论文标题
三维准晶体中的第三个Chern数字的拓扑差距标记
Topological gap labeling with the third Chern numbers in three-dimensional quasicrystals
论文作者
论文摘要
我们研究了一般3D准晶体的拓扑间隙标记，我们发现频谱中的每个差距都具有一组第三个Chern数字。我们表明，准周期结构具有由冗余波形定义的多个Brillouin区域，并且差距下方的状态数量被量化为这些Brillouin区域体积的整数线性组合。通过考虑在6D绝缘子中，在准周期性电位的循环变形下泵送的绝热电荷在循环变形下泵送的绝热电荷之间的形式关系，可以将其表征为第三个Chern数字来表达的量子数。
We study the topological gap labeling of general 3D quasicrystals and we find that every gap in the spectrum is characterized by a set of the third Chern numbers. We show that a quasi-periodic structure has multiple Brillouin zones defined by redundant wavevectors, and the number of states below a gap is quantized as an integer linear combination of volumes of these Brillouin zones. The associated quantum numbers to characterize energy gaps can be expressed as third Chern numbers by considering a formal relationship between an adiabatic charge pumping under cyclic deformation of the quasi-periodic potential and a topological nonlinear electromagnetic response in 6D insulators.
