Geometric Amplitude Accompanying Local Responses: Spinor Phase Information from the Amplitudes of Spin-Polarized STM Measurements,Physical Review Letters

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Geometric Amplitude Accompanying Local Responses: Spinor Phase Information from the Amplitudes of Spin-Polarized STM Measurements
Physical Review Letters ( IF 8.1 ) Pub Date : 2024-07-19 , DOI: 10.1103/physrevlett.133.036204
Shu-Hui Zhang ₁ , Jin Yang ₂ , Ding-Fu Shao ₃ , Jia-Ji Zhu ₄ , Wen Yang ₂ , Kai Chang _{5,

6}

Affiliation

Solving the Hamiltonian of a system yields the energy dispersion and eigenstates. The geometric phase of the eigenstates generates many novel effects and potential applications. However, the geometric properties of the energy dispersion go unheeded. Here, we provide geometric insight into energy dispersion and introduce a geometric amplitude, namely, the geometric density of states (GDOS) determined by the Riemann curvature of the constant-energy contour. The geometric amplitude should accompany various local responses, which are generally formulated by the real-space Green’s function. Under the stationary phase approximation, the GDOS simplifies the Green’s function into its ultimate form. In particular, the amplitude factor embodies the spinor phase information of the eigenstates, favoring the extraction of the spin texture for topological surface states under an in-plane magnetic field through spin-polarized STM measurements. This work opens a new avenue for exploring the geometric properties of electronic structures and excavates the unexplored potential of spin-polarized STM measurements to probe the spinor phase information of eigenstates from their amplitudes.

中文翻译：

伴随局部响应的几何幅度：来自自旋偏振 STM 测量幅度的自旋相位信息

求解系统的哈密顿量可以得到能量色散和本征态。本征态的几何相位产生许多新颖的效应和潜在的应用。然而，能量色散的几何特性却被忽视了。在这里，我们提供了对能量色散的几何见解，并引入了几何振幅，即由恒定能量轮廓的黎曼曲率确定的几何态密度（GDOS）。几何振幅应伴随各种局部响应，这些响应通常由实空间格林函数表示。在固定相近似下，GDOS 将格林函数简化为其最终形式。特别是，振幅因子体现了本征态的旋量相位信息，有利于通过自旋极化STM测量提取面内磁场下拓扑表面态的自旋纹理。这项工作为探索电子结构的几何特性开辟了一条新途径，并挖掘了自旋极化 STM 测量的未开发潜力，可从振幅探测本征态的旋量相位信息。

更新日期：2024-07-19

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