[en] By using the Faddeev—Senjanovic path integral quantization method, we quantize the composite fermions in quantum electrodynamics (QED). In the sense of Dirac's conjecture, we deduce all the constraints and give Dirac's gauge transformations (DGT). According to that the effective action is invariant under the DGT, we obtain the Noether theorem at the quantum level, which shows the fractional charges for the composite fermions in QED. This result is better than the one deduced from the equations of motion for the statistical potentials, because this result contains both odd and even fractional numbers. Furthermore, we deduce the Noether theorem from the invariance of the effective action under the rotational transformations in 2-dimensional (x, y) plane. The result shows that the composite fermions have fractional spins and fractional statistics. These anomalous properties are given by the constraints for the statistical gauge potential. (general)

[en] Electronic transport of graphene through a modulated magnetic superlattice where the barrier heights present Gaussian profile is studied. It is found that the incident electron could be completely transmitted in the miniband regions and be completely reflected in the bandgap regions. The results suggest an application of the structure as an effectively band pass filter, which can be controlled by the structural parameters. It is concluded that the positions of miniband and bandgap are robust to the Gaussian variation of barrier heights. The effect of this modulated magnetic superlattice is also available for the conventional electrons described by Schrödinger equation

[en] We study the transmission through a step-barrier in gapped graphene and propose a method to enlarge the band gap. The step-barrier structure consists of two or more barriers with different strengths. It is found that the band gap could be effectively enlarged and controlled by adjusting the barrier strengths in the light of the mass term. Klein tunneling at oblique incidence is suppressed due to the asymmetry of step-barrier, contrary to the cases in single-barrier and superlattices. Furthermore, a tunable conductance channel could be opened up in the conductance gap, suggesting an application of the structure as an electron switch

[en] A model including a periodically corrugated thin layer with a GaAs substrate is employed to investigate the effects of the corrugations on the transmission probability of the nanostructure. We find that transmission gaps and resonant tunneling domains emerge from the corrugations, in the tunneling domains the tunneling peaks and valleys result from the boundaries between adjacent regions in which an electron has different effective masses, and can be slightly modified by the layer thickness. These results can provide a way to design a curvature-tunable filter. (paper)

[en] We studied the effect of a defect of superlattice on the spin and valley dependent transport properties in silicene, where there is an abnormal barrier in height. It is found that the transmission resonance is greatly suppressed, because the symmetry of superlattice structure is destroyed by the defect. The spin-up and spin-down electrons near the K and $K\prime$ valleys are dominated by different effective superlattices and defects. Therefore, the conductances are strongly dependent on the spin and valley of electron. By adjusting the defect strength properly, the spin and valley polarizations could be dramatically enhanced in a wide energy region. Furthermore, the result suggests an application of the structure as a defect-controlled switch.

[en] We study the transmission of Dirac electrons through the one-dimensional periodic, Fibonacci, and Thue–Morse magnetic superlattices (MS), which can be realized by two different magnetic blocks arranged in certain sequences in graphene. The numerical results show that the transmission as a function of incident energy presents regular resonance splitting effect in periodic MS due to the split energy spectrum. For the quasiperiodic MS with more layers, they exhibit rich transmission patterns. In particular, the transmission in Fibonacci MS presents scaling property and fragmented behavior with self-similarity, while the transmission in Thue–Morse MS presents more perfect resonant peaks which are related to the completely transparent states. Furthermore, these interesting properties are robust against the profile of MS, but dependent on the magnetic structure parameters and the transverse wave vector.