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An example of diperiodic crystal structure with semi-Dirac electronic dispersion

机译：具有半狄拉克电子弥散的二倍体晶体结构的示例

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In the physics of two-dimensional materials, notion semi-Dirac dispersion denotes electronic dispersion which is Dirac-like along one direction in the reciprocal space, and quadratic along the orthogonal direction. In our earlier publication (DamljanoviAc and GajiAc in J Phys Condens Matter 29:185503, 2017) we have shown that certain layer groups are particularly suitable for hosting semi-Dirac dispersion in the vicinity of some points in the Brillouin zone (BZ). In the present paper we have considered tight-binding model up to seventh nearest neighbors, on a structure belonging to layer group Dg5. According to our theory, this group should host semi-Dirac dispersion at A and B points in the BZ. The structure has four atoms per primitive cell, and it is isostructural with sublattice occupied by phosphorus atoms in the layered material SnPSe. While the first order perturbation theory of double degenerate level gives two pairs of semi-Dirac cones and correctly reproduces dispersion in the Dirac-like direction, exact diagonalisation of four-by-four tight-binding Hamiltonian shows node lines caused by accidental degeneracy in the band structure. We discuss these degeneracies in the context of von Neumann-Wigner theorem, and conclude that although dispersion remains semi-Dirac in the exact diagonalisation method, the band structure does not necessarily form cones. In order to get full picture of behavior of bands in the vicinity of semi-Dirac points, first order perturbation theory may not be sufficient and one may need higher order corrections.
机译：在二维材料的物理学中，概念半狄拉克色散表示电子色散，该电子色散在倒数空间中沿一个方向呈狄拉克型，而沿正交方向呈二次方。在我们较早的出版物中（DamljanoviAc和GajiAc在J Phys Condens Matter 29：185503，2017）中，我们显示了某些层组特别适合在布里渊区（BZ）的某些点附近承载半狄拉克色散。在本文中，我们已经考虑了属于层组Dg5的结构上的紧绑定模型，直到第七个最近的邻居。根据我们的理论，该组应在BZ的A和B点处进行半狄拉克频散。该结构每个原始单元具有四个原子，并且是同构结构，亚晶格被层状材料SnPSe中的磷原子占据。虽然双简并级的一阶摄动理论给出了两对半狄拉克锥，并正确地再现了狄拉克样方向上的色散，但四乘四紧束缚哈密顿量的精确对角线化显示了由意外简并引起的节点线。带结构。我们在von Neumann-Wigner定理的背景下讨论这些简并性，并得出结论，尽管在精确的对角化方法中色散仍然是半狄拉克，但能带结构不一定形成圆锥。为了获得半狄拉克点附近频带的行为的全貌，一阶微扰理论可能不够充分，可能需要更高阶的校正。

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