Breakdown of the quantum anomalous Hall effect under microwave drives

Technical Summary: Breakdown of the Quantum Anomalous Hall Effect under Microwave Drives

Problem Statement
Quantum Anomalous Hall (QAH) insulators, such as vanadium-doped (Bi,Sb)₂Te₃ (V-BST), exhibit chiral dissipationless edge states without external magnetic fields, making them promising candidates for quantum metrology and non-reciprocal microwave components. However, the practical application of these materials is hindered by the breakdown of the zero-resistance state at low currents and temperatures. This breakdown is attributed to dissipative bulk transport mechanisms, including variable-range hopping (VRH), electron heating, and percolation through charge puddles formed by Coulomb disorder. While low- and high-frequency longitudinal dissipation signatures of VRH have been observed, the specific mechanisms driving the breakdown of QAH systems under microwave (RF) fields (1–25 GHz) remain largely unexplored. A critical question is whether RF photons directly promote hopping (photon-assisted VRH) or if RF signals induce Joule heating that elevates the electron temperature, thereby increasing bulk transport.

Methodology
The authors investigated the breakdown of the QAH state using V-BST films (8 nm thick) grown via molecular beam epitaxy and capped with Al₂O₃. They fabricated two distinct device geometries:

1. RF Hall Bars (Samples A and C): Used to measure longitudinal resistance ($R_{xx}$) and transverse Hall resistance ($R_{yx}$).
2. RF Corbino Rings (Sample B): Used to directly measure bulk conductance, isolating edge contributions.

The experiments were conducted in a dilution refrigerator with a base temperature below 20 mK. Microwave signals (1–25 GHz) were applied via narrow capacitive contacts connected to a Vector Network Analyzer (VNA). To probe the breakdown frequency-independently, the authors measured the longitudinal DC conductance ($\sigma = \sigma_{xx}$) using a small probe current (1 nA) while applying varying RF amplitudes ($U$) and frequencies ($f$). They systematically analyzed the dependence of $\sigma$ on RF amplitude, frequency, sample temperature ($T_p$), and DC bias current ($I_{DC}$).

Key Results

• Frequency and Amplitude Dependence: The longitudinal conductance $\sigma$ remains at a residual value at low RF amplitudes but exhibits a sharp increase (breakdown) once a threshold amplitude ($U_{BD}$) is exceeded. This threshold $U_{BD}$ decreases significantly as the microwave frequency increases.
• Temperature Dependence: At higher sample temperatures, the breakdown effect becomes less visible and shifts to higher RF amplitudes. Conversely, at very low temperatures, the conductance increases sharply with RF amplitude.
• DC and RF Mixed Bias: Under mixed DC and RF biases, the conductance saturates at a minimum value dependent on the RF amplitude before increasing sharply with DC current. The breakdown curves overlay at very high DC currents, independent of the RF amplitude.
• Model Validation: The authors tested photon-assisted VRH and quantum Hall transition models but found them unsatisfactory. Instead, the data is well-described by a Joule heating model. In this model, RF power is absorbed by electron-hole puddles, raising the electron temperature ($T_e$) above the lattice temperature ($T_p$). The increased $T_e$ activates phonon-assisted variable-range hopping, increasing bulk conductance.
• Quantitative Fits:
  • The cooling power follows a power law $P_{out} = \Sigma(T_e^\alpha - T_p^\alpha)$ with $\alpha \approx 3.5$ (RF regime) to $4$ (DC regime).
  • The effective conductance absorbing RF power, $G(\omega)$, scales with frequency as $G(\omega) \propto \omega^s$ with $s \approx 1.05$. This linear scaling suggests absorption by finite-size puddles for frequencies below the inverse Thouless time ($f < 1/\tau_{Th}$).
  • The breakdown threshold amplitude follows the prediction $U_{BD} \propto 1/\sqrt{\omega}$, derived from the condition of constant heating power required to reach the breakdown conductance.

Key Contributions

1. Mechanism Identification: The study definitively identifies RF-induced heating of electron-hole puddles as the primary driver for the breakdown of the QAH state under microwave irradiation, ruling out direct photon-assisted hopping as the dominant mechanism in this regime.
2. Microscopic Modeling: The authors provide a microscopic model linking RF absorption in charge puddles to electron heating and subsequent VRH transport. This model successfully reproduces the dependence of conductance on RF amplitude, frequency, and temperature without adjustable parameters once initial DC parameters are fixed.
3. Frequency Scaling Law: The work establishes a quantitative scaling law for the breakdown threshold ($U_{BD} \propto 1/\sqrt{\omega}$), providing a predictive tool for the performance limits of QAH devices at GHz frequencies.

Significance
The paper claims that its findings are critical for the development of GHz-range QAH applications. By demonstrating that the zero-resistance state breaks down due to heating in charge puddles, the study highlights a fundamental limitation for using QAH insulators in lossless high-frequency quantum devices. The results clarify that both the role of disorder (puddles) and AC dissipation (heating) are intertwined. Furthermore, the distinct breakdown behavior observed here differs from that of quantum Hall systems, which involve slow relaxation dynamics and Landau level physics. The derived breakdown thresholds impose stringent conditions on the viability of QAH-based quantum metrology and microwave components, suggesting that managing electron heating in disordered regions is essential for future device optimization.