固态高次谐波产生的实验和模拟经常利用带间和带内电流之间的区别。这两个贡献的总电流已与定性不同的过程，以及物理上可测量的签名，例如在谐波发射的光谱阶段。然而，最近有人认为[P. Földi，Phys. Rev. B 96，035112（2017）]这些量可能取决于计算中使用的规范。由于预期物理量具有与规范无关的值，这就提出了一个问题，即将总电流分解为带间和带内贡献是否具有物理意义，或者仅仅是自然的特定数学表示的一个特征。在这篇文章中，我们将探讨这种明显的模糊性。我们发现，一个密切相关的问题时，计算瞬时波段人口。在这两种情况下的带间/带内电流和瞬时带种群的情况下，我们提出的定义是规范不变的，从而使这些数量计算一致的任何规范。
英文摘要：
Experiments and simulations in solid-state high harmonic generation often make use of the distinction between interband and intraband currents. These two contributions to the total current have been associated with qualitatively different processes, as well as physically measurable signatures, for example in the spectral phase of harmonic emission. However, it was recently argued [P. Földi, Phys. Rev. B 96, 035112 (2017)] that these quantities can depend on the gauge employed in calculations. Since physical quantities are expected to have gauge-independent values, this raises the question of whether the decomposition of the total current into interband and intraband contributions is physically meaningful, or merely a feature of a particular mathematical representation of nature. In this article, we explore this apparent ambiguity. We show that a closely related issue arises when calculating instantaneous band populations. In both the case of inter/intraband currents and in the case of instantaneous band populations, we propose definitions which are gauge-invariant, and thus allow these quantities to be calculated consistently in any gauge.
Size and temperature dependent intraband optical studies of heavily n-doped PbS quantum dot solids
通过重掺杂，胶体量子点（CQD）中带内跃迁的稳态访问允许在带隙以下的能量处利用电磁波谱。CQD带内光电子学为廉价的中长波长红外光电探测器和发光器件开辟了一条新的道路，这些器件目前主要采用外延材料。作为一个新的实验研究领域，对量子点带内跃迁的基本性质的深入研究还很缺乏。本文研究了重掺杂PbS量子点（QD）薄膜的带内跃迁随尺寸和温度的变化。我们测量的带内跃迁的吸收系数是在$10^4$ cm $^{-1}$的顺序，这是可比的带间吸收系数的值。此外，我们确定的带内跃迁的振子强度的大小依赖性。我们证明了带内能量与温度的负相关性，相反的带间跃迁的正相关性。
Second-order dc conductivity in the velocity-gauge Keldysh formalism: gauge-invariant decomposition into nonlinear Drude, Berry-curvature-dipole, and quantum-metric responses
