College of Chemistry and Molecular Engineering, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, and Beijing National Laboratory for Molecular Sciences (BNLMS), Peking University, Beijing 100871, China.
Phys Chem Chem Phys. 2013 Nov 21;15(43):18855-62. doi: 10.1039/c3cp53257g.
The influence of lattice symmetry on the existence of Dirac cones was investigated for two distinct systems: a general two-dimensional (2D) atomic crystal containing two atoms in each unit cell and a 2D electron gas (2DEG) under a periodic muffin-tin potential. A criterion was derived under a tight-binding approximation for the existence of Dirac cones in the atomic crystal. When the transfer hoppings are assumed to be single functions of the distance between atoms, it was shown that the probability of observing Dirac cones in the atomic crystal gradually decreases before being reduced to zero when the lattice changes from hexagonal to square. For a 2DEG with full square symmetry, a Dirac point exists at the Brillouin zone corners, where the energy dispersion is parabolic not linear. These results suggest that conventional Dirac fermions (such as those in graphene) are difficult to achieve in a square lattice with full symmetry (wallpaper group p4mm).
研究了晶格对称性对狄拉克锥存在的影响，研究了两个不同的系统：一个包含每个单元中两个原子的一般二维（2D）原子晶体和一个在周期 muffin-tin 势下的二维电子气（2DEG）。在紧束缚近似下，为原子晶体中狄拉克锥的存在导出了一个判据。当假设转移跳跃仅是原子之间距离的单函数时，当晶格从六边形变为正方形时，观察到原子晶体中狄拉克锥的概率逐渐减小，直到减小为零。对于具有完全正方形对称性的 2DEG，在布里渊区角处存在狄拉克点，其中能量色散是抛物线而不是线性的。这些结果表明，在具有完全对称性（壁纸群 p4mm）的正方形晶格中，很难实现传统的狄拉克费米子（如石墨烯中的那些）。
