Oscillatory tunneling between quantum Hall systems

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Abstract
Electron tunneling between quantum Hall systems on the same two-dimensional plane separated by a narrow barrier is studied. We show that in the limit where the inelastic scattering time is much longer than the tunneling time, which can be achieved in practice, electrons can tunnel back and forth through the barrier continuously, leading to an oscillating current in the absence of external drives. The oscillatory behavior is dictated by a tunneling gap in the energy spectrum. We shall discuss ways to generate oscillating currents and the phenomenon of natural dephasing between the tunneling currents of edge states. The noise spectra of these junctions are also studied. They contain singularities reflecting the existence of tunneling gaps as well as the inherent oscillation in the system.
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