically larger than that for the 8-AGNR one. The findings here suggest the design of GNR-based spintronic devices by using a metallic AGNR, but it is more favorable to fabricate a current-controlled magnetic memory element by using a semiconducting AGNR.

Magnetotransport and current-induced spin transfer torque in a ferromagnetically contacted graphene.

We theoretically investigate the spin-dependent transport through a graphene sheet between two ferromagnetic (FM) leads with arbitrary polarization directions at low temperatures, where a magnetic insulator is deposited on the graphene to induce an exchange splitting between spin-up and spin-down carriers. By using standard nonequilibrium Green's function (NGF) techniques, it is demonstrated that the density of states (DOS) decreases for spin-up and increases for spin-down when the polarization strength of the two leads in parallel alignment increases. For the electron energy around the exchange splitting, the DOS for both spin-up and spin-down channels is independent of the polarization. In contrast, the conductance increases for spin-up but decreases for spin-down with an increase of the polarization. Interestingly, the magnitude of tunneling magnetoresistance (TMR) can be dramatically suppressed with the increase of the exchange splitting in graphene. Furthermore, the current-induced spin transfer torque (STT) dependence on the relative angle θ between the magnetic moments of the two leads shows a sine-like behavior and is enhanced with an increase of the polarization and/or the bias voltage. We attribute these spin-resolved effects to the breaking of the insulator-type properties of graphene with an exchange splitting between spin-up and spin-down carriers.

Localized magnetic states in biased bilayer and trilayer graphene.

We study the localized magnetic states of an impurity in biased bilayer and trilayer graphene. It is found that the magnetic boundary for bilayer and trilayer graphene shows mixed features of Dirac and conventional fermions. For zero gate bias, as the impurity energy approaches the Dirac point, the impurity magnetization region diminishes for bilayer and trilayer graphene. When a gate bias is applied, the dependence of impurity magnetic states on the impurity energy exhibits a different behavior for bilayer and trilayer graphene due to the opening of a gap between the valence and the conduction band in the bilayer graphene with an applied gate bias. The magnetic moment and the corresponding magnetic transition of the impurity in bilayer graphene are also investigated.