We report quantitative microwave Faraday rotation measurements conducted with a high-mobility two-dimensional electron gas (2DEG) in a GaAs/AlGaAs semiconductor heterostructure. In a magnetic field, the Hall effect and the Faraday effect arise from the action of Lorentz force on electrons in the 2DEG. As with the Hall effect, a classical Faraday effect is observed at low magnetic field along with a quantized Faraday effect at high magnetic field. The high electron mobility of the 2DEG enables a giant single-pass Faraday rotation of ${\theta }_F^{\max }\simeq {45}^{\circ }(\simeq 0.8$ rad) to be achieved at a modest magnetic field of $B\simeq 100$ mT. In the quantum regime, we find that the Faraday rotation ${\theta }_F$ is quantized in units of ${\alpha }^{*}=2.80\left(4\right)\alpha$, where $\alpha \simeq 1/137$ is the fine-structure constant. The enhancement in rotation quantum ${\alpha }^{*}>\alpha$ is attributed to electromagnetic confinement within a waveguide structure.

• Received 8 August 2019
• Revised 19 May 2020
• Accepted 15 July 2020

DOI:https://doi.org/10.1103/PhysRevB.102.085302