Circulators Based on Coupled Quantum Anomalous Hall Insulators and Resonators

This paper demonstrates that topological circulators based on coupled quantum anomalous Hall insulators and resonators, modeled by an asymmetric non-Hermitian Hatano-Nelson system, achieve superior non-reciprocal performance with up to 50 dB isolation across a broad power range, offering a promising platform for integrating microwave devices with superconducting quantum information systems.

The Gist

Imagine you are trying to build a city where traffic can only flow in one direction. In the world of electronics, this is called a "non-reciprocal" device. Usually, if you send a signal from Point A to Point B, it's easy for that signal to bounce back from B to A. This "echo" or feedback can ruin sensitive equipment, much like shouting in a canyon and having your own voice bounce back so loudly it drowns out the next person trying to speak.

To stop this, engineers use devices called circulators. Think of a circulator as a magical roundabout for electronic signals. If you enter at the North entrance, you are forced to exit at the East. If you enter at the East, you must exit at the South. You cannot go backward.

The Problem with Old Roundabouts
For a long time, making these electronic roundabouts has been tricky. They often work well only if you shout (send power) at them just the right amount. If you whisper too softly or shout too loudly, the roundabout stops working, and the traffic gets stuck or goes the wrong way. This is a big problem for quantum computers and ultra-sensitive detectors, which often need to operate with extremely faint signals (whispers).

The New Solution: A One-Way River
In this paper, the researchers built a new kind of circulator using a special material called a Quantum Anomalous Hall (QAH) insulator.

To understand how this works, imagine the edge of this material as a one-way river.

• The River (Edge Magnetoplasmons): Inside this material, electricity doesn't flow everywhere; it flows only along the very edge, like water in a river. Because of the material's special "topological" nature, this river only flows in one direction (clockwise or counter-clockwise). It's impossible for the water to flow backward.
• The Boats (LC Resonators): The researchers attached two small "boats" (electronic circuits called LC resonators) to the banks of this river.
• The Magic Trick: They arranged the boats so that the river connects them in a very specific way. When a signal (a wave) enters the first boat, it hops onto the one-way river, travels around the edge, and lands perfectly in the second boat.

The "Hatano-Nelson" Effect
The paper describes this setup using a mathematical model called the Hatano-Nelson model. In simple terms, this model explains how the connection between the two boats is "asymmetric."

• Imagine trying to walk from your house to a friend's house. Usually, the path is the same both ways.
• In this device, the path from House A to House B is a smooth, open highway.
• But the path from House B back to House A is blocked by a giant wall and a maze.
• Because of this, the signal flows easily one way but is almost completely stopped the other way.

The Results: A Super-Strong One-Way Street
The researchers tested this new device and found some impressive things:

1. It works with whispers: Unlike older devices that need a loud signal to work, this one works perfectly even when the signal is incredibly faint (as low as -149 dBm). This is crucial for quantum computers, which deal with very weak signals.
2. It blocks the echo: It achieved a "isolation" of up to 50 dB. To use an analogy, if you shout "Hello" into the device, the person on the other side hears it clearly, but the person trying to shout back hears nothing but silence. It's like having a soundproof wall that only works in one direction.
3. It's stable: The device kept working well across a wide range of power levels, from very quiet to moderately loud.

Why This Matters
The paper suggests that this new way of building circulators—using the "one-way river" of a magnetic topological insulator—is a major step forward. It offers a way to protect sensitive quantum computers from noise and helps in detecting dark matter (which requires listening to the faintest whispers in the universe) without the signal getting messed up by feedback.

In short, they built a traffic cop for electrons that never gets tired, works even with the tiniest signals, and ensures that traffic always goes the right way.

Technical Summary

Technical Summary: Circulators Based on Coupled Quantum Anomalous Hall Insulators and Resonators

Problem Statement
Integrated plasmonics is rapidly advancing, yet the development of integrated non-reciprocal devices remains a critical bottleneck for applications in information processing, quantum sensing, and dark-matter detection. While non-reciprocal devices have been realized in edge magnetoplasmon (EMP) materials via classical interference, their operational utility is often constrained by a limited input power range. Furthermore, while non-Hermitian systems (specifically Hatano–Nelson types) offer theoretical potential for realizing isolators through asymmetric coupling and exceptional points (EPs), accessing strongly asymmetric transport regimes in practical EMP systems has remained largely unexplored. There is a need for a platform that can engineer asymmetric non-Hermitian couplings at radio frequencies (RF) with robust performance across a wide dynamic range, particularly for integration with superconducting quantum circuits where magnetic fields can be detrimental.

Methodology
The authors investigate a hybrid system comprising a Quantum Anomalous Hall (QAH) insulator, specifically Cr-doped (Bi$_x$Sb$_{1-x}$)$_2$Te$_3$, coupled to external LC resonators. The device architecture features a circular QAH mesa (100 $\mu$m radius) with a chiral edge conductance of $e^2/h$. Three lumped-element wire-loop inductors (180 nH) are wire-bonded to the mesa, forming LC resonators that capacitively couple to the edge magnetoplasmonic modes via an edge capacitor ($C_{edge}$).

Theoretical modeling treats the system as a non-Hermitian four-mode coupled-mode matrix, which is reduced to an effective two-site Hatano–Nelson model. In this model, the coupling between the two LC resonators (ports 1 and 3) is mediated by the chiral EMP modes propagating along the mesa edge. The model posits that asymmetric directional couplings ($\lambda_{ab}$ and $\lambda_{ba}$) arise from the interference between the chiral plasmonic pathway and parasitic capacitive pathways. The system is characterized experimentally in a dilution refrigerator at approximately 10 mK, measuring transmission coefficients ($S_{31}$ and $S_{32}$) across a broad range of input microwave powers (from -149 dBm to -90 dBm) and frequencies (450–650 MHz).

Key Contributions

1. Demonstration of Asymmetric Non-Hermitian Coupling: The work provides experimental evidence that a QAH-based plasmonic system can be described by an effective Hatano–Nelson model with asymmetric directional couplings. The non-reciprocal behavior is driven by the interference between the chiral EMP propagation and parasitic capacitance, leading to direction-dependent coupling strengths.
2. Power-Dependent Non-Reciprocity: The study identifies a mechanism where the coupling strength and phase accumulation are sensitive to input microwave power. This allows for the dynamic modulation of the interference condition, enabling the system to reach a regime of strong directional suppression.
3. High-Performance Circulator Operation: The device functions as a circulator with a broad operational bandwidth and exceptional isolation metrics, specifically tailored for low-power quantum applications.

Results

• Isolation and Bandwidth: The coupled system exhibits an average isolation of 20 dB over a bandwidth of approximately 50 MHz. At a specific frequency of 543.8 MHz and an input power of -119 dBm, the device achieves a peak isolation exceeding 50 dB.
• Power Range: The circulator remains operational down to input powers of -149 dBm, with stable non-reciprocal behavior observed over a range spanning more than 50 dBm (from -150 to -90 dBm). This represents a significant improvement in power handling compared to previous EMP-based non-reciprocal devices.
• Transmission and Phase: The device demonstrates a transmission dip in the $S_{31}$ channel (port 1 to 3) accompanied by a positive $\pi$ phase shift relative to the $S_{32}$ channel. This sharp transmission contrast and phase transition occur within a narrow input-power window, consistent with the system approaching an exceptional point where eigenvalue and eigenvector coalescence occurs.
• Insertion Loss: The LC-resonator-coupled configuration achieves an insertion loss of approximately 6 dB at the transmission peak, attributed to impedance matching between the port impedance and the high-impedance QAH edge state ($Z \sim 25.8$ k$\Omega$).
• Model Validation: Experimental transmission spectra and phase responses align qualitatively with the effective two-site Hatano–Nelson model. Theoretical fits using coupled-mode theory successfully reproduce the observed Lorentzian-like resonance and phase shifts, with fitted parameters indicating power-dependent changes in coupling strength ($g$) and dissipation ($\kappa_m$).

Significance and Claims
The authors claim that these results demonstrate a new mechanism for harnessing the intrinsic unidirectionality of QAH edge states to engineer non-reciprocal devices. The work highlights that magnetic topological insulators provide a promising platform for realizing asymmetric non-Hermitian couplings at radio frequencies. The device's ability to operate at ultra-low input powers makes it particularly suitable for integration with superconducting quantum information platforms, where protecting qubits from amplifier back-action is critical. Additionally, the broadband, low-noise signal routing capabilities are relevant for axion dark matter searches (e.g., ADMX). The paper suggests that this approach could facilitate the realization of topological circulators with near-unitary forward transmission and exceptionally high reverse isolation, potentially extending to higher microwave frequencies through device scaling and material engineering. The results also open avenues for exploring regimes of strong directional suppression and exceptional-point physics in microwave devices.