Time evolution of topological magneto-optics and superconducting qubits

我们研究了由电导率张量表征的外加驱动电场E的非线性响应。在拓扑绝缘体中观察到的准粒子(螺旋狄拉克费米子)具有一个重要的特征：费米等值线在小处是圆形的，在化学势的大小处获得雪花形状。如果间隙打开(例如，通过掺杂磁性杂质)，则反转对称性被破坏。我们发展了一个基于广义Kubo公式的非线性响应理论来解释拓扑绝缘体中的频率上转换。由于某些紧束缚哈密顿量的对称性或微调而出现的平带被描述为完全无色散的单粒子能谱。值得注意的是，平带的特点是存在“紧凑的局域态”，没有任何动力学演化，形状可定制，后者通过明智地叠加完全简并的Bloch态而实现。我们从十字绣模型开始，它最简单地描述了平带(FB)和色散带(DB)。并通过设置相关随机数的现场能量来考虑无序效应。无序将导致从Fb到Db的衰变以及动量空间的退相。这将限制FB状态的生命周期。

We study the nonlinear response to an external driving electric field E characterized by a conductivity tensor which depends on the magnitude of E. The quasiparticles (helical Dirac fermions) observed in topological insulators possess an important feature: the Fermi contours are circular for small acquire a snowflake shape at large values of the chemical potential. If a gap opens (e.g., by doping with magnetic impurities) the inversion symmetry is broken. We develop a nonlinear response theory based on a generalized Kubo formula to explain the frequency up-conversion in topological insulators.Flatbands, which may emerge as a consequence of symmetries or finetuning in certain tight-binding Hamiltonians, are characterized by a completely dispersionless single-particle energy spectrum. Remarkably, flat bands feature the existence of “compact localized states”, free of any dynamical evolution and with tailorable shape, the latter by judiciously superposing the entirely degenerate Bloch states. We start from the cross-stitch model that most simply describes a flat-band (FB) and a dispersive-band (DB). And consider the disorder effect by setting on-site energies with correlated random numbers. The disorder will induce decay from FB to DB together with dephasing in momentum space. This will limit the lifetime of the FB state.