A topology optimization method for designing phononic Dirac-like cones and topological insulators by achieving the specific modes at specific frequencies is developed. At first, the Dirac-like cone is created by degenerating one monopolar mode and two dipolar modes at the desired frequency. It is demonstrated that the optimized phononic crystals with Dirac-like exhibit exotic zero-index wave manipulation phenomena. Next, by triggering the dipolar and quadrupolar modes simultaneously to form the double Dirac cone and then breaking it to realize band inversion, topological phase transition around the desired frequency is achieved. The robust one-way edge transport associated with topological phase transition is presented.

中文翻译：

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具有按需操作频率的声子狄拉克锥和拓扑绝缘体的拓扑优化

开发了一种拓扑优化方法，用于通过在特定频率下实现特定模式来设计声子狄拉克锥和拓扑绝缘体。首先，通过在所需频率下退化一个单极模式和两个偶极模式来创建类狄拉克锥。结果表明，优化后的类狄拉克声子晶体表现出奇异的零折射率波操纵现象。接下来，通过同时触发偶极和四极模式形成双狄拉克锥，然后将其破坏以实现带反转，实现了在所需频率附近的拓扑相变。提出了与拓扑相变相关的鲁棒单向边缘传输。