This work addresses the problem of elastic scattering on a localized impurity in a one-dimensional crystal with sublattice degrees of freedom. The impurity yields long-range interferences in the local density of states known as Friedel oscillations. Here we show that the internal degrees of freedom of Bloch waves are responsible for a geometrical phase shift in Friedel oscillations. The Fourier transform of the energy-resolved interference pattern reveals a topological property of this phase shift, which is intrinsically related to a wave-function topological property (Zak phase) in the absence of impurity. As a result, Friedel oscillations in the local density of states can be regarded as a probe of wave topological properties in a broad class of classical and quantum systems, such as acoustic and photonic crystals, ultracold atomic gases in optical lattices, and electronic compounds.

中文翻译：

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Friedel振荡中的几何相移

这项工作解决了在具有亚晶格自由度的一维晶体中局部杂质上的弹性散射问题。杂质会在所谓的Friedel振荡状态的局部密度中产生远距离干扰。在这里，我们证明了Bloch波的内部自由度是造成Friedel振荡的几何相移的原因。能量分辨干涉图的傅立叶变换揭示了该相移的拓扑特性，该特性本质上与不存在杂质时的波函数拓扑特性（Zak相）有关。结果，在局部经典密度和量子系统（例如声和光子晶体），