Hendrik J. Bluhm | Searcharxiv

arXiv2026

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

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.

cond-mat.mes-hall↗

arXiv2026

Valley-Enabled Intrinsic Dresselhaus Spin-Orbit Coupling in Silicon

We develop a symmetry-based theory of spin-orbit-valley coupling in silicon that reveals an intrinsic source of Dresselhaus spin-orbit coupling independent of interfaces or external electric fields. Treating the valley degree of freedom as a symmetry-carrying quantum degree of freedom, we show that the Dresselhaus interaction is necessarily valley off-diagonal and that a bulk contribution proportional to the valley Pauli matrix $τ_1$ is symmetry allowed. Tight-binding calculations yield a bulk coupling more than an order of magnitude larger than typical interface-induced spin-orbit coupling; achieving the same energy scale through the interface-induced mechanism would require electric fields roughly 50 times larger than typical fields. We further derive the symmetry-allowed spin-valley couplings generated by magnetic-field gradients and show how they account for the valley-dependent Zeeman splitting observed in micromagnet experiments. A slight tilt of the background magnetic field out of the plane produces an additional isotropic contribution linear in $B_z$, providing an experimentally accessible signature of the corresponding coupling constant. Finally, we predict a spin-independent micromagnet-induced valley splitting in the $τ_3$ channel, which is distinct from the $τ_{1,2}$ channels generated by alloy disorder and therefore remains robust against disorder-induced cancellation. These results establish valley symmetry as a fundamental ingredient in the spin-orbit physics of silicon and provide new mechanisms for controlling and probing spin and valley degrees of freedom in silicon quantum devices.

cond-mat.mtrl-sci↗