AI 中文总结
研究层状异质结构近邻效应，通过推导动态近邻算符克服静态参数表示的局限，将哈密顿量降维到万尼尔子空间，精确再现光谱，揭示静态投影局限，为低能相关计算建立无拟合微观基础。
AI 中文摘要
层状异质结构中的近邻效应通常由拟合第一性原理能带的静态参数表示，这忽略了虚拟杂化、动量转移和空间结构的能量依赖性。我们通过直接从密度泛函理论推导动态近邻算符\(\mathcal{V}(\mathbf{k},\mathbf{k}';\omega)\)来克服这一限制，将异质结构的Kohn-Sham哈密顿量降维到固定的低能目标万尼尔子空间，并在该子空间内精确再现其光谱。该构造通过所有剩余状态将直接矩阵元素与虚拟杂化分开。在hBN/Co(0001)上的石墨烯中，虚拟杂化产生了超过99%的近邻交换，并赋予其由Co d态设定的共振频率依赖性。在石墨烯/PtSe₂中，它解决了具有\(\sqrt{3}\times\sqrt{3}\)电荷调制的亚晶格选择性谷间耦合，在石墨烯/WSe₂中，它解决了0.24 meV的键分辨Rashba耦合，而仅直接投影时低于1 μeV。我们的结果揭示了静态投影的局限性，并为低能建模、自旋弛豫理论和输运计算建立了无拟合的微观基础。
英文摘要
Proximity effects in layered heterostructures are usually represented by static parameters fitted to first-principles bands, which discards the energy dependence of the virtual hybridization, the momentum transfer, and the spatial structure. We overcome this limitation by deriving a dynamical proximity operator $\mathcal{V}(\mathbf{k},\mathbf{k}';ω)$ directly from density functional theory, downfolding the Kohn-Sham Hamiltonian of the heterostructure onto a fixed low-energy target Wannier subspace and reproducing its spectrum exactly within that subspace. The construction separates direct matrix elements from virtual hybridization through all remaining states. In graphene on hBN/Co(0001), virtual hybridization generates more than $99\%$ of the proximity exchange and gives it a resonant frequency dependence set by the Co $d$ states. In graphene/PtSe$_2$ it resolves a sublattice-selective intervalley coupling with a $\sqrt{3}\times\sqrt{3}$ charge modulation, and in graphene/WSe$_2$ a bond-resolved Rashba coupling of $0.24$~meV, against below $1$~$μ$eV for the direct projection alone. Our results expose the limitations of static projections and establish a fitting-free microscopic foundation for low-energy modeling, spin-relaxation theory, and transport calculations.
