论文标题
周期性施罗丁运营商的带结构中的双狄拉克锥
Double Dirac cones in band structures of periodic Schrödinger operators
论文作者
论文摘要
狄拉克锥是圆锥形的奇异性，在带结构中的退化点附近发生。这种奇异性导致相应物理系统的巨大异常现象。这项工作研究了某些操作员带结构中四倍变性点附近发生的双狄拉克锥。众所周知，这种堕落起源于哈密顿人的对称性。我们使用具有新型设计对称性作为我们的原型的二维周期性施罗丁运营商。首先，我们表征可允许的电位，称为超级蜂窝状晶格电位。它们是蜂窝状晶格电位，具有关键的其他翻译对称性。严格证明，具有这种潜力的Schrödinger经营者几乎可以保证在Brillouin区的起源γ点的频段上存在双狄拉克锥。我们进一步表明，通过扰动分析，其他翻译对称性是必不可少的成分。实际上，如果额外的翻译对称性被打破，双锥消失了。提供了许多数值模拟，这与我们的分析非常吻合。
Dirac cones are conical singularities that occur near the degenerate points in band structures. Such singularities result in enormous unusual phenomena of the corresponding physical systems. This work investigates double Dirac cones that occur in the vicinity of a fourfold degenerate point in the band structures of certain operators. It is known that such degeneracy originates in the symmetries of the Hamiltonian. We use two dimensional periodic Schrödinger operators with novel designed symmetries as our prototype. First, we characterize admissible potentials, termed as super honeycomb lattice potentials. They are honeycomb lattices potentials with a key additional translation symmetry. It is rigorously justified that Schrödinger operators with such potentials almost guarantee the existence of double Dirac cones on the bands at the Γ point, the origin of the Brillouin zone. We further show that the additional translation symmetry is an indispensable ingredient by a perturbation analysis. Indeed, the double cones disappear if the additional translation symmetry is broken. Many numerical simulations are provided, which agree well with our analysis.
