Heterodyne Hall Effect in a Two Dimensional Electron Gas

TL;DR

This paper explores a novel heterodyne quantum Hall effect in a 2D electron gas with oscillating magnetic and electric fields, revealing frequency-shifted currents and quantum analogues of Landau levels.

Contribution

It introduces the concept of a heterodyne Hall effect driven by time-dependent fields and analyzes its classical and quantum behaviors using Floquet theory.

Findings

Bulk current with frequency shifted by integer multiples of the driving frequency

Classical electron trajectories form loops at specific frequency ratios

Quantum case shows an analogue of Landau quantization

Abstract

We study the hitherto un-addressed phenomenon of Quantum Hall Effect with a magnetic and electric fields oscillating in time with resonant frequencies. This phenomenon realizes an example of heterodyne device with the magnetic field acting as a driving and is analyzed in detail in its classical and quantum versions using Floquet theory. A bulk current flowing perpendicularly to the applied electric field is found, with a frequency shifted by integer multiples of the driving frequency. When the ratio of the cyclotron and driving frequency takes special values, the electron's classical trajectory forms a loop and the effective mass diverges, while in the quantum case we find an analogue of the Landau quantization. Possible realization using metamaterial plasmonics is discussed.