Quantization of band tilting in modulated phononic crystals
Quantization of band tilting in modulated phononic crystals
复制标题
DOI：
10.1103/physrevb.97.014305
复制
发表时间：
2018-01-08
影响因子：
3.7
通讯作者：
Huang, G. L.
中科院分区：
文献类型：
--
作者：
Nassar, H.;Chen, H.;Huang, G. L.
本文建立了声子晶体中色散带倾斜的一般理论。倾斜调制速度的比率计算，第一次，在贝里的相位和曲率，并被证明是一个强大的整数值陈数。推导是基于一个版本的绝热定理的弹性波证明感谢WKB渐近。结果举例说明的情况下，3周期离散弹簧质量晶格。倾斜的色散图绘制的完全数值模拟和半解析计算的基础上的数值规范不变表达式的贝里的相位显示出完美的协议。单向阻塞波由于倾斜，并最终打破互易性，数值说明，并显示在有限数量的单元格是非常显着的，这表明实验演示的可行性。最后，一个版本的散装边缘对应原理有关的散装带的倾斜单向无带隙边缘状态的数量被证明。
A general theory of the tilting of dispersion bands in phononic crystals whose properties are being slowly and periodically modulated in space and time is established. The ratio of tilt to modulation speed is calculated, for the first time, in terms of Berry's phase and curvature and is proven to be a robust integer-valued Chern number. Derivations are based on a version of the adiabatic theorem for elastic waves demonstrated thanks to WKB asymptotics. Findings are exemplified in the case of a 3-periodic discrete spring-mass lattice. Tilted dispersion diagrams plotted using fully numerical simulations and semianalytical calculations based on a numerically gauge invariant expression of Berry's phase show perfect agreement. One-way blocking of waves due to the tilt, and ultimately to the breaking of reciprocity, is illustrated numerically and shown to be highly significant across a limited number of unit cells, suggesting the feasibility of experimental demonstrations. Finally, a version of the bulk-edge correspondence principle relating the tilt of bulk bands to the number of one-way gapless edge states is demonstrated.