Using transfer-matrix and stationary phase methods, we study the tunneling time (group delay time) in a ferromagnetic monolayer graphene superlattice. The system we peruse consists of a sequence of rectangular barriers and wells, which can be realized by putting a series of electronic gates on the top of ferromagnetic graphene. The magnetization in the two ferromagnetic layers is aligned parallel. We find out that the tunneling time for normal incident is independent of spin state of electron as well as the barrier height and electron Fermi energy while for the oblique incident angles the tunneling time depends on the spin state of electron and has an oscillatory behavior. Also the effect of barrier width on tunneling time is also investigated and shown that, for normal incident, the Hartman effect disappears in a ferromagnetic graphene superlattice but it appears for oblique incident angles when the x component of the electron wave vector in the barrier is imaginary

Based on transfer-matrix and stationary phase methods, we have investigated the tunneling time (group delay time) through monolayer graphene superlattice in the presence of Rashba spin-orbit interaction. It is found that the tunneling time has an oscillatory behavior with respect to Rashba spin-orbit interaction strength. Furthermore, the tunneling time for normal incident angle is independent of spin state of electron, while for oblique incident angles, it depends on the spin state of electron. It is also shown that, for normal incident, the Hartman effect vanishes, while for oblique incident, the Hartman effect appears whenever the x (the growth direction of superlattice) component of the electron wave vector inside the barriers is imaginary.

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Based on the transfer-matrix method, this paper has investigated the electrical transport properties in monolayer and bilayer graphene superlattices modulated by a homogeneous electric field. It is found that the angular range of the transmission probability can be efficiently controlled by the number of barriers. In addition, current density has an oscillatory behavior with respect to external field and Fermi energy. In other words, the current density in monolayer and bilayer graphene superlattices can be controlled by changing either the external field or the Fermi energy. Meanwhile, in the bilayer system unlike monolayer structure the value of current density can be zero. So, for designing electronic devices, bilayer graphene is more efficient.

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The effect of the strain on the spin and valley dependent transport properties, including the conductance and polarization, through a monolayer MoS2 superlattice under Rashba spin–orbit coupling is theoretically investigated. It is found that the conductance strongly depends on the spin and valley degrees of freedom, and spin-inversion can be achieved by MoS2 superlattice. Also, the spin and valley dependent conductance in a monolayer MoS2 superlattice can be efficiently adjusted via strain and the number of the superlattice barriers. Moreover, it is demonstrated that both the magnitude and sign of the spin and valley polarization depend on the strain strength, the number of barriers, and electrostatic barrier height. Both full spin and valley polarized current (with 100% or − 100% efficiency) can be realized in a MoS2 superlattice under strain.