Crystal-Field and Strain Effects on Minimum-Spin-Splitting Surfaces in Bulk Wurtzite Materials

概要

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The spin-splitting energies in strained bulk wurtzite aluminum nitride (AlN) are studied using the linear combination of atomic orbital method. It is found that strain and crystal field induce not only a linear-$k$ ($\alpha_{\text{wz}}$) but also two cubic-$k$ terms ($\gamma'$ and $\lambda'$) in the two-band $\mathbf{k} \cdot \mathbf{p}$ Hamiltonian $H_{\text{SO}}(\mathbf{k}) = (\alpha_{\text{wz}}-\gamma'k_{\|}^{2} + \lambda'k_{z}^{2})(\sigma_{x}k_{y}-\sigma_{y}k_{x}) + H_{\text{SO}}^{0}$, where $H_{\text{SO}}^{0} = (-\gamma_{0}k_{\|}^{2} + \lambda_{0}k_{z}^{2})$ $(\sigma_{x}k_{y}-\sigma_{y}k_{x})$ is for ideal wurtzite and generates a cone-shaped minimum-spin-splitting (MSS) surface. As biaxial strain increases, the shape of the MSS surface changes from a hexagonal hyperboloid of two sheets in unstrained AlN to a hexagonal cone, and eventually becomes a hyperboloid of one sheet.
2010-09-15