AI 中文总结
本文通过变分波函数和谷轨道基建立非微扰解析框架，研究硅量子阱中剪切应变与摆动阱势对谷分裂的影响，发现振荡依赖、应变调谐方法及高振幅下的渐近自由行为。
AI 中文摘要
谷分裂设定了硅量子阱量子比特中自旋与谷自由度混合的能量尺度，但其对界面结构的敏感性使其难以预测。利用谷轨道基，我们在有限量子阱中建立了用于谷间耦合的双带有效质量模型，并发展了一个解析框架来处理剪切应变和摆动阱势的非微扰效应。对于与$z$无关的耦合$V_s\tau_2$（对应均匀剪切应变），我们从精确平面波谷轨道和硬壁包络构造了一个变分态。这给出了两个最低态及其分裂的闭式表达式，包括特征振荡的$|\sin(k_{\rm min}L)|$依赖关系。变分结果与精确对角化在现实耦合下吻合至$\sim1\\%$以内，并提供了一种简单的方法来调节剪切应变远离节点以增强谷分裂。我们进一步表明，有限势垒高度主要重整化量子阱的有效宽度，同时保持振荡依赖关系。对于摆动阱耦合$V_w\cos(k_wz)\tau_1$，谷轨道表示揭示了在$k_w=2k_1$共振附近从摆动主导分裂到轨道量子化的交叉。值得注意的是，在高摆动阱振幅下，空盒能量尺度主要决定近共振谷分裂，而摆动阱势仅作为次主导修正进入。这种行为可视为自旋量子比特的渐近自由。远离共振时，分裂随失谐表现出宽峰共振，并带有类似衍射的旁瓣。
英文摘要
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.
