Non-perturbative theory of valley splitting in Si qubits from variational wave function: periodic effects of shear strain and asymptotic freedom in the wiggle-well potential
Abstract
Valley splitting sets the energy scale at which spin and valley degrees of freedom hybridize in silicon quantum-well qubits, but its sensitivity to interface structure makes it difficult to predict. Using the valleyor basis, we formulate a two-band effective-mass model for intervalley coupling in a finite quantum well and develop an analytical framework for treating non-perturbative effects of shear strain and wiggle-well potentials. For a z-independent coupling Vsτ2, corresponding to uniform shear strain, we construct a variational state from the exact plane-wave valleyors and a hard-wall envelope. This yields closed-form expressions for the two lowest states and their splitting, including the characteristic oscillatory |sin(kminL)| dependence. The variational result agrees with exact diagonalization to within ∼1% for realistic couplings, and provides a simple prescription for tuning the shear strain away from the nodes to enhance the valley splitting. We further show that finite barrier heights primarily renormalize the effective width of the quantum well while preserving the oscillatory dependence. For a wiggle-well coupling Vwcos(kwz)τ1, the valleyor representation reveals a crossover near the kw=2k1 resonance from wiggle-dominated splitting to orbital quantization. Remarkably, at high wiggle-well amplitudes, the empty-box energy scale predominantly dictates the near-resonant valley splitting, while the wiggle-well potential enters only as a sub-leading correction. This behavior can be viewed as asymptotic freedom for spin qubits. Away from resonance, the splitting exhibits a broadly peaked resonance with diffraction-like side-lobes as a function of detuning.
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BibTeX
@misc{steinschuld2026nonperturbative,
title = {{Non-perturbative theory of valley splitting in Si qubits from variational wave function: periodic effects of shear strain and asymptotic freedom in the wiggle-well potential}},
author = {Johannes L. P. Steinschuld and Hendrik J. Bluhm and Seyed Akbar Jafari},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08839},
eprint = {2609.08839},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08839},
}
RIS
TY - UNPB
TI - Non-perturbative theory of valley splitting in Si qubits from variational wave function: periodic effects of shear strain and asymptotic freedom in the wiggle-well potential
AU - Johannes L. P. Steinschuld
AU - Hendrik J. Bluhm
AU - Seyed Akbar Jafari
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08839
UR - https://arxiv.org/abs/2609.08839
AB - Valley splitting sets the energy scale at which spin and valley degrees of freedom hybridize in silicon quantum-well qubits, but its sensitivity to interface structure makes it difficult to predict. Using the valleyor basis, we formulate a two-band effective-mass model for intervalley coupling in a finite quantum well and develop an analytical framework for treating non-perturbative effects of shear strain and wiggle-well potentials. For a z-independent coupling V_sτ_2, corresponding to uniform shear strain, we construct a variational state from the exact plane-wave valleyors and a hard-wall envelope. This yields closed-form expressions for the two lowest states and their splitting, including the characteristic oscillatory |sin(k_minL)| dependence. The variational result agrees with exact diagonalization to within ∼1% for realistic couplings, and provides a simple prescription for tuning the shear strain away from the nodes to enhance the valley splitting. We further show that finite barrier heights primarily renormalize the effective width of the quantum well while preserving the oscillatory dependence. For a wiggle-well coupling V_wcos(k_wz)τ_1, the valleyor representation reveals a crossover near the k_w=2k_1 resonance from wiggle-dominated splitting to orbital quantization. Remarkably, at high wiggle-well amplitudes, the empty-box energy scale predominantly dictates the near-resonant valley splitting, while the wiggle-well potential enters only as a sub-leading correction. This behavior can be viewed as asymptotic freedom for spin qubits. Away from resonance, the splitting exhibits a broadly peaked resonance with diffraction-like side-lobes as a function of detuning.
ER -