Abstract: Magnetotransport in bilayer graphene in the presence of a weak and periodic potential is investigated in the presence of a perpendicular magnetic field B. The modulation broadens the Landau levels into bands and for weak magnetic fields leads to the well-known Weiss oscillations in their bandwidth and their transport coefficients at very low B and to the Shubnikov-de Haas oscillations at larger B. The amplitude of the Weiss oscillations is severely reduced if the periodic potentials applied to the two layers oscillate out of phase. We also contrast some results with those corresponding to single-layer graphene. Relative to them the flat-band condition and the oscillation amplitude differ substantially, due to the interlayer coupling, and agree only when this coupling is extremely weak. We further show that the Hall conductivity exhibits the well-known steps at half-integer and integer multiples of 4e(2)/h in single-layer and bilayer graphene, respectively, even for very weak magnetic fields. The results are pertinent to weak and periodic corrugations when the potential modulation dominates the strain-induced magnetic modulation.

Abstract: Electron transport through multiterminal rectangular arrays of quantum rings is studied in the presence of Rashba-type spin-orbit interaction (SOI) and of a perpendicular magnetic field. Using the analytic expressions for the transmission and reflection coefficients for single rings we obtain the conductance through such arrays as a function of the SOI strength, of the magnetic flux, and of the wave vector k of the incident electron. Due to destructive or constructive spin interferences caused by the SOI, the array can be totally opaque for certain ranges of k, while there are parameter values where it is completely transparent. Spin resolved transmission probabilities show nontrivial spin transformations at the outputs of the arrays. When pointlike random scattering centers are placed between the rings, the Aharonov-Bohm peaks split, and an oscillatory behavior of the conductance emerges as a function of the SOI strength.

Abstract: The electronic properties of monolayer phosphorene are exotic due to its puckered structure and large intrinsic direct band gap. We derive and discuss its band structure in the presence of a perpendicular magnetic field. Further, we evaluate the magneto-optical Hall and longitudinal optical conductivities as functions of temperature, magnetic field, and Fermi energy, and show that they are strongly influenced by the magnetic field. The imaginary part of the former and the real part of the latter exhibit regular interband oscillations as functions of the frequency omega in the range (h) over bar omega similar to 1.5-2 eV. Strong intraband responses in the latter and weak ones in the former occur at much lower frequencies. The magneto-optical response can be tuned in the microwave-to-terahertz and visible frequency ranges in contrast with a conventional two-dimensional electron gas or graphene in which the response is limited to the terahertz regime. This ability to isolate carriers in an anisotropic structure may make phosphorene a promising candidate for new optical devices.

Abstract: We study magnetic flux interacting with arrays of pinning sites (APSs) placed on vertices of hyperbolic tesselations (HTs). We show that, due to the gradient in the density of pinning sites, HT APSs are capable of trapping vortices for a broad range of applied magnetic fluxes. Thus, the penetration of magnetic field in HT APSs is essentially different from the usual scenario predicted by the Bean model. We demonstrate that, due to the enhanced asymmetry of the surface barrier for vortex entry and exit, this HT APS could be used as a “capacitor” to store magnetic flux.