Interaction between Surface Acoustic Wave and Quantum Hall Effects

Technical Summary: Interaction between Surface Acoustic Wave and Quantum Hall Effects

Problem Statement
Surface acoustic waves (SAW) serve as a powerful, contactless probe for investigating transport properties in two-dimensional electron systems (2DES). The interaction is traditionally described by a relaxation model, where the SAW's piezoelectric field is screened by the 2DES, leading to attenuation ($\Gamma$) and velocity shifts ($\eta$) governed by the 2DES conductivity ($\sigma_{xx}$). While this model has successfully interpreted data from studies using large SAW amplitudes, recent observations suggest its insufficiency when dealing with strongly correlated electron solid phases, such as those found in the quantum Hall effect (QHE). Specifically, discrepancies arise in how these models predict the behavior of SAW attenuation and velocity shifts at low filling factors and under varying power conditions.

Methodology
The authors investigated the interaction between SAW and a high-mobility GaAs/AlGaAs 2DES (electron density $n \approx 1.12 \times 10^{11} \text{ cm}^{-2}$, mobility $\mu \sim 10^6 \text{ cm}^2\text{V}^{-1}\text{s}^{-1}$) using a significantly lower SAW amplitude than in previous literature.

• Sample Design: A 1.2 mm square van der Pauw mesa was fabricated with four Ohmic contacts. Four interdigital transducers (IDTs) were symmetrically arranged around the mesa, generating SAWs with a wavelength of $\lambda = 5 \, \mu\text{m}$ at a resonance frequency of $f_c \approx 580.5 \text{ MHz}$.
• Experimental Conditions: Measurements were conducted in a dilution refrigerator at a base temperature of $\sim 10 \text{ mK}$.
• Key Variable: The study systematically varied the SAW input power (ranging from 1 nW to 80 nW) and applied DC/AC currents to the 2DES.
• Measurements: The team measured the longitudinal magneto-resistance ($R_{xx}$) via conventional lock-in techniques, alongside the SAW attenuation coefficient ($\Gamma$) and normalized velocity shift ($\eta$) across a range of magnetic fields (up to $\sim 1.8 \text{ T}$) and filling factors.

Key Results

1. Anomalous Attenuation at Low Power: At high magnetic fields where the 2DES forms incompressible quantum Hall states, the authors observed an anomalously large SAW attenuation ($\Gamma$) at sufficiently low SAW powers. Contrary to the relaxation model, which predicts that attenuation should decrease as the system becomes incompressible (vanishing $\sigma_{xx}$), $\Gamma$ increased significantly at integer and fractional filling factors.
2. Velocity Shift Behavior: While the attenuation was anomalous, the acoustic velocity shift ($\eta$) remained considerably high, often retaining values close to its zero-field magnitude even at integer fillings where the 2DES is theoretically incompressible. This behavior is inconsistent with the conventional relaxation model, which predicts a velocity shift proportional to the screening capability.
3. Power Dependence: The anomalous large attenuation peak observed at integer fillings (e.g., $\nu=4$) was power-dependent. As the SAW power increased from 1 nW to 80 nW, the anomalous $\Gamma$ peak diminished, and the system's response began to align more closely with the relaxation model. The anomaly exists only when the SAW power is sufficiently low.
4. Current Effects: The presence of a conducting current significantly altered the SAW response.
   • At $\nu=1$, increasing DC current slightly increased $\Gamma$ but increased $\eta$, whereas increasing SAW power decreased both.
   • At specific fractional fillings (e.g., $\nu=4/3, 2/5$) where the QHE is fragile, the applied current induced a substantial negative change in velocity shift ($\kappa$), suggesting the current makes the 2DES more efficient at slowing the acoustic wave.
   • A threshold effect for current-induced changes was observed at low SAW powers (approx. 300 nA), which disappeared at higher SAW powers.
5. Deviation from Relaxation Model: The relationship between $\Gamma$ and $\eta$ deviated from the predictions of Eqs. (1) and (2) derived from the relaxation model. At low filling factors, $\Gamma$ increased nearly linearly with $\eta$ without saturation, whereas the model predicts a specific saturation curve. The data suggests that at low filling factors, the interaction is governed by mechanisms other than simple single-particle screening, possibly involving electron-electron scattering in correlated states like Wigner crystals or composite fermion Fermi seas.

Significance and Claims
The paper claims that the conventional relaxation model is insufficient for describing the SAW-2DES interaction under conditions of very low SAW power and when the 2DES forms strongly correlated states. The authors demonstrate that the interaction is highly sensitive to both the acoustic power and the presence of current, factors missed by the standard model.

The study highlights that:

• The "anomaly" of large attenuation coexisting with high acoustic speed is a real physical phenomenon observable only at low excitation powers.
• The formation of correlated states (such as quantum Hall liquids, Wigner crystals, or stripe phases) likely damps SAW piezoelectric fields through mechanisms like electron-electron scattering, while their long-range correlations prevent the reduction of acoustic velocity.
• There is currently no suitable theoretical modeling for this specific SAW-2DES interaction regime.

The authors conclude that their systematic experimental observations, particularly the power dependence and the distinct behavior at low filling factors, provide clear evidence that challenges existing theoretical frameworks. They posit that these findings should stimulate future investigations into comprehensive theoretical models that can account for the complex interplay between SAWs and strongly correlated electron phases.