Time evolution of topological magneto-optics and superconducting qubits

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：小的费米等高线是圆形的，在大的化学势值下获得雪花形状。如果间隙打开（例如，通过掺杂磁性杂质），则反转对称性被打破。本文建立了基于广义Kubo公式的非线性响应理论来解释拓扑绝缘子的频率上变频。平坦带可能是由于某些紧密结合的哈密顿量的对称性或微调而出现的，其特征是完全无色散的单粒子能谱。值得注意的是，平坦带具有“紧致局域态”的存在，不受任何动态演化的影响，具有可定制的形状，后者是通过明智地叠加完全简并的布洛赫态来实现的。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）。并通过设置具有相关随机数的现场能量来考虑无序效应。这种失序会引起从FB到DB的衰减，同时在动量空间中发生减相。这将限制FB状态的生存期。

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.