Webinar Q&A Summary - Quantum Hall Resonances: A Wideband Detection
In this webinar, we had the pleasure of hosting Gerbold Ménard from the ENS Paris, who presented recent results on gate-tunable Edge Magneto-Plasmon (EMP) resonators in the quantum Hall regime. This research, published in Communication Physics journal, shows a new platform for probing collective excitations in two-dimensional electron gases (2DEGs) under strong magnetic fields.
The ENS team fabricated micrometer-scale resonators where the resonance frequency can be finely tuned using both magnetic fields and electrostatic gates. By reducing the cavity size, they revealed finite-size effects where the measurement probes themselves become part of the resonator. These experiments show continuous control of the resonance frequency in the 0.5–8.5 GHz range, with quality factors up to ~18, opening the way for interferometric devices that could probe anyonic quasiparticles relevant for topological material and computing.
The Zurich Instruments SHFLI GHz Lock-in Amplifier (with a frequency range of 100 MHz to 8.5 GHz) played a key role in the detection, enabling wideband measurements with high sensitivity at cryogenic temperatures.
Q&A Highlights
The session closed with lively discussions. Participants raised the following questions:
Thank you for the presentation. I noticed that the SNR could be a problem in your devices, as you stated in the presentation. Is it possible to increase that by cascading multiple devices?
Answer: Cascading multiple devices is probably not a good solution for our system. I see two main reasons why. First, two devices are never exactly identical, no matter how close they might be on a design level. This might be due to local impurities, defects in fabrication, misalignment, 2DEG defects or other. For this reason, two QPCs on two different devices might have different working parameters and then we would have to tune not only one device but two in order to reach the same configuration, all that before even turning on the rf excitation. The second issue is due to dissipation in the system. The low quality factor of our device is most likely due to some parasitic capacitances in our system (to gates, to the ground, etc.). Therefore, adding a second cascading device would only increase the dissipation and thus reduce the resulting signal to noise ratio even more.
I was wondering if you were able to notice any phase shift between input and output besides resonance measurement. Could you perform frequency tracking?
Answer: We do measure the full R and theta measurement of the signal. As such, we do have access to the phase. We can have phase maps that show the resonance. However this is a signal even harder to see than the bare resonance (mostly due to phase wrapping) and therefore it is more convenient to concentrate on the amplitude signal. Concerning frequency tracking, if I understand correctly, you would be talking about time variation of the resonance frequency. This could be done in principle and would correspond to a tank circuit measurement at high frequency. Given the current quality of our signal, this would produce poor results. However, in the future, if we manage to increase our signal quality, this could theoretically be doable, but we are far from the sensitivity of other methods currently used for this.
Sending signal at the GHz can lead to many reflections in the signal path and in the cryostat. How do you make sure that the signal you send is the one actually reaching your sample or that you don't create other typesmof interferences?
Answer: Indeed, the frequency range at which we are operating creates issues linked to reflection on the measurement line and other resonances. The way we discriminate between those and the actual signal we are interested in is two-fold. First, by looking at the magnetic field dependence, any change that we might observe will be linked only to the part of the measurement setup that are field sensitive. In our fridge, only the sample is sensitive to the field. As such, we can compare our signal at different magnetic fields and from that extract a reference signal that includes all resonances and mess from the measurement line and subtract it from the raw signal. The second way we can make sure that our signal is really linked to the device is through the use of our electrostatic gates. Indeed, if we decide to open a QPC used originally to define the cavity, then our signal should disappear. And we could actually check that it is the case and from that extract only the relevant signal.
Your measured Quality factor is rather small (<18). Would you benefit from higher sensitivity if you could improve it, and what would be your strategy to reach higher Q ?
Answer: Yes, a larger quality factor would definitely be beneficial. It would be especially interesting in a device with a smaller quality factor to investigate whether we might observe signal from other modes (linked to the complex combination of the different edge states that play a role at fillings factors larger than 1). Also, a larger quality factor would probably lead to clearer gaps in between plateaus of the quantum Hall effect and thus give us better confidence in our extraction of parameters in a given configuration. The origin of this low Q is probably the capacitive coupling to the different elements of the environment. As such, one goal could be to use some specifically designed gates that would be transparent to rf signal (like Zn oxyde). We would then need to properly model our system to estimate the main cause of dissipation. Some effort working on the quality of the 2DEG might also improve the signal level, but that is still an open question.
Can you explain what would be the problem with adding a circulator into the setup? Can it be done at low temperature?
Answer: Adding a circulator to the system would (in theory) be great. However, while we have large band circulators, it is still limited and cannot usually cover the full frequency range of our measurement. Apart from this minor detail, circulators react badly to magnetic fields. In order to fit one in our refrigerator, we have no way to shield it from the strong magnetic fields that we need to apply in order to generate our resonances. After attempting it, the frequency response of the circulator simply changes two much between 1 T and 8 T such that we cannot reliably perform the calibration procedure that we usually do. Some fridges are equipped with field cancellation at the level of the mixing chamber and in that case a circulator could be used.
Outlook
These results highlight how GHz lock-in technology accelerates the study of quantum Hall physics, enabling measurements with unprecedented bandwidth and sensitivity at cryogenic temperatures. Looking ahead, this platform may become a crucial building block for interferometric experiments aimed at detecting exotic quasiparticles.
- Watch the full webinar replay here: YouTube link
- Learn more about the SHFLI GHz Lock-in Amplifier: Product page
- Contact our experts to discuss how wideband detection can advance your research.