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REVIEW 3 major objections 5 minor 48 references

MBE-grown titanium nitride on sapphire sustains internal quality factors above one million in the single-photon limit, reaching over twenty million at high photon numbers.

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2026-08-01 23:46 UTC pith:KBMPRUQS

load-bearing objection Solid MBE TiN resonator paper worth refereeing, but the abstract's >20e6 high-photon Qi is a single maximum with huge error; the robust result is the ~1.3e6 low-photon average. the 3 major comments →

arxiv 2607.15230 v2 pith:KBMPRUQS submitted 2026-07-16 cond-mat.supr-con cond-mat.mtrl-sci

High-Q superconducting microwave resonators using MBE titanium nitride

Anand Ithepalli , Haoran Lu , Eegene Clara Chung , Xiangqin Wang , Amit Rohan Rajapurohita , Keun-Yeol Park , Celesta S. Chang , Peter McMahon
show 4 more authors
Huili Grace Xing David Muller Valla Fatemi Debdeep Jena
This is my paper
classification cond-mat.supr-con cond-mat.mtrl-sci
keywords titanium nitridemolecular beam epitaxysuperconducting microwave resonatorinternal quality factorsingle-photon limitc-plane sapphireepitaxial qubitX-ray rocking curve
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to show that titanium nitride grown by molecular beam epitaxy on c-plane sapphire is an exceptionally low-loss superconductor for microwave circuits. Internal quality factors exceed one million at the single-photon limit and twenty million at high photon numbers, without any acid surface treatment, while X-ray rocking curves show the narrowest width ever reported for TiN. The authors interpret these results as evidence that a crystalline, epitaxial nitride film can serve as the base layer for future all-epitaxial qubits, replacing amorphous alumina tunnel barriers with a crystalline MgO barrier. A sympathetic reader would care because eliminating amorphous interfaces is a promising route to longer qubit coherence times.

Core claim

The central discovery is that MBE-grown TiN films on c-plane sapphire, despite their twinned, columnar microstructure, deliver state-of-the-art microwave performance: an averaged internal quality factor of about 1.26 × 10^6 (maximum 2.2 × 10^6) in the single-photon regime and an averaged 5.1 × 10^6 (maximum 25 × 10^6) at ⟨n⟩≈10^6 at 10 mK. The same films show an atomically sharp interface with sapphire and a record 18 arcsec rocking-curve FWHM. The paper further reports the first observation of subsurface dislocations in the sapphire substrate that seed defects in the TiN, linking substrate preparation to film microstructure. The results are positioned as a step toward all-epitaxial supercon

What carries the argument

The load-bearing measurement is the internal quality factor Qi of quarter-wavelength coplanar-waveguide resonators, extracted from a diameter-corrected fit of the transmission S21 as a function of frequency and power. Qi serves as the quantitative proxy for microwave loss in the film and its interfaces. Alongside this, the paper uses multislice electron ptychography and high-resolution X-ray diffraction to tie the film's crystalline perfection (record 18 arcsec rocking-curve width) and interface structure to the microwave result. The comparison of two photoresist-stripping chemistries, 1165 versus AZ300T, acts as a processing lever that changes Qi by a factor of three, identifying chemistry-

Load-bearing premise

The measured high quality factor is attributed to the TiN film, but the paper does not separately measure the loss from the annealed sapphire substrate or from the 3–4 nm overetch into the sapphire, so if those dominate, the high Qi would not demonstrate that MBE TiN itself is low-loss.

What would settle it

Fabricate the same CPW resonator pattern on the same batch of annealed sapphire using a different superconductor (for instance sputtered aluminum) with identical geometry and measurement conditions, and compare the single-photon internal quality factor. If the control resonator shows a Qi close to or above the TiN value, the loss budget is substrate- or interface-dominated rather than set by the MBE TiN film.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • TiN-on-sapphire resonators achieve Qi above 10^6 at the single-photon limit without HF or BOE treatment, meaning loss can be low even when acid-based oxide removal is skipped.
  • The record 18 arcsec rocking-curve width for TiN (8 times narrower than the previous best) indicates TiN(111) planes extremely parallel to the sapphire (001) planes, a favorable structural basis for epitaxial overlayers.
  • Switching the photoresist stripper from 1165 to AZ300T improves average single-photon Qi by a factor of three and reduces variance, reproducing a known effect for Nb on Si and pointing to controllable fabrication-related loss.
  • The near-zero lattice mismatch between TiN and MgO, both rocksalt, makes TiN/MgO/TiN a concrete candidate for an all-crystalline Josephson junction, which could reduce two-level-system loss from amorphous barriers.
  • The observation that low-angle columnar grain boundaries in this TiN cannot host chemical impurities (reported to be published separately) would imply that the structural defects present do not limit the measured Qi.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the high Qi is genuinely set by the TiN film rather than the annealed sapphire substrate, MBE could become a preferred growth route for qubit-grade nitride films, since MBE offers monolayer-level interface control that sputtering lacks.
  • The subsurface dislocations in the sapphire, revealed by ptychography, suggest that substrate polishing and annealing choices—not just film growth—set a floor on achievable Qi; a systematic study varying the anneal would quantify this floor.
  • A testable extension: if the same resonator mask and processing were applied to a different superconductor on the same sapphire batch, the resulting Qi would separate film loss from substrate/interface loss and directly test the paper's attribution.
  • The success of In surfactant for smoothing other nitride films suggests a concrete path to reduce the ~2 nm surface undulations of TiN, which currently match the thickness of typical tunnel barriers; smoother TiN could make the epitaxial Josephson junction stack more feasible.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper reports MBE-grown TiN films on c-plane sapphire and characterizes their structural, electronic, and microwave properties. A record X-ray rocking-curve FWHM of 18 arcsec is reported for TiN(111), along with a sharp Tc ≈ 5.1 K. Quarter-wavelength CPW resonators fabricated from the film are measured at 10 mK; the AZ300T-processed chip shows average Qi ≈ 1.26×10^6 in the single-photon limit, while the abstract claims rising to >20×10^6 at high photon number. The authors benchmark against literature and motivate future all-epitaxial TiN/MgO/TiN junctions.

Significance. If correct, the single-photon Qi > 10^6 without acid treatment, together with the extremely narrow rocking curve, makes MBE TiN on c-plane sapphire a competitive base layer for superconducting circuits and supports the long-term goal of epitaxial Josephson junctions. The work also presents valuable structural characterization: atomically resolved interface imaging by MEP, identification of substrate subsurface dislocations nucleating defects in the film, and a careful two-chip comparison of resist-stripping processes. The main caveats are that the high-photon claim is based on a single outlier, and the attribution of the measured loss to the TiN film rather than the annealed sapphire substrate/overetch interface is not directly demonstrated.

major comments (3)
  1. [Abstract; Microwave characterization (Fig. 4(d-e))] The abstract's claim 'rising to >20×10^6 at ⟨n⟩~10^6' is not supported by the reported data. The AZ300T chip has an average Qi,HP ≈ 5.11(1.13)×10^6; the value 25.0(17.3)×10^6 is the maximum of a single resonator and carries a relative standard error of ~69%, making it statistically compatible with the average. The 1165 chip's average is 3.63(0.43)×10^6. Please report aggregate statistics and phrase the abstract as 'best observed value up to ...' or use the average, and state which chip the claim refers to. The low-photon average Qi,LP ≈ 1.26(0.45)×10^6 is robust, but it also applies specifically to the AZ300T chip, which should be stated.
  2. [Introduction; Fig. 3(c); Conclusion] The attribution of the high Qi to the TiN film itself is not established. The substrates are commercially annealed sapphire, already known to have reduced loss tangent [15], and Fig. 3(c) shows 3–4 nm of sapphire overetch. The statement that this overetch has 'negligible effect' on microwave loss is based on HFSS participation-ratio simulations that are not included in the main text (only referenced as supplementary). Without a substrate/interface control or the participation-ratio numbers, the result cannot distinguish film loss from substrate/interface loss. Please either provide the supporting simulation data, add a control experiment, or explicitly frame Qi as total resonator loss and temper the claim that the result demonstrates low-loss MBE TiN as a film.
  3. [Conclusion and outlook] The sentence claiming that columnar grain boundaries are 'low angle boundaries incapable of hosting chemical defects such as O, C impurities' is explicitly said to be published separately. As written, this assertion is not evidence in the present manuscript yet is used to support the claim that TiN retains high Qi despite columnar structure. Please remove or clearly mark this as a conjecture, or include the supporting 3D MEP analysis. Similarly, the microwave Tc ≈ 5.1 K from a quasi-particle model fit is stated without showing the fit/data; if used as a cross-check, it should be shown in the main text or supplement.
minor comments (5)
  1. [Abstract] The phrase 'at 5.8 GHz' is not tied to any specific measurement in the main text; the detailed single-photon example in Fig. 4 is a resonator at f0 ≈ 4.37 GHz. Please state the actual frequency range or point to the specific resonator.
  2. [Fig. 1(d)] The record FWHM of 18 arcsec is reported without an uncertainty. Since this is a headline claim, please provide the measurement uncertainty and the scan step size.
  3. [Introduction vs. Fig. 3(c)] The introduction says the resonators were made 'without ... any overetch into the substrate', but Fig. 3(c) and its caption state that 3–4 nm of sapphire is etched. Please reconcile this contradiction.
  4. [Resonator measurement] Eq. (1) defines S21 through Q, Qc, and φ, but Qc is not explicitly defined as the coupling quality factor until Eq. (2). A one-sentence definition of all symbols would improve readability.
  5. [Throughout] There are several typographical issues: 'F atemi' should likely be 'Fatemi', 'Eegene Clara Chung' has an unusual first name (possibly 'Eugene'), and '3 extmu m/6 extmu m/3 extmu m gap/strip/gap lines' in the abstract is awkward. A careful proofreading pass is needed.

Circularity Check

0 steps flagged

No significant circularity; Qi values come from a standard independent hanger fit, and the supporting microstructural/substrate claims are external or measured.

full rationale

This is a measurement and materials-characterization paper, not a derivation from assumptions. The central microwave result is obtained from a standard transmission fit: S21(f) is modeled by Eq. 1 and the loaded quality factor is decomposed via 1/Q = 1/Qi + 1/Qc (Eq. 2). Qi is thus extracted from independent fits to the resonance circle, magnitude, and phase; no fitted parameter is renamed as a prediction, and no definitional relation forces the outcome. The claim about high Qi is benchmarked against external literature (Figs. 5a-b), and the comparison is not structured by an equation that presupposes the TiN result. The substrate-loss assumption is an acknowledged limitation rather than a circular step: the paper states that the shallow sapphire overetch 'results in a much higher energy participation ratio' and that etch damage 'may cause amorphization and increase the SA interface loss tangent,' but it does not use substrate loss as an input to conclude TiN is low-loss. The microstructural explanation of columnar boundaries relies on an unpublished separate analysis ('this result will be published separately'), which is missing support but not circularity. One citation to prior work with an overlapping author ([13]) is used as secondary support for the AZ300T stripping effect, but that effect is directly measured in this paper, so the citation is not load-bearing. The abstract's '>20e6 at <n>~1e6' overstates the reported average (Qi,HP ~ 5.11(1.13)e6 with a maximum of 25.0(17.3)e6); this is a statistical representativeness concern, not a circularity concern. Overall, the derivation chain is self-contained against standard resonator fitting and external benchmarks, with no equation or construction reducing a claimed result to its inputs.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

No new physical entities are introduced. The load-bearing assumptions are standard resonator fitting plus several unverified microstructural and substrate-loss assumptions. The headline Qi depends on fit quality and on substrate/interface losses being negligible relative to the film.

free parameters (2)
  • DCM resonator fit parameters (f0, Qc, φ, Qi) = e.g., f0≈4.37 GHz; Qi,LP average 1.26(0.45)×10^6
    All Qi values are obtained by least-squares fitting of Eq. (1) to each S21 trace. Systematic errors in the hanger model or background would propagate directly into the headline quality factors.
  • Quasiparticle-model microwave Tc fit = Tc≈5.1 K
    A fit to Qi vs T from a different, similarly processed film is used to argue that microwave Tc matches DC Tc; no data or fit is shown in the preprint.
axioms (5)
  • domain assumption Eq. (1) with diameter correction (DCM) adequately models the measured hanger resonator response.
    All Qi values are extracted from this model; unmodeled background, crosstalk, or mode coupling would bias the reported values.
  • domain assumption Commercially annealed sapphire has a cryogenic loss tangent tan δ ~ 2×10^-8 and remains low-loss through subsequent MBE and etch processing.
    Cited to Ganjam et al. [15]; not re-measured in this work, and no separate substrate loss measurement is presented.
  • ad hoc to paper The 3-4 nm sapphire overetch has negligible effect on microwave loss participation.
    Supported only by HFSS simulations described as in the supplementary material, not by direct loss measurements; the text itself notes the overetch raises tri-junction participation ratios.
  • ad hoc to paper Columnar grain boundaries in this TiN film are low-angle and contain no chemical defects such as O or C.
    Explicitly deferred to a separate publication; used to explain why high Qi is consistent with the observed columnar microstructure.
  • domain assumption Piranha cleaning and AZ300T photoresist stripping do not degrade the TiN surface.
    Surface preparation conditions are taken from prior work on Nb and Ta resonators [13,15]; no surface chemical analysis is shown for these TiN films.

pith-pipeline@v1.3.0-alltime-deepseek · 10398 in / 11370 out tokens · 94986 ms · 2026-08-01T23:46:51.969048+00:00 · methodology

0 comments
read the original abstract

Using molecular beam epitaxy, we have realized thin films of titanium nitride (TiN) on c-plane sapphire that exhibit the lowest observed full-width at half maximum X-ray rocking curve width of 18 arcsec. Though the (111) oriented TiN exhibits an abrupt and crystalline interface with sapphire, for the first time we observe sub-surface defects in the sapphire substrate, which nucleate structural defects in the epitaxial TiN layer. Using quarter-wavelength coplanar waveguide (CPW) resonators in a 3 \textmu m/6 \textmu m/3 \textmu m gap/strip/gap lines in a hanger geometry, we find the internal quality factor of the TiN resonators to be $>10^{6}$ in the single-photon $\langle n \rangle \sim 1$ limit at 5.8 GHz and 10 mK, rising to $>20 \times 10^{6}$ at $\langle n \rangle \sim 10^{6}$. The results are of high interest for applications of superconducting TiN in several areas, and provide a path towards epitaxial Josephson junctions with crystalline barriers in the future for high coherence qubits.

Figures

Figures reproduced from arXiv: 2607.15230 by Amit Rohan Rajapurohita, Anand Ithepalli, Celesta S. Chang, David Muller, Debdeep Jena, Eegene Clara Chung, Haoran Lu, Huili Grace Xing, Keun-Yeol Park, Peter McMahon, Valla Fatemi, Xiangqin Wang.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Sample schematic of the MBE-grown TiN film used in this study. (b) Experimental multislice electron ptychography [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Cross-section schematic of the processed resonator [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Columnar growth of TiN is seen from a broader [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Measured data (black, solid circles) of the TiN resonator with [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Benchmark plots of representative results from literature (a) low power [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗

discussion (0)

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Reference graph

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