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二维材料TERS理论，包括出平面拉曼响应

Theory for tip-enhanced Raman spectroscopy of two-dimensional materials including out-of-plane Raman response

Universidade Federal do Rio de Janeiro（里约热内卢联邦大学）；Universidade Federal de Minas Gerais（米纳斯吉拉斯联邦大学）

Raul Corrêa, Luiz G. Cançado, Ado Jorio

备注：
44 pages, 7 figures. Abbreviations in the title expanded. Parts of section V became Appendix B. New section VII-D included
发表信息：
Phys. Rev. B 114, 175406 (2026)
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AI总结：

本文提出包含出平面响应的TERS理论，分析了TERS信号对出平面拉曼响应的敏感性，并展示了介质折射率对增强因子的影响，为研究不同拉曼模式的差异提供了理论基础。

摘要：

Tip-Enhanced Raman Spectroscopy (TERS) 可用于对二维材料如石墨烯和过渡金属二硫化物进行纳米尺度空间测量。然而，之前提出的TERS理论是为石墨烯设计的，忽略了出平面拉曼响应。本文在TERS理论中引入了出平面响应，提供了尖端与样品之间场传播的精确解析表达式，并表明当出平面响应显著时，首先在样品上散射然后在尖端上散射（样品-尖端，或TS）的贡献才重要。我们广泛研究了系统物理参数变化对TERS实验测量的影响，如尖端半径、出平面响应、TERS相干长度等。结果表明，TERS增强对声子模式的出平面拉曼响应非常敏感，而归一化尖端接近测量更敏感于相干长度，并展示了介质折射率导致有效尖端增强因子$ f_e $。我们的结果得出结论，强TERS增强是研究此处物理现象的必要条件，即调查不同拉曼模式之间的TERS信号差异。我们使用模型分析了一些石墨烯TERS实验，显示其与可忽略的出平面拉曼响应和非零的TERS相干长度一致。

英文摘要：

Tip-Enhanced Raman Spectroscopy (TERS) can be used to make nanoscale spatial measurements of 2D materials, such as graphene and transition metal dichalcogenides (TMDs). The TERS theory introduced in [L. Cançado et al., Phys. Rev. X 4, 031054 (2014)], however, was tailored for graphene, whose out-of-plane Raman response is neglected. In the present work, we include the out-of-plane response in the TERS theory. In doing so, we provide an exact analytical expression for the field propagation between the tip and the sample, and show that the contribution to the TERS signal that scatters first at the sample, then at the tip (sample-tip, or TS) is important only when the out-of-plane response is significant. We extensively study the variation of TERS experimental measurements when varying physical parameters of the system, like the tip radius, the out-of-plane response, the TERS coherence length, and others. It becomes evident that the TERS enhancement is very sensitive to the out-of-plane Raman response of the phonon mode, while normalized tip-approach measurements are more sensitive to the coherence length, and we show that the medium refractive index leads to an effective tip enhancement factor $f_e$. Our results lead to the conclusion that, in general, a strong TERS enhancement is a necessary condition for investigating the physics discussed here, which here means surveying the difference in TERS signals between different Raman modes. We use our model to analyze some graphene TERS experiments, showing that they are consistent with a negligible out-of-plane Raman response and a nonzero TERS coherence length in the fitting.

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