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We show that the spectral weights $W_{m\vec K}(\vec k)$ used for theunfolding of two-component spinor eigenstates $| {\psi_{m\vec K}^\mathrm{SC}} >= | \alpha > | {\psi_{m\vec{K}}^\mathrm{SC, \alpha}} > + | \beta > |{\psi_{m\vec{K}}^\mathrm{SC, \beta}} >$ can be decomposed as the sum of thepartial spectral weights $W_{m\vec{K}}^{\mu}(\vec k)$ calculated for eachcomponent $\mu = \alpha, \beta$ independently, effortlessly turning a possiblycomplicated problem involving two coupled quantities into two independentproblems of easy solution. Furthermore, we define the unfolding-densityoperator $\hat{\rho}_{\vec{K}}(\vec{k}_{i}; \, \varepsilon)$, which unfolds theprimitive cell expectation values $\varphi^{pc}(\vec{k}; \varepsilon)$ of anyarbitrary operator $\mathbf{\hat\varphi}$ according to$\varphi^{pc}(\vec{k}_{i}; \varepsilon) =\mathit{Tr}(\hat{\rho}_{\vec{K}}(\vec{k}_{i}; \,\varepsilon)\,\,\hat{\varphi})$. As a proof of concept, we apply the method toobtain the unfolded band structures, as well as the expectation values of thePauli spin matrices, for prototypical physical systems described bytwo-component spinor eigenfunctions.

Unfolding spinor wavefunctions and expectation values of general operators: Introducing the unfolding-density operator