Hybrid superinductance with Al/InAs

Technical Summary: Hybrid Superinductance with Al/InAs

Problem Statement
The development of high-impedance superconducting circuits, particularly for fluxonium qubits, relies on "superinductors"—devices with a characteristic impedance $Z$ exceeding the resistance quantum $R_Q = \hbar/(2e)^2 \approx 1.027$ k$\Omega$. Traditional superinductors realized via chains of tunnel junctions face a fundamental trade-off: avoiding quantum phase slips requires a small charging energy ($E_C \ll E_J$), but this necessitates a small plasma frequency ($\omega_p \sim \sqrt{E_C E_J}$), limiting operating frequencies. Conversely, hybrid superconductor-semiconductor junctions (specifically Al/InAs) offer high transparency and gate tunability but possess a planar geometry that inherently leads to a large charging energy ($E_C > E_J$). This raises the question of whether such hybrid systems can achieve superinductance without being degraded by quantum phase slips, or if the large $E_C$ prevents their utility as high-frequency superinductors.

Methodology
The authors fabricated and characterized chains of 800 planar Josephson junctions formed from an epitaxial Al/InAs heterostructure. The devices were patterned using electron-beam lithography and selective etching to create "mesa" structures of semiconducting layers capped by Aluminum islands. Three distinct devices were measured in a dilution refrigerator at a base temperature of 23 mK:

• Device 1 & 2: Junction lengths ($l_J$) of 700 nm.
• Device 3: Junction length ($l_J$) of 400 nm.

The chains were integrated into on-chip resonators capacitively coupled to a coplanar waveguide in a "hanger" geometry. Microwave spectroscopy was performed using a vector network analyzer. To map the dispersion relation across a broad frequency range, the authors employed two-tone spectroscopy, sweeping a secondary pump tone to detect cross-Kerr shifts in the resonator modes. The experimental data was compared against finite-element electromagnetic simulations modeling the chain as alternating regions of large sheet inductance (junctions) and vanishing inductance (Aluminum).

Key Results

1. Superinductance Regime: The devices successfully achieved the superinductance regime. The extracted characteristic impedances were $Z \approx 4.7$ k$\Omega$ (Device 1), $5.17$k$\Omega$ (Device 2), and $1.07$k$\Omega$ (Device 3), all exceeding $R_Q$.
2. Dispersion and Plasma Frequency: The measured mode frequencies exhibited a nearly linear dispersion relation up to at least 12 GHz (Device 1 and 2). Unlike conventional Al/AlO$_x$ superinductors, which show significant dispersion due to Josephson shunt capacitance, the Al/InAs planar junctions showed negligible shunt capacitance ($C_J$). Consequently, no deviations from ideal dispersion attributable to a single-junction plasma frequency were observed up to 12 GHz. The slight curvature in dispersion was attributed to the electromagnetic environment and coupling capacitors rather than intrinsic junction limitations.
3. Quality Factors and Loss Mechanisms: The internal quality factors ($Q_i$) were found to be orders of magnitude lower than those of Al/AlO$_x$ devices. Crucially, $Q_i$ decreased sharply with increasing frequency, following an approximate inverse relationship ($Q_i \propto 1/f_r$) for the 700 nm devices. This behavior contradicts the expectation for phase-slip dominated loss (which typically increases with frequency) and dielectric loss.
4. Loss Modeling: The authors propose a phenomenological model where the loss arises from a resistive shunt ($R_J$) across the Josephson junctions. In the weak-shunt limit, this results in a frequency-dependent attenuation. Fitting the data yielded shunt resistances of $R_J \approx 10-11$ k$\Omega$ for the 700 nm devices and $R_J \approx 3$ k$\Omega$ for the 400 nm device.
5. Temperature Dependence: The quality factor decreased strongly with temperature, particularly for the longer junctions (Devices 1 and 2) below 100 mK. This suggests an intrinsic loss mechanism related to the diffusive nature of the long junctions, where the Thouless energy ($E_{Th}$) may be comparable to or lower than the thermal energy ($k_B T$).

Significance and Claims
The paper demonstrates that Al/InAs hybrid chains can function as superinductors with characteristic impedances exceeding the resistance quantum, effectively breaking the "barrier" of $E_C/E_J > 1$ without immediate failure due to phase slips. The planar geometry allows for high plasma frequencies, enabling operation well into the GHz regime without the dispersion limitations seen in tunnel-junction arrays.

However, the authors are modest regarding the current viability of these devices for high-coherence qubits. They acknowledge that the observed quality factors are currently too low for fluxonium qubit applications, which typically require higher coherence. Instead, they suggest that at current quality levels, these devices are promising for readout applications for spin and parity qubits at modest frequencies (< 1 GHz). In this context, they could potentially outperform dominant coil inductors by offering a higher quality factor, reduced capacitance, and a more compact form factor.

The study identifies the microscopic origin of the loss as likely intrinsic to the junction geometry, specifically the diffusive limit of the long junctions. The authors conclude that while the current devices face loss challenges, the approach is viable if mitigation strategies—such as using shorter junctions or incorporating electrostatic gates to maintain inductance while reducing junction participation—are implemented to reduce the parallel loss channel.