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

• URL: http://arxiv.org/abs/2609.08839v1
• Date: Tue, 08 Sep 2026 14:56:28 GMT
• 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
• Abstract summary: Valley splitting sets the energy scale at which spin and valley degrees of freedom hybridize in silicon quantum-well qubits.<n>We develop an analytical framework for treating non-perturbative effects of shear strain and wiggle-well potentials.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $V_sτ_2$, 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 $|\sin(k_{\rm min}L)|$ dependence. The variational result agrees with exact diagonalization to within $\sim1\%$ 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 $V_w\cos(k_wz)τ_1$, 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.

Related papers

• Valley-Enabled Intrinsic Dresselhaus Spin-Orbit Coupling in Silicon [0.0]
  We show a symmetry-based theory of spin-orbit-valley coupling in silicon.<n>We derive the symmetry-allowed spin-valley couplings generated by magnetic-field gradients.<n>These results establish valley symmetry as a fundamental ingredient in the spin-orbit physics of silicon.
  arXiv  Detail & Related papers  (2026-08-30T13:25:34Z)
• Tailoring pure valley-Zeeman spin-orbit coupling in WSe$_2$-encapsulated monolayer graphene [42.39722022913058]
  Engineering proximity effects in twisted van der Waals heterostructures offers a powerful platform for designing electronic properties.<n>We report pure valley-Zeeman spin-orbit coupling in monolayer graphene, achieved by encapsulation between two parallel twisted WSe$$ monolayers.<n>We also demonstrate the ability to completely quench the proximity spin-orbit coupling by tuning the encapsulated geometry.
  arXiv  Detail & Related papers  (2026-06-02T07:43:48Z)
• Singlet-triplet oscillations in multivalley Si double quantum dots [0.0]
  We present a theoretical description of the process of charge separation and singlet-triplet mixing.<n>We focus on magnetic fields for which the electron spin Zeeman splitting is close to the valley splitting in one of the dots.<n>We give a detailed description of singlet-triplet dynamics near these spin-valley resonances and compare the results of calculations with measurements on double quantum dots in two distinct Si/SiGe heterostructures.
  arXiv  Detail & Related papers  (2026-04-27T16:49:48Z)
• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Constrained many-body phases in a $\mathbb{Z}_2$-Higgs lattice gauge theory [39.58317527488534]
  We study a one-dimensional $mathbbZ$ lattice gauge theory coupled to soft-core bosonic matter at unit filling.<n>Through a combination of analytical perturbative approaches, we uncover a rich phase diagram driven by gauge-field-mediated resonant pair hopping.<n>The presence of a bunching state with large number fluctuations motivates experimental realizations in hybrid boson-qubit quantum simulation platforms.
  arXiv  Detail & Related papers  (2025-03-05T19:00:07Z)
• Photon Generation in Double Superconducting Cavities: Quantum Circuits Implementation [41.94295877935867]
  We studied photon generation due to the Dynamical Casimir Effect (DCE) in a one dimensional (1+1) double superconducting cavity. The total length of the double cavity $L$, the difference in length between the two cavities $Delta L$, and the electric susceptibility $chi$ are tunable parameters.
  arXiv  Detail & Related papers  (2024-07-19T14:33:45Z)
• Unifying Floquet theory of longitudinal and dispersive readout [33.7054351451505]
  We devise a Floquet theory of longitudinal and dispersive readout in circuit QED.<n>We apply them to superconducting and spin-hybrid cQED systems.
  arXiv  Detail & Related papers  (2024-07-03T18:00:47Z)
• Photon-induced droplet-like bound states in one-dimensional qubit array [0.0]
  We study the bandgap regime where the energy of two excited qubits is off-resonant with the two-photon bound state band. A two-step adiabatic elimination of the photonic degrees of freedom gives rise to a one-dimensional spin Hamiltonian with effective interactions.
  arXiv  Detail & Related papers  (2023-07-12T01:46:55Z)
• Quantum vibrational mode in a cavity confining a massless spinor field [91.3755431537592]
  We analyse the reaction of a massless (1+1)-dimensional spinor field to the harmonic motion of one cavity wall. We demonstrate that the system is able to convert bosons into fermion pairs at the lowest perturbative order.
  arXiv  Detail & Related papers  (2022-09-12T08:21:12Z)
• Valleytronic full configuration-interaction approach: An application to the excitation spectra of Si double-dot qubits [0.0]
  We study the influence of strong electron-electron interactions and Wigner-molecule (WM) formation on the spectra of Si qubits. We present results for both the $E_rm ST E_V$ and $E_rm ST E_V$ cases.
  arXiv  Detail & Related papers  (2022-08-11T03:55:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.