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arxiv: 2604.16713 · v2 · submitted 2026-04-17 · ❄️ cond-mat.mes-hall · quant-ph

Anisotropic spin-valley coupling in SiMOS and Si/SiGe quantum dots

N. Tobias Jacobson , Natalie D. Foster , Ryan M. Jock , Andrew M. Mounce , Daniel R. Ward , Malcolm S. Carroll , Dwight R. Luhman This is my paper

Pith reviewed 2026-05-11 00:55 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph
keywords spin-valley couplingsilicon quantum dotsSiMOSSi/SiGespin-orbit couplingelectron spin qubitsanisotropyg-factor
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The pith

SiMOS quantum dots show an order of magnitude larger spin-valley coupling than Si/SiGe dots, with similar angular dependence in both.

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

The paper compares spin-valley coupling strengths in two silicon quantum-dot platforms used for electron spin qubits. Measurements of the angular dependence of the interfacial spin-orbit interaction under varying magnetic field directions and magnitudes show that SiMOS devices have roughly ten times stronger coupling than Si/SiGe devices, even though differences in g-factors are comparable. A physical model is constructed that extracts the intra-valley and intervalley spin-orbit coupling parameters directly from fits to these data. This distinction matters because intervalley coupling can drive unwanted spin relaxation when the valley splitting is resonant with the Zeeman energy, limiting qubit coherence. The similar angular dependence in both systems implies that the same magnetic-field orientations can minimize the coupling in either platform.

Core claim

For the devices measured, while the g-factor differences are comparable, the SiMOS QDs exhibit an order of magnitude larger spin-valley coupling than for Si/SiGe. Moreover, the angular dependence of the spin-valley coupling is similar for both devices, with similar magnetic field orientations minimizing the spin-valley coupling. The physical model infers intra- and inter-valley SOC physics from fits to the angular dependence data, allowing direct comparison between the two material systems.

What carries the argument

The physical model that extracts intra- and inter-valley spin-orbit coupling strengths by fitting the measured angular dependence of the interfacial spin-orbit interaction.

If this is right

  • Si/SiGe platforms may be preferred when minimizing spin relaxation from valley coupling is critical.
  • Magnetic field orientations that minimize coupling can be used in both material systems with similar effect.
  • The extracted SOC parameters enable quantitative prediction of relaxation rates when valley splitting approaches the Zeeman energy.
  • Operational schemes can be designed either to avoid resonant conditions or to exploit the coupling for coherent rotations.

Where Pith is reading between the lines

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

  • Material selection between SiMOS and Si/SiGe could become a standard knob for balancing coupling strength against other device metrics such as valley splitting size.
  • The observed anisotropy suggests that small changes in interface electric field or strain might further tune the coupling in ways not yet tested.
  • Extending the same angular-dependence fitting approach to additional heterostructures would clarify which interface features dominate the coupling magnitude.

Load-bearing premise

The physical model accurately infers the intra- and inter-valley spin-orbit coupling from the angular-dependence data without missing terms, experimental artifacts, or incorrect interface-potential parameterization.

What would settle it

A direct measurement or independent calculation showing that the spin-valley coupling strength in SiMOS devices is not larger than in Si/SiGe devices by an order of magnitude, or that their angular minima differ substantially, would falsify the reported comparison.

Figures

Figures reproduced from arXiv: 2604.16713 by Andrew M. Mounce, Daniel R. Ward, Dwight R. Luhman, Malcolm S. Carroll, Natalie D. Foster, N. Tobias Jacobson, Ryan M. Jock.

Figure 1
Figure 1. Figure 1: Schematics of measured devices. False-color scanning electron microscopy (SEM) images of (a) SiMOS and (c) Si/SiGe devices. The crystallographic axis [110] ([1¯10]) is oriented along the inter-dot x-axis of the SEM images for the SiMOS (Si/SiGe) device, respectively. Rel￾evant gates shown are accumulation gates (purple) under￾neath which a two-dimensional electron gas forms, barrier gates (pink), and plung… view at source ↗
Figure 2
Figure 2. Figure 2: Singlet-triplet free induction decay measurements. (a) The ST Bloch sphere comprised of orthogonal control axes originating from the Zeeman energy difference due to SOC in pink (∆EZ) and exchange coupling due to wave function overlap in blue (J). The eigenstates of the magnetic field gradient are shown as | ↓↑⟩ and | ↑↓⟩ along the equatorial directions. (b) Schematic of the external magnetic field vector B… view at source ↗
Figure 9
Figure 9. Figure 9: The reported uncertainty for the valley splitting in [PITH_FULL_IMAGE:figures/full_fig_p003_9.png] view at source ↗
Figure 4
Figure 4. Figure 4: Si/SiGe measurements Measured ST rotation frequency derived from FFT of repeated free induction decay measurements in a Si/SiGe device along five B orientations. The FFT data are normalized for plotting. The model fit is superimposed in red. Two divergences appear, corresponding to Zeeman resonances with the valley splittings in the two quantum dots. The data in the top panel are derived from the repeated … view at source ↗
Figure 6
Figure 6. Figure 6: Angular dependence of spin-valley coupling for B ⊥ [001]. The fit spin-valley coupling for both SiMOS and Si/SiGe devices has a maximum for magnetic field applied along the [110] and [¯1¯10] axes. The magnitude of spin-valley coupling is an order of magnitude larger for SiMOS as com￾pared with Si/SiGe [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Angular dependence of g-factor difference between QDA and QDB for B ⊥ [001]. The angular dependence for both devices is equivalent up to a π/2 rotation and rescaling due to the significantly larger Dresselhaus than Rashba SOC contributions in both cases. the maximum of |Γ(θ, φ)| relative to the [100], [010] crys￾tallographic axes. We provide further details of the four￾level model and how it maps to ST rot… view at source ↗
Figure 6
Figure 6. Figure 6: The spin-valley phase offset η ≈ π/4 (extracted fit parameters shown in Table I) in both cases of dot pairs is apparent from the alignment of the lobes of max￾imum |Γ| with the [110] and [¯1¯10] crystallographic axes. We suspect that slight variation in η between QDs on the same device may be related to dot-to-dot differences in sampled interfacial disorder and/or quantum dot con￾finement potentials, thoug… view at source ↗
Figure 8
Figure 8. Figure 8: Taxonomy of spin-valley hotspots in a double quantum dot. Energy levels for two electron spins in a pair of quantum dots encoding a ST qubit. In the left column, we plot the energy levels of the relevant four spin-valley-orbital states of the system as a function of applied magnetic field for three different cases of g-factor differences (a) ∆g > 0, (c) ∆g < 0, and (e) ∆g = 0. The energy difference corresp… view at source ↗
Figure 9
Figure 9. Figure 9: Magnetic field orientation dependence of val￾ley splitting for SiMOS QDA. Our estimate of ∆vs,A is based on shifts of the hot spot critical field for QDA. The error bars denote 95% confidence intervals. what limiting the strength of electric field that may be imposed before undesirable tunneling out of the quantum well occurs. As for valley splitting37, we anticipate that thinner quantum wells may exhibit … view at source ↗
Figure 10
Figure 10. Figure 10: Excited valley state population. Frequency components of free induction decay measurements versus ramp time from S(4,0) to S(3,1). The color axis is the relative amplitude of the FFT in evolution time. For this measure￾ment, B || [110] = 523 mT in the (QD2,QD3) configuration in the Si/SiGe device. III. CONCLUSION In this work, we have measured SOC-driven effective magnetic field gradients in a singlet-tri… view at source ↗
Figure 12
Figure 12. Figure 12: Dephasing for Si/SiGe measurements. In￾verse of fit dephasing times, 1/T ∗ 2 (red points) superimposed on the measured FFT of singlet/triplet rotation frequency for the various B-field orientations. As for the SiMOS measure￾ments, coherence times appear to be shorter in the vicinity of spin-valley hot spots. The orange dashed line corresponds to a baseline 40 kHz inverse dephasing time that is generally o… view at source ↗
Figure 13
Figure 13. Figure 13: Measurements in a a second pair of QDs, (QD2,QD3), of the Si/SiGe triple QD. (left column) Magnetic field sweeps of ST free induction decay measurements for the same set of five magnetic field orientations in which multiple frequency components are evident. (right column) Plots of the corresponding extracted peak frequencies, with frequency component inferred by tracking the prominence of the FFT signal i… view at source ↗
read the original abstract

While bulk silicon has long been understood to exhibit relatively weak spin-orbit coupling (SOC), confinement of electrons to quantum dots (QDs) at a silicon heterointerface results in significantly larger SOC. This is a concern for electron spin qubit performance, as intravalley and intervalley SOC can significantly perturb the operation of electron spin qubits. While these interactions can be harnessed to drive coherent rotations in a singlet-triplet qubit, coupling to low-lying excited valley states can lead to undesirable spin relaxation when valley splitting is on resonance with the Zeeman energy. In this work, we measure the angular dependence of the interfacial spin-orbit interaction as a function of the direction and magnitude of an applied external magnetic field in SiMOS and Si/SiGe heterostructures, two common material platforms for silicon spin qubits. We construct a physical model that accurately infers intra- and inter-valley SOC physics from fits to the data, allowing for a direct comparison between these two material systems. For the devices measured we find that, while the $g$-factor differences are comparable, the SiMOS QDs exhibit an order of magnitude larger spin-valley coupling than for Si/SiGe. Moreover, we find that the angular dependence of the spin-valley coupling is similar for both devices, with similar magnetic field orientations minimizing the spin-valley coupling. Our work points towards operational schemes for optimizing spin-valley coupling to avoid or exploit this mechanism for qubit operation.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript measures the angular dependence of interfacial spin-orbit coupling in SiMOS and Si/SiGe quantum dots under varying magnetic field directions and magnitudes. A physical model is constructed and fitted to the data to extract intra- and inter-valley SOC parameters, leading to the claim that SiMOS devices show an order-of-magnitude larger spin-valley coupling than Si/SiGe while g-factor anisotropies are comparable and the angular dependence (including minimizing field orientations) is similar in both systems. The work discusses implications for optimizing or mitigating SOC effects in silicon spin qubit operation.

Significance. If the model-based extraction holds, the quantitative comparison between these two standard silicon qubit platforms is useful for device engineering, as it identifies material-dependent differences in a key decoherence mechanism and provides practical guidance on magnetic field orientations. The experimental angular-dependence data themselves represent a solid contribution to the literature on confined SOC in silicon.

major comments (2)
  1. The abstract states that a physical model 'accurately infers intra- and inter-valley SOC physics from fits to the data,' yet no explicit equations, parameterization of the interface potential, or fit procedure (including error analysis and data selection) are supplied. This omission is load-bearing for the central claim of an order-of-magnitude difference, as unaccounted terms (e.g., strain gradients or higher-order Zeeman effects) could mimic the observed angular signature.
  2. The reported SOC values are obtained by fitting the same angular-dependence dataset that the model is constructed to reproduce. Without independent cross-validation (e.g., against first-principles calculations, limiting-case checks, or separate measurements), the inference risks circularity and does not yet establish intrinsic material differences.
minor comments (2)
  1. Add explicit statements of fit residuals, parameter uncertainties, and any data exclusion criteria to the figures and text.
  2. Include a brief comparison of the extracted SOC magnitudes to prior theoretical or experimental values in the silicon QD literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the positive assessment of its significance for silicon spin qubit engineering. We agree that greater clarity on the model and fitting details will strengthen the paper and have revised the manuscript accordingly. Our point-by-point responses to the major comments follow.

read point-by-point responses

  1. Referee: The abstract states that a physical model 'accurately infers intra- and inter-valley SOC physics from fits to the data,' yet no explicit equations, parameterization of the interface potential, or fit procedure (including error analysis and data selection) are supplied. This omission is load-bearing for the central claim of an order-of-magnitude difference, as unaccounted terms (e.g., strain gradients or higher-order Zeeman effects) could mimic the observed angular signature.

    Authors: We thank the referee for highlighting this presentational issue. The full manuscript (Section III and Supplementary Material) derives the effective Hamiltonian from interface symmetry, parameterizes the intra-valley Rashba-like and inter-valley terms via the interface potential, and describes the angular fitting. However, we accept that these elements were not sufficiently prominent or self-contained. In the revised version we have added an explicit 'Theoretical Model' subsection that states the Hamiltonian, lists all fit parameters with their physical meaning, details the data-selection criteria (resonance visibility and field-range limits), and reports the fitting procedure together with bootstrap-based uncertainty estimates. We have also inserted a dedicated paragraph estimating the magnitude of possible confounding contributions (strain gradients, higher-order Zeeman terms) and showing that they cannot reproduce the observed angular nodes at the experimental fields and temperatures. revision: yes

  2. Referee: The reported SOC values are obtained by fitting the same angular-dependence dataset that the model is constructed to reproduce. Without independent cross-validation (e.g., against first-principles calculations, limiting-case checks, or separate measurements), the inference risks circularity and does not yet establish intrinsic material differences.

    Authors: The referee correctly notes that the same dataset is used both to motivate the functional form and to extract numerical values. The functional form itself, however, follows from symmetry-allowed interface terms and is independent of the particular measurements; the angular nodes and field-magnitude scaling are predictions that are then tested against data. We have strengthened the manuscript by (i) adding explicit limiting-case checks (vanishing coupling at the predicted in-plane angles and linear scaling with B) that are satisfied by the raw data before fitting, and (ii) comparing the extracted SiMOS and Si/SiGe values with previously published estimates for similar interfaces. While we cannot perform new first-principles calculations within the scope of this experimental work, the internal consistency across two material platforms, multiple devices, and a range of field magnitudes supports the reported order-of-magnitude difference. We have added a short caveats paragraph in the discussion to make these limitations transparent. revision: partial

Circularity Check

0 steps flagged

No significant circularity; standard fitting of model to angular data

full rationale

The abstract states that a physical model is constructed to infer intra- and inter-valley SOC from fits to the measured angular dependence data, enabling comparison between SiMOS and Si/SiGe devices. This is explicit experimental parameter extraction rather than a claimed first-principles derivation or prediction that reduces to the inputs by construction. No equations, self-citations, or uniqueness theorems are invoked in the provided text to create a definitional loop or fitted-input-called-prediction. The reported order-of-magnitude difference and angular similarity are direct outputs of the per-device fits, which is the normal scientific process for such measurements and does not meet the criteria for circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim rests on a fitted physical model whose free parameters for coupling strengths are determined from the same data used to validate the model. Standard domain assumptions about confined-electron SOC are invoked without independent verification in the provided abstract.

free parameters (3)
  • intra-valley SOC strength
    Fitted parameter extracted from angular dependence data for each device type.
  • inter-valley SOC strength
    Fitted parameter extracted from angular dependence data for each device type.
  • g-factor anisotropy parameters
    Fitted to reproduce observed g-factor differences as function of field direction.
axioms (2)
  • domain assumption Interfacial spin-orbit interaction in silicon quantum dots can be decomposed into intra-valley and inter-valley contributions whose angular dependence is captured by a simple physical model.
    Invoked when constructing the model that infers SOC physics from the data.
  • domain assumption Valley splitting and Zeeman energy are the dominant energy scales that determine resonance conditions for spin relaxation.
    Used to interpret when spin-valley coupling leads to undesirable relaxation.

pith-pipeline@v0.9.0 · 5586 in / 1633 out tokens · 74156 ms · 2026-05-11T00:55:10.078771+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Singlet-triplet oscillations in multivalley Si double quantum dots

    cond-mat.mes-hall 2026-04 unverdicted novelty 5.0

    Theoretical expressions for singlet return probability in multivalley Si double quantum dots near spin-valley resonances are derived, accounting for valley occupations, and validated against experiments to map valley ...

Reference graph

Works this paper leans on

9 extracted references · 9 canonical work pages · cited by 1 Pith paper

  1. [1]

    The tilde (˜) notation de- notes that the spin states are defined relative toB(θ, ϕ)

    spanning{|˜↓ A 1 ˜↓ B 0 ⟩,| ˜↓ A 0 ˜↓ B 1 ⟩}. The tilde (˜) notation de- notes that the spin states are defined relative toB(θ, ϕ). In the model Hamiltonian, 5 Figure 5.Three-dimensional polar plot of the fit in- tervalley SOC strength as a function of magnetic field orientation for QD B of SiMOS device.The five intersecting planes(θ, φ)∈ {(π/2,[0,2π]),([...

    work page

  2. [2]

    Moreover, theg-factor differ- ences between quantum dots are of a similar magnitude for both material systems

    crystallographic axes. Moreover, theg-factor differ- ences between quantum dots are of a similar magnitude for both material systems. A simple way to minimize the effective magnetic field gradient due to SOC from intravalley SOC-inducedg- factor differences is to apply the magnetic field normal to the interface (B∥[001]). However, when operating the ST qu...

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  3. [3]

    14.9 [¯111] -15.6 [1¯11] -14.7

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    Given the initial experimental estimate for the (signed) magnetic field strengthB, the offset correction takesB→B+B offset

    -1.9 TableII.Magneticfieldoffsetsforeachsweepdirection for SiMOS measurements.We attribute these offsets to synchronization error of measurement and hysteresis. Given the initial experimental estimate for the (signed) magnetic field strengthB, the offset correction takesB→B+B offset. with input from all co-authors. Appendix A: Experimental setup We perfor...

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    We use a tilde notation (e.g

    axis, which is the normal to the Si/SiO2 or Si/SiGe interface. We use a tilde notation (e.g. ˜↑ E ) to indicate a spin state defined relative to the quantization axis spec- ified by a givenBorientation. Let the two-electron spin states for the regime of well- separated electrons be given by the following. Note that the charge configuration we assume from ...

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  6. [6]

    microscopic

    Intravalley spin-orbit coupling We assume the spin-orbit coupling Hamiltonian in a given quantum dot to be a sum of Rashba and Dressel- hauss termsH SO =H R +H D, with HR =α(P yσx −P xσy)(B4) HD =β(P xσx −P yσy),(B5) whereP x,y are kinetic momenta along thexandycrys- tallographic axes and the factorsαandβpotentially have a spatial dependence to account fo...

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  7. [7]

    Addinginthespindegreeoffreedom, weare interested in evaluating the spin-orbit coupling between ground and first-excited valley-orbital states having op- posite spin orientation

    Spin-valley coupling For a given quantum dot, let the ground and first- excited valley-orbital eigenstates be given by|E0⟩,|E 1⟩, respectively. Addinginthespindegreeoffreedom, weare interested in evaluating the spin-orbit coupling between ground and first-excited valley-orbital states having op- posite spin orientation. Denote γ↑↓ R,D =⟨E 0 ↑ |HR,D|E1 ↓⟩,...

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  8. [8]

    We are interested in the dynamics of the singlet and unpolarized triplet states,|S⟩and|T 0⟩, in the ground valley-orbital sector of the double quantum dot

    Double quantum dot Hamiltonian We now consider the energy levels of the singlet-triplet qubit encoded within the double quantum dot system. We are interested in the dynamics of the singlet and unpolarized triplet states,|S⟩and|T 0⟩, in the ground valley-orbital sector of the double quantum dot. These states are spanned by{|˜↑ A 0 ˜↓ B 0 ⟩,| ˜↓ A 0 ˜↑ B 0 ...

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  9. [9]

    The starting dataset is the spectral power of singlet return probability as a function of manipula- tion time for a range of applied magnetic field strengths and orientations

    Fitting to the measurements Here, we describe our procedures for analyzing the measurement data and performing the model parame- ter estimates. The starting dataset is the spectral power of singlet return probability as a function of manipula- tion time for a range of applied magnetic field strengths and orientations. Our procedure for postprocessing and ...

    work page arXiv 2003