TLS loss in superconducting resonators on epitaxial hBN thin films

AI summary

Overview

Research area: Superconducting quantum devices and materials — specifically dielectric loss (two-level system, or TLS, loss) in niobium microwave resonators fabricated on epitaxial few-layer hexagonal boron nitride (hBN).

Technical level: Intermediate. The paper is readable for someone with basic familiarity with superconducting resonators and quality factors, but the noise-spectroscopy and participation-ratio analysis requires some background.

Scope (one sentence): The authors grow few-layer epitaxial hBN by molecular beam epitaxy on sapphire, build Nb coplanar waveguide resonators on it and on bare sapphire as a control, and use power, temperature, and time-domain radiofrequency measurements to quantify how much TLS loss the added hBN introduces.

What This Paper Is About

Athermal phonons traveling through a device substrate can break Cooper pairs in a superconductor, producing quasiparticle bursts that cause correlated errors across many qubits or that set the sensitivity of phonon-mediated detectors. Inserting a 2D material at the superconductor–substrate interface could reflect or spread those phonons, but any new dielectric layer risks adding TLS loss that degrades the resonator quality factor.

The goal here is to test whether ordered, epitaxial hBN can be added to a conventional superconducting stack without significantly degrading performance — a prerequisite for the phonon-blocking idea to be useful.

Key Contributions

1. Growth and integration of epitaxial few-layer hBN into a superconducting device stack. hBN films were grown by high-temperature molecular beam epitaxy with laser substrate heating on c-plane sapphire, characterized as rotationally aligned, well ordered, wrinkle-free, and approximately 3 nm thick, then capped with 61 nm of sputtered Nb without an RF clean step.

2. A 1:1 controlled comparison of hBN and bare-sapphire devices. Both chips used the same open-source eight-resonator coplanar waveguide layout with a common feedline, with participation ratios designed to be sensitive to metal–substrate interface loss, and the Nb for both was sputtered in the same batch to limit variation in film purity or thickness.

3. A multi-probe loss characterization. Power sweeps, temperature sweeps of the fractional frequency shift, finite element modeling of participation ratios, and both fast and slow time-domain noise measurements were combined to separate time-averaged TLS loss from TLS noise and frequency switching.

4. Demonstration that hBN keeps loss at the 10⁻⁶ level. The hBN resonators retain low-power internal loss tangents on the order of 10⁻⁶, which the authors present as evidence that hBN can be added to a conventional qubit stack with minimal quality factor degradation.

Main Findings

• Low-power internal loss is only modestly higher with hBN. The hBN resonators had a median low-power internal loss δ_i^LP of 4.50 × 10⁻⁶ with a standard deviation of 1.7 × 10⁻⁶, versus a control median of 1.65 × 10⁻⁶ with a standard deviation of 0.50 × 10⁻⁶ — elevated, but on the same order of magnitude.

• The control devices are competitive with the state of the art. For comparison, high-Q Nb-on-Si resonators of the same layout achieved a median δ_i^LP of 1.2 × 10⁻⁶, and the broader literature range quoted is (0.1–3) × 10⁻⁶.

• Power dependence is consistent with TLS saturation. For ⟨n⟩ > 10⁴, δ_i converged for most resonators regardless of hBN presence. The authors note they could not reliably fit resonances at ⟨n⟩ ≤ 1 and did not observe the flattening of δ_i at low ⟨n⟩ that would mark the onset of TLS saturation.

• Temperature-sweep fits give a consistent loss picture. The extracted median Fδ_TLS⁰ was 5.54 × 10⁻⁶ (standard deviation 3.9 × 10⁻⁷) for hBN and 3.43 × 10⁻⁶ (standard deviation 6.1 × 10⁻⁷) for control — a factor of approximately 1.6 increase from the hBN. Literature Nb-on-Si values extracted the same way fall between 1.8 × 10⁻⁶ and 2.5 × 10⁻⁶.

• An anomalous low-temperature downturn was observed near 1 K. The fractional frequency shift trends downward near 1 K in both device types, but the onset is inconsistent with a Tc near 9 K as expected for Nb; fitting Mattis–Bardeen equations gives a Tc near 2 K. The authors note compressively strained Nb can have reduced Tc but did not investigate film stress. They restricted fitting to the low end of the sweep and, assuming Tc > 8.5 K and α < 0.1, bounded the thermal quasiparticle contribution at |(δf(T)/f₀)_QP| < 1.7 × 10⁻⁷. A separate Nb film from the same sputtering system and procedure measured Tc = 8.9 K.

• Finite element modeling suggests nearly identical interface loss. Using AWS Palace on resonator R5, participation ratios for the control were 3.1 × 10⁻⁶ (metal–air), 1.0 × 10⁻³ (substrate–air), and 0.34 × 10⁻³ (metal–substrate); for the hBN device they were 3.2 × 10⁻⁶, 1.0 × 10⁻³, and 0.71 × 10⁻³. Treating the hBN as a 6 nm metal–substrate interface and assuming δ_SA = 1.5 × 10⁻³ for sapphire and δ_MA = 1.0 × 10⁻³ for Nb oxide, the extracted δ_MS was 5.67 × 10⁻³ for control and 5.69 × 10⁻³ for hBN. The authors explicitly caution about the difficulty of isolating a material loss from coplanar waveguide measurements.

• TLS noise is higher in the hBN resonators. At 1 kHz and −30 dBm input power (⟨n⟩ ~ 10⁴), the mean TLS noise component was 4.65 × 10⁻¹⁸ for hBN and 8.16 × 10⁻¹⁹ for control. Power scaling of the TLS noise component was P^−0.51 (control) and P^−0.59 (hBN), close to the expected P^−0.5; for the selected pair, the hBN TLS noise component was about 1.5 orders of magnitude larger.

• hBN resonators show frequency switching over hours. In a roughly 200-minute timestream, most hBN resonators showed pronounced frequency switching while control resonators remained steady. Allan deviation showed τ^−1/2 behavior at low τ, and Lorentzian-like features in the hBN data did not align with other known noise components. The model used did not fit those Lorentzian features well across the set, which the authors suggest might require a sum of many Lorentzians.

• No direct phonon-blocking measurement is reported. The paper frames phonon blocking as motivation and a future application; the measurements presented are of dielectric loss only.

Methodology in Plain English

The team grew very thin hBN films on sapphire using molecular beam epitaxy — an ultra-high-vacuum deposition technique with slow, controlled growth that favors purity and crystallinity, plus laser-based local substrate heating that limits contaminant migration compared with conventional resistance heating. They verified the films with electron diffraction, Raman spectroscopy, cross-sectional electron microscopy (about 3 nm total thickness), and atomic force microscopy (0.3 nm RMS roughness, wrinkle-free).

They then sputtered niobium onto both the hBN and bare sapphire wafers in the same batch, patterned eight microwave resonators plus a shared feedline by photolithography and chlorine plasma etching, and packaged the chips identically. Because hBN etches about three times slower than Nb, the authors reason the hBN likely survived only under the protected Nb regions and was removed from the gap areas. Both chips were cooled simultaneously on the same copper bar in a deep-underground dilution refrigerator with 100 m of rock overburden shielding more than 99% of cosmic ray muons, behind a double-walled magnetic shield, with 77 dB of input attenuation.

They then measured the microwave transmission through each resonator three ways: as a function of drive power (to saturate TLS and see the loss drop), as a function of temperature from 15 mK to 1.1 K (to extract a zero-temperature TLS loss from the characteristic frequency-shift "hook"), and as a function of time (to see TLS noise and switching). Resonances were fit in the complex plane with a diameter correction method to extract resonant frequency and internal, coupling, and loaded quality factors. A separate simulation step computed how much of the electric field sits in each material region, so that measured total loss could be apportioned between interfaces.

Why This Matters

Impact on research. The paper fills a stated gap between two extremes in the literature: exfoliated single-crystal hBN, which has a loss tangent of 5 × 10⁻⁶ in the single-photon regime but poor area, yield, and reproducibility, and sputtered amorphous BN, where roughly 100 nm on superconducting resonators gave a zero-temperature TLS loss of 6 × 10⁻⁵. It shows that a deposited, ordered, wafer-scale-compatible 2D dielectric can land at 10⁻⁶, which is the range needed for qubit readout and control.

Real-world applications:

• Superconducting quantum computers: suppressing correlated, phonon-mediated quasiparticle poisoning that can affect multiple qubits over millisecond and centimeter scales.
• Kinetic inductance phonon-mediated (KIPM) detectors: blocking phonons from escaping into passive metal films, where collection efficiency is currently limited to 1–25%.
• Quantum sensors and low-threshold particle detectors more generally, where TLS noise currently limits sensitivity.
• Cryogenic electronics and microwave components that need low-loss deposited dielectrics compatible with standard fabrication.

Industry relevance. The work addresses a manufacturing question, not just a physics question: whether a new material can be inserted into an existing process flow without wrecking yield or quality factor. The authors point to chemical vapor deposition as an alternative to MBE that has produced wafer-scale, wrinkle-free, epitaxial few-layer hBN of comparable quality, making the approach plausibly scalable. For deposited dielectrics generally, loss tangents span 10⁻² to 10⁻⁵; amorphous hydrogenated SiC microstrip resonators show 3.1 × 10⁻⁵ and amorphous hydrogenated SiN LC resonators 2.5 × 10⁻⁵, so a 10⁻⁶ deposited 2D dielectric is a meaningful step.

Future Directions

1. Directly demonstrate phonon blocking. The central hypothesis — that hBN at the superconductor–substrate interface reflects and laterally diffuses athermal phonons — is not tested here; the paper measures only dielectric loss.

2. Reduce TLS noise and frequency switching in the hBN devices. The hBN resonators showed higher TLS noise and pronounced long-timescale frequency switching. The authors suggest the spread in δ_i^LP may come from the distribution of crystalline defects, such as stacking faults aligned under a resonator trace, so improving film quality is a clear lever.

3. Grow epitaxial hBN on a superconductor rather than a substrate. The authors propose this as a route to a scalable, low-loss dielectric for superconducting junctions and parallel-plate capacitors, which would allow a clean extraction of the hBN's intrinsic loss tangent without the ambiguity of interface deconvolution in coplanar geometries.

4. Adopt scalable growth. Replacing MBE with chemical vapor deposition would test whether comparable loss performance survives a wafer-scale, manufacturable process.

Target Audience

Quantum device and materials researchers working on superconducting circuits, dielectric loss, and two-level systems; groups developing phonon-mediated detectors and quasiparticle-mitigation strategies; thin-film growers interested in integrating 2D materials into cryogenic device stacks; and fabrication engineers who need to judge whether a new dielectric can enter a qubit process flow without a quality-factor penalty.

Authors’ abstract

The integration of low-loss dielectrics into superconducting circuits is of importance to the functionality of quantum computers and sensors. In this work, we fabricate and measure niobium resonators atop few-layer, epitaxial hexagonal boron nitride (hBN) grown by Molecular Beam Epitaxy on a sapphire substrate and compare against a control counterpart without hBN. We conduct radiofrequency measurements which probe the responses to power, temperature, and temporal fluctuations of two-level systems. The resonators integrating hBN maintain low dielectric loss with a low-power internal loss tangent on the order of $10^{-6}$, and demonstrate hBN can be added to the conventional superconducting qubit stack with minimal degradation of the quality factor. This research represents a first step towards a materials-driven strategy to eliminate phonon-mediated correlated errors in solid-state quantum systems, which leverages the thermal properties of 2D materials to prevent athermal phonons excited in the device substrate from transmitting across the superconductor-substrate interface. The same technique applied to quantum sensors would maximize phonon collection by blocking phonons from entering passive metal films.