研究目的
To study the evolution of the integer quantum Hall effect at high frequencies (69–1100 GHz) in GaAs/AlGaAs heterojunctions, focusing on the behavior of Hall conductivity beyond the previously explored range.
研究成果
The integer quantum Hall effect plateaus in Hall conductivity disappear above approximately 100 GHz, replaced by weak quantum oscillations that diminish with increasing frequency. No quantization features are observed near 1 THz. The imaginary part of the conductivity shows oscillations not present at zero frequency. These findings contradict some existing theoretical predictions and highlight the need for improved models and further experimental studies on samples with varying mobilities and masses to fully understand the high-frequency QHE.
研究不足
The experimental setup was limited by sample dimensions, affecting measurements at lower frequencies due to diffraction corrections. The method could not fully eliminate depolarization effects from optical imperfections. Theoretical models did not satisfactorily describe the observed high-frequency behavior, indicating a need for further development. The study was conducted on specific GaAs/AlGaAs samples, and results may not generalize to other materials without additional experiments.
1：Experimental Design and Method Selection:
The study used continuous-wave terahertz spectroscopy with a two-beam Mach-Zehnder interferometer to measure the complex Hall conductivity. The method involved transmission spectroscopy of a two-dimensional electron gas (2DEG) under a magnetic field, where linearly polarized incident waves become elliptically polarized after passing through the sample. The complex transmission coefficients were measured and used to calculate Hall conductivity without additional model assumptions.
2：Sample Selection and Data Sources:
Two GaAs/AlGaAs heterojunctions (Sample 1 and Sample 2) grown by molecular beam epitaxy were used. Their parameters (electron density, mobility, relaxation time, cyclotron mass, size) were characterized at 1.9 K using dc and spectroscopic experiments. Samples were selected for their suitability in studying dc QHE, with differences in silicon doping levels affecting electron properties.
3：9 K using dc and spectroscopic experiments. Samples were selected for their suitability in studying dc QHE, with differences in silicon doping levels affecting electron properties.
List of Experimental Equipment and Materials:
3. List of Experimental Equipment and Materials: Equipment included backward wave oscillators (BWOs) for generating continuous monochromatic waves, a two-beam Mach-Zehnder interferometer, dielectric lenses, metallic mirrors, freestanding wire-grid polarizers, a helium-cooled Si bolometer for intensity measurement, a superconducting magnet with optical windows, and indium electrical contacts. Materials included GaAs/AlGaAs heterostructure samples, liquid helium for cooling, and black paper to block visible light and avoid persistent photoconductivity effects.
4：Experimental Procedures and Operational Workflow:
Samples were cooled to 1.9 K in a superconducting magnet. Transmission coefficients (parallel and crossed) were measured at fixed frequencies by filtering polarized components and using a reference beam for phase shifts. Data were symmetrized to reduce depolarization effects. Simultaneous dc resistance measurements were conducted to monitor effects of THz radiation. Frequencies were chosen near transmission maxima of the substrate to enhance signal quality.
5：9 K in a superconducting magnet. Transmission coefficients (parallel and crossed) were measured at fixed frequencies by filtering polarized components and using a reference beam for phase shifts. Data were symmetrized to reduce depolarization effects. Simultaneous dc resistance measurements were conducted to monitor effects of THz radiation. Frequencies were chosen near transmission maxima of the substrate to enhance signal quality.
Data Analysis Methods:
5. Data Analysis Methods: Complex Hall conductivity was calculated from transmission coefficients using a derived formula. Classical Drude theory was used for fitting to obtain parameters like cyclotron mass and relaxation time. Quantum deviations from classical behavior were analyzed by subtracting Drude fits from experimental data. Data were plotted as functions of magnetic field and filling factor to observe frequency-dependent evolution.
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