Introduction

Resonators can take multiple forms and use various mechanisms. The first one most of us ever encounter are swings. From an early age we are taught how to move our bodies forward or backward in rhythm with the balancing movement so as to get as high as possible. In our recently published work [1] we apply the same kind of reasoning to a very different object. Our work focuses on Edge-MagnetoPlasmon (EMP) resonators which are built out of GaAs heterostructures. These heterostructures harbor a two-dimensional electron gas of very high purity and under a perpendicular external magnetic field manifest a phenomenom called the quantum Hall effect. In such state, the 2DEG becomes insulating in its bulk, leaving only its edge to be conductive. These edge states are chiral, meaning that the direction of the magnetic field imposes a direction for the current with no back-scattering allowed.  EMPs are the elementary excitations of these conducting edges and also propagate chirally. By looping the edge states onto themselves, we have created an EMP resonator whose resonant condition depend on the velocity v of the EMPs and the length L of the loop through f≈v/L.

Experimental procedure

In order to probe such resonance, we excite (the push a child receives on the swing) our system using an radiofrequency radiation in the GHz range. When the frequency of the incoming wave is equal to the intrinsic frequency of the resonator, then the signal gets amplified and can be detected at the other side (imagine pushing a swing hard enough that the feet of the child then hit the face of the person in front of the swing). The detected signal is then amplified and measured using a lock-in amplifier as a function of  the magnetic field and other parameters.

The schematics of the device used in our study is shown below. The shape of our resonant cavity is defined electrostatically with gates. It allows us to define different sizes of the resonator. The radiofrequency signal (the adult pushing the swing) is sent to the EMPs via one of the gates coupled capacitively to the two-dimensional electron gas and is collected (the person getting hit by the child's feet in the face) by a different one, that is larger so as to measure a stronger signal.

In the schematics below, we use the central brown gate (top part of a QPC) to inject the microwave signal. The detector/output gate is the large gate on the left of the device, also shown in brown. We use a large gate in order to detect as strong a signal as possible.

Results

Using this set of gates we are able to study the evolution of the resonance frequency as a function of the size of the resonator. The five QPCs can selectively be activated (being off or on) so as to  decrease or increase the size of the resonator. Doing so, we can change the perimeter from 30 to 42 µm. In each case we find that the resonance follows a 1/B behavior (where B is the amplitude of the magnetic field).

However, we find that the f=v/L relation does not hold for very small (~20 µm sized) cavities. Using a magnetoplasmon scattering formalism we elucidate the role of the input and output gates and in particular how their spatial extension explain the deviation from the 1/L law. In particular, the detection gate plays the most important role as it does cover most of the two-dimensional electron gas. In our simulations we find that the linear behavior is recovered for large cavities.

On top of the fundamental resonance of our system, we also observe the first harmonic of the signal. This harmonic corresponds to existing the EMPs twice as fast so that the wavelength is divided by two compared to the fundamental mode. This harmonic disappears when the cavity is reduced in size. We explain this disappearance by finite-size filtering effects of the detection gate and compare our results with numerical simulations based on the physical parameters of our experiment.

We also show that the gates can be manipulated continuously so as to tune the resonance frequency as desired. By applying a negative voltage only on the bottom part of the QPCs, then we do not completely close cavities but deviate sufficiently the magnetoplasmons to increase the size of the cavity to a detectable value. This opens ways for realizing interferometers in the future by transforming the single cavity into two cavities interconnected by a QPC. 

Future studies

Our goal for the future is to transform such device into a radiofrequency interferometer. Adding a tunnel junction in the cavity effectively creates a beam splitter for the EMPs, creating the interferometer. Following the theoretical description of Cano et al. [2] such scheme would allow us to probe the interference between the path of EMPs in both cavities under the effect of the external magnetic field. More interestingly, such device would be a powerful tool to detect exotic phases of matter, namely abelian and non-abelian anyons. These anyons are quasiparticles that are neither bosons nor fermions and can be "braided" so that the history of their manipulation can be encoded in the phase of their wavefunction. The plasmonic interferometer would allow us to study these new types of quasiparticles and better understand their behavior.

References

[1] E. Frigerio et al. Comm. Phys. 7, 314 (2024).

[2] J. Cano et al. Phys. Rev. B 88, 165305 (2013).