We theoretically study the low-energy electromagnetic response of Bardeen-Cooper-Schrieffer–type superconductors focusing on propagating collective modes that are observable with terahertz near-field optics. The interesting frequency and momentum range is $\omega <2\mathrm{\Delta }$ and $q<1/\xi$, where $\mathrm{\Delta }$ is the gap and $\xi$ is the coherence length. We show that it is possible to observe the superfluid plasmons, amplitude (Higgs) modes, Bardasis-Schrieffer modes, and Carlson-Goldman modes using the terahertz near-field technique, although none of these modes couple linearly to far-field radiation. Coupling of terahertz near-field radiation to the amplitude mode requires particle-hole symmetry breaking, while coupling to the Bardasis-Schrieffer mode does not and is typically stronger. For parameters appropriate to layered superconductors of current interest, the Carlson-Goldman mode appears in the near-field reflection coefficient as a weak feature in the subterahertz frequency range. In a system of two superconducting layers with nanometer-scale separation, an acoustic phase mode appears as the antisymmetric density fluctuation mode of the system. This mode produces well-defined resonance peaks in the near-field terahertz response and has strong anticrossings with the Bardasis-Schrieffer and amplitude modes, enhancing their response. In a slab consisting of many layers of quasi-two-dimensional superconductors, realized for example in samples of high-$T_c$ cuprate compounds, many branches of propagating Josephson plasmon modes are found to couple to the terahertz near-field radiation.

中文翻译：

---

超导体的集体模和太赫兹近场响应

我们从理论上研究Bardeen-Cooper-Schrieffer型超导体的低能电磁响应，重点是传播太赫兹近场光学器件可观察到的集体模式。有趣的频率和动量范围是$\omega <2\mathrm{\Delta }$ 和 $q<\mathrm{1个}/\xi$，在哪里 $\mathrm{\Delta }$ 是差距， $\xi$是相干长度。我们展示了使用太赫兹近场技术可以观察超流体等离子体激元，振幅（Higgs）模式，Bardasis-Schrieffer模式和Carlson-Goldman模式，尽管这些模式均未线性耦合至远场辐射。太赫兹近场辐射与振幅模式的耦合需要打破粒子-孔对称性，而与Bardasis-Schrieffer模式的耦合则不需要，而且通常更强。对于适合当前感兴趣的分层超导体的参数，卡尔森-高德曼模式在太赫兹频率范围内以弱特征出现在近场反射系数中。在具有纳米级分离的两个超导层的系统中，声相模式作为系统的反对称密度波动模式出现。该模式在近场太赫兹响应中产生明确定义的共振峰，并且与Bardasis-Schrieffer模式和振幅模式具有很强的抗交叉性，从而增强了它们的响应。在由多层准二维超导体组成的平板中，例如在${Ť}_C$ 铜酸盐化合物，许多传播的约瑟夫森等离振子模式分支被发现与太赫兹近场辐射耦合。