Hybrid superinductance with Al/InAs

TL;DR

The paper investigates Al/InAs hybrid Josephson junction chains as high-impedance superinductors for quantum circuits. Using long-junction planar arrays (~800 junctions), the authors achieve a dispersion-free, high impedance with $Z>R_Q$ and observe no plasma-frequency limitation up to $12~\mathrm{GHz}$, with dispersion well captured by a periodic-inductor model. A strong, frequency-dependent internal loss is reported and modeled by a resistively shunted junction framework, yielding $Q_i\propto1/f_r$ and per-junction resistances in the $3$–$11~\mathrm{k}\Omega$ range, suggesting diffusive-junction loss as the origin. The results point to practical routes to optimize hybrid superinductors, such as employing shorter junctions or electrostatic gating to suppress loss, potentially enabling high-coherence readout or qubit operations at modest frequencies.

Abstract

We report microwave spectroscopy of Josephson junctions chains made from an epitaxial Al/InAs heterostructure. The chains exhibit superinductance, with characteristic wave impedance exceeding $R_{Q} = \hbar/(2e)^{2}$. The planar nature of the junctions results in a large plasma frequency, with no measurable deviations from ideal dispersion up to $12~\mathrm{GHz}$. Internal quality factors decrease sharply with frequency, which we describe with a simple loss model. The possibility of a loss mechanism intrinsic to the superconductor-semiconductor junction is considered.

Figures (4)

• Figure 1: (a) Left: Optical image of a chain of 800 Josephson junctions is capacitively coupled to a coplanar waveguide (CPW) in the hanger geometry. Right: the close-up image taken with a scanning electron microscope, Al islands (blue) above the InAs 2D electron gas (orange) are separated by the junction length $l_J$, forming Josephson junction chains. The unit cell size is $d=1.2~\mathrm{\mu m}$ for all devices. Scale bar on the bottom right is 1 $\mu$m. (b) Lumped element model of a Josephson junction chain. (c) Top layers of the material stack. InGaAs/InAs/InGaAs layers form 2D electron gas. The two capacitors at each end of the chain represents coupling capacitors. (d) $S_{21}$ phase data (points) and the fit (solid line) of the mode 3 of the 700 nm Device 1 at the base temperature.
• Figure 2: (a-d) Mode 1 - 4 of Device 1 measured through two-tone spectroscopy. The phase shift $\Delta \phi$ of the mode 3 was measured while a secondary pump was swept through each mode. The pump power was kept sufficiently low to stay in linear regime. The solid lines are fits to Lorentzian. (e) Mode frequencies and (f) mode spacing ($\Delta f$) extracted from the fit as a function of mode number. Up to mode 8, the dispersion is nearly linear. The dashed grey line represents the dispersion simulated using an EM solver with 800 unit cells of alternating inductance. The dotted black line is the simulation result for a strip with a uniform inductance.
• Figure 3: (a) The mode frequencies and (b) the mode spacing for all measured devices. EM simulation results with periodic inductance are shown in dashed lines.
• Figure 4: (a) $Q_{l}$ as a function of frequency for all devices in log-log scale. Dashed lines represent fits to Eq. \ref{['eq:qi']} assuming $Q_c \gg Q_i$ such that $Q_l \approx Q_i$. For device 3 the simulated $Q_c$ (solid line) approaches $Q_i$ for the lowest-frequency point, which is therefore excluded from the fit. For devices 1 and 2, $Q_c$ is much larger than $Q_l$ for all points. Each color correspond to a device as in Fig. 3. (b) Temperature dependence of the $Q_l$ for a mode near 4 GHz (mode 3 for Device 1,2 and mode 1 for device 3). Temperatures $\geq 50~\mathrm{mK}$ shown, for thermalization reasons. (c) Lumped circuit model of a resistively shunted Josephson junction. (d) Equivalent series circuit model of a unit cell.