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Strong electrostatic confinement can raise valley splitting above 4 K in buried silicon quantum wells while keeping disorder low.

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2026-07-13 02:03 UTC pith:DDG5NBKP

load-bearing objection Clean experimental result: gate confinement systematically lifts single-electron valley splitting to ~0.4–0.76 meV inside the same low-disorder Si/SiGe wells already used for shuttling, with the numbers cross-checked by multiple spectroscopies. the 2 major comments →

arxiv 2607.09570 v1 pith:DDG5NBKP submitted 2026-07-10 cond-mat.mes-hall quant-ph

Confinement drives valley splitting above 4K in buried silicon quantum wells

Davide Degli Esposti , Emma Catherine Brann , Asser Elsayed , Davide Costa , Mark Friesen , Giordano Scappucci This is my paper
classification cond-mat.mes-hall quant-ph PACS 73.21.La73.63.Kv85.35.Gv
keywords silicon spin qubitsvalley splittingSi/SiGe quantum wellselectrostatic confinementorbital energysinglet-triplet splittingquantum-dot arraysshuttling architectures
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.

Silicon spin qubits suffer from nearly degenerate conduction-band valleys that open leakage channels out of the computational basis, blocking high-temperature operation and shuttling. This paper shows that the same buried, low-disorder Si/SiGe quantum wells already valued for quiet environments can be driven to large valley splitting simply by tightening the electrostatic confinement of the dots. Across a four-dot array the authors measure average orbital energies of 2.4 meV, single-electron valley splittings of 0.40 meV, and two-electron singlet-triplet splittings of 0.24 meV. In three dots valley splitting rises linearly with orbital energy (coefficient ~0.22 meV/meV), so stronger gate confinement adds hundreds of microelectronvolts of splitting. One outlier reaches 0.76 meV with almost no correlation, a new high for buried wells. The result implies that device designers can keep the low-disorder advantages of buried wells while still meeting the energy thresholds needed for shuttling and sparse architectures.

Core claim

In low-disorder buried 28Si/SiGe quantum wells, electrostatic confinement alone can raise single-electron valley splitting by several hundred microelectronvolts. Three of four dots show a strong linear correlation (average coefficient ≈0.22 meV/meV) between valley splitting and orbital energy; the fourth reaches a record 0.76(2) meV with little correlation. Average values across the array are EV = 0.40(6) meV and EST = 0.24(7) meV, placing the valley gap above the thermal energy of liquid-helium temperatures.

What carries the argument

The measured linear relation EV ≈ α EO + b (with α ≈ 0.22 meV/meV) obtained from detuning-axis pulsed spectroscopy while the barrier voltages systematically vary the orbital energy EO. The slope quantifies how strongly tighter in-plane confinement increases the electron wave-function's sampling of Ge alloy disorder at the Si/SiGe interface.

Load-bearing premise

The paper assumes that the rise in valley splitting with orbital energy is caused mainly by stronger confinement making the electron sample more Ge alloy disorder at the interface; other microscopic sources such as local pinning centers are not ruled out for the highest-splitting dot.

What would settle it

A systematic series of devices fabricated on the same heterostructure but with deliberately varied plunger-gate widths (or barrier voltages) that produce a wide range of orbital energies; if the EV-versus-EO slope remains near 0.22 meV/meV and the absolute EV values stay high, the confinement-driven mechanism is confirmed; a flat or vanishing slope would falsify it.

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

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

2 major / 5 minor

Summary. The manuscript reports spectroscopic measurements of single- and two-electron energy scales in a four-dot array fabricated on shallow, low-disorder 28Si/SiGe quantum wells. Using detuning-axis pulsed spectroscopy (DAPS), temperature-activated lever arms, magnetospectroscopy, and Pauli spin blockade, the authors extract average orbital energy EO = 2.4(2) meV, single-electron valley splitting EV = 0.40(6) meV, and two-electron singlet-triplet splitting EST = 0.24(7) meV (the latter averaged over 17 lithographically identical dots). In three dots they find a strong EV–EO correlation with linear coefficient ≈0.22 meV/meV; the remaining dot (P2) shows the highest EV = 0.76(2) meV with weak correlation. They conclude that electrostatic confinement can systematically raise valley splitting in buried wells, supporting shuttling and sparse-occupation architectures without intentionally enhancing alloy disorder.

Significance. Valley leakage remains a central obstacle for scaling and shuttling in Si/SiGe spin qubits. Demonstrating gate-tunable EV of several hundred µeV—and a peak of 0.76 meV—in conventional low-disorder buried wells is of clear practical importance and is on par with the best SiMOS values. Strengths include multiple independent spectroscopies on the same devices, lever-arm cross-checks (temperature activation vs magnetospectroscopy), an expanded EST statistics set across devices and wafers, and public data/code deposition. The experimental energy scales and their gate dependence are the load-bearing results; if they hold, the work supplies a concrete co-design path that preserves the low-disorder environment of buried wells while addressing the valley problem.

major comments (2)
  1. [Fig. 2c and Methods] Fig. 2c and Methods (valley-splitting correlations): the theoretical probability density is obtained only after fitting a single phenomenological disorder parameter η_yz ≈ 4.12 meV²·nm to the same experimental EV distribution that the theory is then said to match; the unfitted calculation under-predicts most values below 0.2 meV. The overlay therefore demonstrates consistency of spread and EO dependence under a fitted scale, not an a-priori validation of alloy-disorder theory. The manuscript should state this limitation explicitly in the main text (not only Methods) and separate the experimental EV–EO correlation claim from the secondary microscopic interpretation.
  2. [Results / Discussion] Results (Single-electron spectroscopy) and Discussion: the high-EV outlier under P2 (0.76(2) meV, correlation ≈0.3) is central to the benchmark claim, yet the text leaves open whether it arises from deterministic enhancement beyond alloy disorder or from local pinning/disorder centers. Given that the architectural conclusion leans on consistently large EV, the paper should either (i) quantify how often such outliers appear across the 17-dot EST set or additional devices, or (ii) clearly mark the outlier as not yet microscopically assigned and avoid implying that the same confinement strategy will routinely produce EV ≳ 0.7 meV.
minor comments (5)
  1. [Throughout] Several section headings and figure labels show residual formatting artifacts (e.g., “T wo-electron spectroscopy”, “RESUL TS”, “DA T A A V AILABILITY”). Clean these for production.
  2. [Fig. 4] Fig. 4: the dashed temperature lines (1.6 K, 4.0 K) are useful, but the caption should note that EST ≈ 0.24 meV still limits spin-to-charge readout below ~3 K even when EV exceeds 4 K, so that the title’s “above 4K” claim is not over-read as applying to all relevant energy scales.
  3. [Abstract / Fig. 2c] Abstract and main text quote α_EV/EO ≈ 0.22 (meV/meV) while the Fig. 2c fit reports 0.22(4) [eV/eV]; units are equivalent but the notation should be made consistent (and the intercept b = −0.12(8) meV discussed briefly, since a negative intercept is unphysical at EO → 0).
  4. [Results (Single-electron spectroscopy)] Supplementary Table S2 is cited for Pearson coefficients and p-values but is not in the main manuscript; ensure the table is available to referees and that the main text quotes the actual coefficients (~0.7 for P1/P3/P4, ~0.3 for P2) with uncertainties or sample sizes.
  5. [Methods] Eq. (1) in Methods (magnetospectroscopy fit) is dense; a short statement of which parameters are free (α, EST, Te) versus fixed (g = 2) would aid reproducibility.

Circularity Check

1 steps flagged

Primary claims are independent experimental measurements of EV/EO/EST; mild secondary circularity only in the alloy-disorder theory overlay, whose overall scale is fitted to the same EV data it is then said to match.

specific steps
  1. fitted input called prediction [Results (Single-electron spectroscopy, Fig. 2c) + Methods (Valley splitting correlations)]
    "We then fit the disorder parameter to the experimental distribution of EV to assess if the theoretical model can predict the spread and dependence of valley splitting as a function of orbital energy. We plot the distribution’s probability density … as a shaded area in Fig. 2(c) … η_yz = σ^{2}_Δ / ∫ dx |ψ(x; EOS)|^{4} ≈ 4.12 meV^{2} · nm. σ^{2}_Δ is computed using maximum likelihood approximation to fit a Rayleigh distribution to the measured values of EVS."

    η_yz (the sole free scale of the alloy-disorder model) is obtained directly from the same measured EV (and EO) values that the theory is subsequently overlaid upon. Once the scale is fixed by construction, the shaded probability density necessarily reproduces the average height and the observed spread of the data points; only the functional rise with EO remains a non-trivial model prediction. The paper presents this overlay as confirmation that “the theoretical model can predict the spread and dependence,” which is therefore partly circular.

full rationale

The load-bearing results (average EV = 0.40(6) meV, EO = 2.4(2) meV, linear coefficient ≈0.22 meV/meV for three dots, peak EV = 0.76(2) meV on P2, EST = 0.24(7) meV) are obtained from independent spectroscopies (DAPS, temperature-activated lever arms, magnetospectroscopy, PSB) and do not depend on any theoretical fit. The sole circular step is interpretive: the unfitted alloy-disorder model under-predicts absolute EV, so a single phenomenological constant η_yz is extracted from the measured EV distribution (Rayleigh MLE for σ^{2}_Δ plus average EOS) and the resulting probability density is overlaid on Fig. 2c as if the theory now “matches” the data. The EO dependence of the wave-function integral remains a model prediction, but the absolute scale and therefore the visual agreement are fixed by construction. This is secondary to the experimental claim that confinement raises EV and does not force the headline numbers or the architectural conclusion. No self-definitional loops, uniqueness theorems, or ansatz smuggling appear in the derivation chain.

Axiom & Free-Parameter Ledger

3 free parameters · 3 axioms · 0 invented entities

The central experimental claim rests on standard quantum-dot electrostatics and spectroscopy protocols plus one fitted phenomenological disorder strength taken from alloy-disorder theory. No new particles or forces are introduced. The free parameters that affect interpretation (not the raw EV numbers) are the lever arms, the linear-fit coefficients, and the single disorder integral η_yz.

free parameters (3)
  • disorder strength η_yz = ≈4.12 meV²·nm
    Phenomenological constant that multiplies the in-plane orbital integral; fitted by maximum-likelihood Rayleigh match to the measured EV distribution after the unfitted theory under-predicted the data (Methods).
  • linear coefficient α_EV/EO = 0.22(4) meV/meV
    Slope of EV versus EO for dots P1, P3, P4; obtained by ordinary least-squares fit to the experimental points (Fig. 2c).
  • plunger lever arms α = 0.08–0.12 eV/V
    Convert gate voltage to energy; extracted from temperature-broadened addition lines and cross-checked by magnetospectroscopy kinks; values 0.08–0.12 eV/V enter every energy scale reported.
axioms (3)
  • domain assumption Valley splitting in Si/SiGe is dominated by random Ge alloy disorder whose matrix element scales with the envelope amplitude at the interfaces.
    Taken from the Losert/Friesen theoretical framework (cited Refs. 41–42) and used to interpret the EV–EO correlation and to construct the shaded probability density in Fig. 2c.
  • domain assumption Electron temperature equals mixing-chamber temperature for T_MC > 0.5 K when extracting lever arms from Fermi-edge broadening.
    Stated in Methods; validated by observing constant lever-arm values between 0.5–1 K, but remains an approximation that propagates into all energy conversions.
  • domain assumption The two-electron singlet-triplet gap is limited by Wigner-molecule formation rather than the single-electron valley gap when EST < EV.
    Invoked in the Discussion to explain why EST averages only 0.24 meV despite larger EV; rests on prior theoretical literature on Wigner molecules in Si dots.

pith-pipeline@v1.1.0-grok45 · 21827 in / 3142 out tokens · 45070 ms · 2026-07-13T02:03:27.828509+00:00 · methodology

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Controlling the energy scales of a quantum system is essential for defining robust qubits. In silicon spin qubits, the nearly degenerate conduction-band valleys create a leakage channel from the single-spin computational basis, posing a challenge to scaling and to shuttling-based architectures. Here, we measure the relevant energy scales of single-electron spin qubits in buried silicon quantum wells co-designed for low disorder and high valley splitting. Across a linear array of four quantum dots with an average orbital energy of 2.4(2) meV, we report an average single-electron valley splitting of 0.40(6) meV and an average two-electron singlet-triplet splitting of 0.24(7) meV. In three dots, we observe a strong correlation between valley splitting and orbital energy, with an average linear coefficient of $\approx 0.22$ (meV/meV), demonstrating that electrostatic confinement can increase the valley splitting by several hundred microelectronvolts. In contrast, the remaining dot exhibits the highest valley splitting of 0.76(2) meV and low correlation, suggesting excellent characteristics for spin-qubit operation. Our findings demonstrate that strong confinement can be exploited in buried quantum wells to effectively enhance the valley splitting, thereby establishing a viable path toward the realization of shuttling and sparse-occupation-based architectures in low-disorder heterostructures.

Figures

Figures reproduced from arXiv: 2607.09570 by Asser Elsayed, Davide Costa, Davide Degli Esposti, Emma Catherine Brann, Giordano Scappucci, Mark Friesen.

Figure 1
Figure 1. Figure 1: Heterostructure and quantum dot gate stack a Quantum dot gate layout and voltage configuration used to achieve single-electron occupancy in the four-dot array. The top-right sensor is fully accumulated and used as an extension of the accumulation gate. The two sensors (S1 and S2) are used to sense the charge state of the four quantum dots (P1 to P4). The black line corresponds to 100 nm. b Double-dot charg… view at source ↗
Figure 2
Figure 2. Figure 2: Single-electron spectroscopy a Detuned axis pulsed spectroscopy (DAPS) maps of dot P1 obtained by sweeping the relative detuning (ve12) for different waiting times twait. Charge tunneling at a specific detuning is en￾hanced by the presence of well-defined quantum states, giving rise to a faster relaxation rate. We extract EO and EV from the separation of the resonant peaks and convert them into energy usin… view at source ↗
Figure 3
Figure 3. Figure 3: Two-electron spectroscopy. a Magnetospec￾troscopy of the second-electron addition line under vP1 as a function of the external in-plane magnetic field B. The thick dark line is a fit of the transition line to the theoreti￾cal model from which we extract the position of the kink at BST = 2.4(1) T, corresponding to a singlet-triplet splitting of EST = 0.28(1) meV, and a lever arm of α = 0.11 eV/V in agreemen… view at source ↗
Figure 4
Figure 4. Figure 4: Single-electron and two-electron energy states in silicon quantum dots. We report the charg￾ing energy (EC ), single electron orbital energy (EO), sin￾gle electron valley splitting (EV ), two-electrons singlet-triplet splitting measured via magnetospectroscopy (EST ) and Pauli￾Spin-Blockade spectroscopy (EP SB) for all the four dots (P1 blue, P2 orange, P3 green, and P4 red). The dashed lines correspond to… view at source ↗

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