氧化黑磷电子能带结构的对称保护简并
Symmetry-Protected Degeneracies in the Electronic Band Structure of Oxidized Black Phosphorous
摘要：
我们用从头算密度泛函理论研究了单层黑磷的氧化过程。我们寻找磷烯氧化物，PO $_x$与不同氧浓度$x$（$0{\le}x{\le}1$）的平衡结构。通过评估不同构型的形成能和它们的振动性质，对于每个不同的$x$值，我们确定了一系列稳定的氧化结构与$x$，并确认氧化自然发生。同时还发现氧化使P-O键中的P-P键的某些模式具有红外活性，这意味着红外光谱可以用来确定磷烯的氧化程度。我们的电子结构计算表明，完全氧化的磷烯（PO）有一个直接的带隙为0.83 eV的原始磷烯类似。有趣的是，PO具有两个非对称对称性与反转对称性破缺，保证了一个受保护的能带结构，包括带简并和四重简并Dirac点。我们的结果可能会提供一个重要的洞察晶格的对称性和电子的能带拓扑结构之间的有趣的关系。
英文摘要：
We explore the oxidation of a single layer of black phosphorous using ab initio density functional theory calculation. We search for the equilibrium structures of phosphorene oxides, PO$_x$ with various oxygen concentrations $x$ ($0{\le}x{\le}1$). By evaluating the formation energies with diverse configurations and their vibrational properties for each of various $x$ values, we identify a series of stable oxidized structures with $x$ and confirm that the oxidation occurs naturally. We also find that oxidation makes some modes from the P-O bonds P-P bonds IR-active implying that the infrared spectra can be used to determine the degree of oxidation of phosphorene. Our electronic structure calculation reveals that the fully oxidized phosphorene (PO) has a direct band gap of 0.83 eV similar to the pristine phosphorene. Intriguingly, the PO possesses two nonsymmorphic symmetries with the inversion symmetry broken, guaranteeing a symmetry-protected band structures including the band degeneracy and four-fold degenerate Dirac points. Our results may provide a significant insight into the intriguing relations between symmetry of lattice and band topology of electrons.
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