Purely cubic spin splittings in the band structure of bulk insulators have not been extensively investigated yet despite the fact that they may pave the way for novel spin-orbitronic applications and can also result in a variety of promising spin phenomena. By symmetry analysis and first-principles simulations, we report symmetry-enforced purely cubic spin splittings (SEPCSS) that can even lead to persistent spin textures. In particular, these SEPCSS can be thought to be complementary to the cubic Rashba and cubic Dresselhaus types of spin splittings. Strikingly, the presently discovered SEPCSS are expected to exist in the large family of materials crystallizing in the $\overline{6}m2$ and $\overline{6}$ point groups, including the ${\mathrm{Ge}}_3{\mathrm{Pb}}_5{\mathrm{O}}_{11}$, ${\mathrm{Pb}}_7{\mathrm{Br}}_2{\mathrm{F}}_{12}$, and ${\mathrm{Pb}}_7{\mathrm{Cl}}_2{\mathrm{F}}_{12}$ compounds.

中文翻译：

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具有持久自旋纹理的纯立方自旋分裂

尽管大体积绝缘子的能带结构中的纯立方自旋分裂可能为新型自旋或双自电子应用铺平道路，并可能导致各种有希望的自旋现象，但尚未进行广泛的研究。通过对称性分析和第一性原理模拟，我们报告了对称增强的纯立方自旋分裂（SEPCSS），甚至可能导致持久的自旋纹理。特别地，这些SEPCSS可以被认为是立方Rashba和立方Dresselhaus类型的自旋分裂的补充。引人注目的是，目前发现的SEPCSS有望存在于大量晶体中。$\overline{6}米2$ 和 $\overline{6}$ 点组，包括 ${\mathrm{通用电器}}_3{\mathrm{铅含量}}_5{\mathrm{Ø}}_{11}$， ${\mathrm{铅含量}}_7{溴}_2{\mathrm{F}}_{12}$和 ${\mathrm{铅含量}}_7{氯}_2{\mathrm{F}}_{12}$ 化合物。