High-quality and field resilient microwave resonators on Ge/SiGe quantum well heterostructures

TL;DR

This paper addresses the challenge of realizing low-loss, field-resilient microwave resonators on Ge/SiGe quantum wells for hybrid quantum devices. It introduces an in-situ grown Ge/SiGe superconductor/semiconductor hybrid with an ultra-thin Al film patterned into eight λ/4 resonators, achieving very high $Q_i$ values, including near $Q_i\approx 49000$ in the single-photon regime, and demonstrated resilience to in-plane magnetic fields up to 850 mT. The study characterizes the film via kinetic inductance, superconducting gap, and temperature dependence, and reveals a rich field-dependent behavior: strong in-plane field tolerance and out-of-plane hysteresis linked to vortex–quasiparticle dynamics. Collectively, the results establish a compact, clean Ge-based platform suitable for fast readout and potential long-range qubit coupling, with insights into loss mechanisms and magnetic-field performance for hybrid quantum technologies.

Abstract

Superconducting resonators integrated with Ge quantum wells (QWs) offer a promising platform for hybrid quantum devices. Yet, in the most common heterostructure architectures, they have so far been limited by sizable photon losses. Here, we report the fabrication and characterization of microwave resonators patterned in the Al thin film of an in-situ grown superconductor/semiconductor hybrid heterostructure (HS). The semiconductor part of this hybrid HS is grown on a commercial Ge substrate. We consistently achieve internal quality factors $Q_i>1000$, surpassing previous results on Ge QW heterostructures grown using the concept of a virtual Ge substrate on Si substrates. We reach $Q_i \approx 49000$ at single-photon occupation and a plateau of $Q_i \approx 20000$ at sub-one photon, an order of magnitude larger than any previously reported value of resonators on Ge QW structures at low power. We further characterize the thin Al film forming the resonator, extracting its kinetic inductance and superconducting gap, and studying its magnetic field dependence. Notably, the resonance remains well-defined up to in-plane magnetic fields of 850 mT. A hysteresis emerges in the out-of-plane magnetic field dependence, for both the resonance frequency and the quality factor, indicating an interesting interplay between vortex- and quasiparticle loss mechanisms.

Figures (7)

• Figure 1: High-Q resonator on a . (a) Cross-sectional schematic (not to scale) of a microwave resonator patterned from an film deposited on a / quantum well, which is epitaxially grown on a substrate. (b - d) Fit (orange solid line) of the I/Q, transmission amplitude and phase response, respectively. The extracted quality factor exceeds 4.8e4 at an average circulating photon number of $<n_\mathrm{p}> \simeq 1.0$.
• Figure 2: Thin film properties extracted from resonator characteristics. (a) The resonance frequency $f_\mathrm{r}$ is inversely proportional to the resonator length $l$. The data (blue dots) are fitted (solid line) to the equation $f_\mathrm{r}(l)$ specified in the main text, yielding a kinetic inductance of 36±2pH/□ (b) The relative shift of the resonance frequency $f_\mathrm{r}$ (blue dots) measured at elevated temperature compared to $f_\mathrm{r,0}:=f_\mathrm{r,T=10mK}$. The solid line is a fit to the theory (see main text), which predicts a decreasing resonance frequency due to the lower density of Cooper pairs which increases the kinetic inductance.
• Figure 3: Photon number dependence of eight $\lambda/4$ resonators connected to a single . (a) Quality factor as a function of average photon number for eight resonators of different frequencies ranging from about 47. (b) Design scheme with eight $\lambda/4$ resonators of different length $l$ hanging to a common . (c) Top view of the sample on which the design in (b) is patterned. The impedance of the resonators at resonance frequency is $Z_\mathrm{r} = \sqrt{L_\mathrm{r}/{C_\mathrm{r}}}$$\simeq$ 66Ω gevorgian_cad_1995. The constant coupling length of $473µm$ (not shown) and its relative variation to resonator length yields a variable coupling quality factor $Q_\mathrm{c}$ ranging from 12009000 in agreement with the simulations shown in SFig.2(b). It is also affected by grounding inhomogeneities, which we try to minimize by bonds connecting different areas of the ground plane. The area marked by red dashed line indicates a region of inhomogeneous etching. (c.inset) Zoom-in on the resonator with the highest quality factor, with details on the feedline width $w=24µm$, gap to ground $s=3µm$, coupling $g =24µm$, constant for all eight resonators.
• Figure 4: Magnetic field dependence. (a) Shift of the resonance frequency and (b) normalized quality factor as a function of in plane magnetic field from zero to $B_\mathrm{\parallel} =850mT$. (c) Shift of the resonance frequency and (d) normalized quality factor as a function of out-of plane magnetic field from zero to $B_\mathrm{\perp} =50µT$. The arrows and the color (orange for increasing fields and blue for decreasing fields, respectively) indicate the direction of the sweep.
• Figure 5: TEM characterization. HAADF image of the super/semi interface indicated by the orange arrow, with on top the and on the bottom the Si$_{0.05}$Ge$_{0.95}$ top barrier of the .