周期驱动的量子系统中的量子自旋霍尔态研究

The quantum spin Hall (QSH) state of matter is usually considered to be protected by time-reversal symmetry(TRS). Ours previous research results showed that the QSH state is being existed when the TR-symmetry is broken. An open question is whether or not we can have a QSH-like phase in a periodically driven quantum systems? Based on the previous studies in this field, this proposal focuses on the QSH states can be induced from a topologically trivial state of TRS-broken systems in the presence of external periodic driving fields. We will characterize phases of periodically driven quantum systems by extending the time-independent topological classification. We will generalize the efficient coupling-matrix method to calculate the topological invariant of disordered systems of periodically driven systems. It is believed that the investigations in this project would help us to re-understand QSH states, and provide an effective approach to characterize topological properties of periodically driven quantum systems.

量子自旋霍尔(QSH)态通常被认为是受时间反演对称保护的。我们曾经的研究结果(PRL,107,066602(2011))表明，QSH态也存在于时间反演对称破缺的量子系统中。一个值得探讨的问题是，在周期驱动的量子系统中是否也有类似于QSH态的存在呢？本项目结合目前的研究现状和申请人的积累，以期处于普通平凡相的时间反演对称破缺的量子系统，在周期外场驱动下能诱导出受拓扑保护的QSH态。我们通过拓展不含时拓扑不变量来刻画周期驱动系统不同的拓扑相。我们将进一步推广耦合矩阵的方法，并将其用于计算含时的无序系统中的拓扑不变量。通过本项目研究，我们相信这将有助于人们重新认识QSH态，并为刻画周期驱动的量子系统的拓扑性质提供一个有效工具。