Damljanović V, Gajić R
Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia.
J Phys Condens Matter. 2016 Mar 2;28(8):085502. doi: 10.1088/0953-8984/28/8/085502. Epub 2016 Feb 1.
We have considered non-magnetic materials with weak spin-orbit coupling, that are periodic in two non-collinear directions, and finite in the third, orthogonal direction. In some cases, the combined time-reversal and crystal symmetry of such systems, allows the existence of Dirac cones at certain points in the reciprocal space. We have investigated in a systematic way, all points of the Brillouin zone of all 80 diperiodic groups and have found sufficient conditions for the existence of s = 1/2 Dirac fermions, with symmetry-provided band touching at the vertex of the Dirac cones. Conversely, complete linear dispersion is forbidden for orbital wave functions belonging to two-dimensional (2D) irreducible representations (irreps) of little groups that do not satisfy certain group theoretical conditions given in this paper. Our results are illustrated by a tight-binding example.
我们考虑了具有弱自旋轨道耦合的非磁性材料，这些材料在两个非共线方向上具有周期性，而在第三个正交方向上是有限的。在某些情况下，此类系统的时间反演对称性和晶体对称性相结合，使得在倒易空间的某些点处存在狄拉克锥。我们系统地研究了所有80个双周期群的布里渊区的所有点，并找到了存在自旋s = 1/2狄拉克费米子的充分条件，其能带在狄拉克锥顶点处由对称性提供接触。相反，对于属于小子群的二维（2D）不可约表示（irrep）且不满足本文给出的某些群论条件的轨道波函数，完全线性色散是被禁止的。我们的结果通过一个紧束缚示例进行说明。
