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We investigate theoretically the Landau levels (LLs) and magneto-transport properties of phosphorene under a perpendicular magnetic field within the framework of the effective k·p Hamiltonian and tight-binding (TB) model. At low field regime, we find that the LLs linearly depend both on the LL index n and magnetic field B, which is similar with that of conventional semiconductor two-dimensional electron gas. The Landau splittings of conduction and valence band are different and the wavefunctions corresponding to the LLs are strongly anisotropic due to the different anisotropic effective masses. An analytical expression for the LLs in low energy regime is obtained via solving the decoupled Hamiltonian, which agrees well with the numerical calculations. At high magnetic regime, a self-similar Hofstadter butterfly (HB) spectrum is obtained by using the TB model. The HB spectrum is consistent with the LL fan calculated from the effective k·p theory in a wide regime of magnetic fields. We find the LLs of phosphorene nanoribbon depend strongly on the ribbon orientation due to the anisotropic hopping parameters. The Hall and the longitudinal conductances (resistances) clearly reveal the structure of LLs.

A high-efficiency rectenna element has been designed and tested at 5.8 GHz for applications involving microwavepower transmission. The dipole antenna and filtering circuitry are printed on a thin duroid substrate. A silicon Schottkybarrier mixer diode with a low breakdown voltage is used as the rectifying device. The rectenna element is tested inside a waveguide simulator and achieves an RF-to-dc conversion efficiency of 82% at an input power level of 50-mW and 327-load. Closed-form equations are given for the diode efficiency and input impedance as a function of input RF power. Measured and calculated efficiency results are in good agreement. The antenna and circuit design are based on a full-wave electromagnetic simulator. Second harmonic power levels are 21 dB down from the fundamental input power.