Damljanović V, Gajić R
Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia.
J Phys Condens Matter. 2017 May 10;29(18):185503. doi: 10.1088/1361-648X/aa6489. Epub 2017 Mar 6.
There have been growing efforts to find new two-dimensional (2D) materials with anisotropic properties due to their potential applications in electronics. Although in such a search, a symmetry based analysis can be useful, it has not been reported so far. Using group theory we have found sufficient conditions for the existence of a linear dispersion in one direction and quadratic one in perpendicular direction, in the vicinity of points of symmetry in the Brillouin zone (BZ) of any non-magnetic, 2D material with negligible spin-orbit coupling. We have formulated a set of symmetry conditions that lead to the semi-Dirac dispersion and analyzed all possible symmetries of 2D materials. In four, out of all eighty symmetry groups, combined time-reversal and crystal symmetry leads, at given points in the BZ, to such dispersion. The result is valid irrespectively of strength of electronic correlations in the system, model used to calculate the band structure, or the actual crystal structure that realizes given groups. We have illustrated our findings using a tight-binding example.
由于二维（2D）材料在电子学中的潜在应用，人们越来越努力寻找具有各向异性特性的新型二维材料。尽管在这样的探索中，基于对称性的分析可能会有所帮助，但迄今为止尚未见相关报道。利用群论，我们已经找到了在任何具有可忽略自旋轨道耦合的非磁性二维材料的布里渊区（BZ）对称点附近，一个方向上存在线性色散而垂直方向上存在二次色散的充分条件。我们已经制定了一组导致半狄拉克色散的对称条件，并分析了二维材料的所有可能对称性。在所有八十个对称群中，有四个群在BZ的给定位置，结合时间反演和晶体对称性会导致这种色散。该结果与系统中电子关联的强度、用于计算能带结构的模型或实现给定群的实际晶体结构无关。我们用一个紧束缚示例说明了我们的发现。
