The conductance oscillation pattern is mediated both by magnetic field and the carrier concentration on bipolar regions. At higher magnetic field, the p–n junction subjected to the quasi-classical regime and the formation of snake states results in periodical backscattering and transmission as magnetic field varies. Under low magnetic field, the transport is determined by the resonant tunneling of Landau levels and conductance versus magnetic field shows a Shubnikov–de Haas oscillation. The electronic transport of graphene p–n junctions under perpendicular magnetic field is investigated in theory. Magnetic field mediated conductance oscillation in graphene p–n junctions With his contributions to the field of quantum It was quite surprising that " magnetic interaction" conditions could cause the apparently weak quantum oscillation effect to have such strong consequences as breaking the sample into magnetic (now called "Shoenberg") domains and forming an inhomogeneous magnetic state. In his pioneering experiments of the 1960's, Shoenberg revealed the richness and deep essence of the quantum oscillation effect and showed how the beauty of the effect is disclosed under nonlinear conditions imposed by interactions in the system under study. Since then, quantum oscillations have been widely used as a tool for measuring Fermi surface extremal cross-sections and all-angle electron scattering times. These theoretical advances seemed to provide a comprehensive description of the effect. Onsager in 1952, and an analytical quantitative theory by I. A theoretical explanation of quantum oscillations was given by L. In particular, he developed techniques for quantitative measurement of this effect in many metals. After that, the dHvA effect became one of his main research topics. Marcus observed similar oscillations in zinc and that persuaded Schoenberg to return to this research. In 1938 Shoenberg went from Cambridge to Moscow to study these oscillations at Kapitza's Institute where liquid helium was available at that time. Shoenberg, whose first research in Cambridge had been on bismuth, found that much stronger oscillations are observed when a bismuth sample is cooled to liquid helium temperature rather than liquid hydrogen, which had been used by de Haas. Studying single crystals of bismuth, they observed oscillatory variations in the magnetization and magnetoresistance with magnetic field. Shubnikov and de Haas when measuring magnetoresistance. van Alphen when measuring magnetization, and by L. The quantum oscillation effect was discovered in Leiden in 1930, by W. Magnetic-field-mediated gates have the potential to significantly reduce the overhead in laser-beam control and motional-state initialization compared to current QIP experiments with trapped ions and will eliminate spontaneous scattering, a fundamental source of decoherence in laser-mediated gates.ĭavid Shoenberg and the beauty of quantum oscillations With fields generated by currents in microfabricated surface-electrode traps, it should be possible to achieve gate speeds that are comparable to those of optically induced gates for realistic distances between the ion crystal and the electrode surface. Oscillating magnetic fields and field gradients can be used to implement single-qubit rotations and entangling multiqubit quantum gates for trapped-ion quantum information processing (QIP). Ospelkaus, C Langer, C E Amini, J M Brown, K R Leibfried, D Wineland, D J Trapped-ion quantum logic gates based on oscillating magnetic fields. The observed quantum oscillations can be attributed to bulk and surface transport. Submicron scale devices exhibit intriguing quantum oscillations at high magnetic fields with dependence on bias voltage. In Hall bar devices, we observe logarithmic dependence of transport coefficients in temperature and bias voltage which can be understood to arise from electron-electron interaction corrections to the conductivity and self-heating. We report magnetotransport measurements on magnetically doped (Bi,Sb ) 2Te3 films grown by molecular beam epitaxy. Logarithmic singularities and quantum oscillations in magnetically doped topological insulators
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