Department of Physics, The Pennsylvania State University, University Park, State College, Pennsylvania 16802, USA.
Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
Nat Commun. 2015 Oct 1;6:8336. doi: 10.1038/ncomms9336.
Realizing topological insulators is of great current interest because of their remarkable properties and possible future applications. There are recent proposals based on Floquet analyses that one can generate topologically non-trivial insulators by periodically driving topologically trivial ones. Here we address what happens if one follows the dynamics in such systems. Specifically, we present an exact study of the time evolution of a graphene-like system subjected to a circularly polarized electric field. We prove that for infinite (translationally invariant) systems the Chern number is conserved under unitary evolution. For systems with boundaries, on the other hand, we show that a properly defined topological invariant, the Bott index, can change. Hence, it should be possible to experimentally prepare topological states starting from non-topological ones. We show that the chirality of the edge current in such systems can be controlled by adjusting the filling.
实现拓扑绝缘体是目前非常关注的，因为它们具有显著的性质和可能的未来应用。最近基于 Floquet 分析的研究提出，通过周期性地驱动拓扑平庸的系统，可以产生拓扑非平庸的绝缘体。在这里，我们将讨论如果在这样的系统中跟踪动力学会发生什么。具体来说，我们对一个类似于石墨烯的系统在圆偏振电场下的时间演化进行了精确研究。我们证明，对于无限（平移不变）的系统，在幺正演化下 Chern 数是守恒的。另一方面，对于具有边界的系统，我们表明，一个适当定义的拓扑不变量，Bott 指标，可以发生变化。因此，从非拓扑的系统开始制备拓扑态应该是可能的。我们表明，通过调整填充，可以控制这种系统中边缘电流的手性。
