晶体中的Higgs模和Goldstone模
Higgs and Goldstone modes in crystalline solids
摘要：
在晶体固体中，声学声子被认为是无频隙的戈德斯通玻色子，它是由晶格引起的连续伽利略对称性的自发破缺而产生的。它也被描述为规范玻色子，当晶体中的自由电子的拉格朗日量被要求相对于无穷小空间平移群T（3）是局部规范不变时出现。然而，T（3）的非阿贝尔性使声学声子成为一个频率带隙模，这与它作为Goldstone玻色子的描述相矛盾。另一种观点克服了这种矛盾。事实上，我们表明，无论是声学和光学声子-后者从来没有出现以下其他两种方法-出现分别为gapless戈德斯通（相位）和gapped希格斯（振幅）波动模式的序参量所产生的自发破缺的全球对称性，而不调用规范原理。光学声子的频隙存在于所有区域，并且由于希格斯机制本身，它产生于拉格朗日中的类质量项。相反，最终的声学声子的频隙仅出现在强非线性区域，并且这是由于非谐项，该非谐项与T（3）的测量产生的项相同，但是该方法没有提供光学声子的任何描述。此外，希格斯机制描述了所有的声子-声子相互作用，包括由最终的光学声子引起的声学声子频率色散关系的可能扰动，这是迄今为止在这些术语中没有描述的特殊行为。
英文摘要：
In crystalline solids the acoustic phonon is known to be the frequency-gapless Goldstone boson emerging from the spontaneous breaking of the continuous Galilean symmetry induced by the crystal lattice. It has also been described as the gauge boson that appears when the free electrons' Lagrangian in the crystal is requested to be locally gauge invariant with respect to T(3), the group of the infinitesimal spatial translations. However, the non-Abelianity of T(3) makes the acoustic phonon a frequency-gapped mode, in contradiction with its description as Goldstone boson. A different perspective overcomes this contradiction. In fact, we show that both the acoustic and optical phonon - the latter never appearing following the other two approaches - emerge respectively as the gapless Goldstone (phase) and the gapped Higgs (amplitude) fluctuation mode of an order parameter arising from the spontaneous breaking of a global symmetry, without invoking the gauge principle. The optical phonon's frequency-gap is present in all regimes, and it arises from a mass-like term in the Lagrangian due to the Higgs mechanism itself. Instead, an eventual acoustic phonon's frequency-gap appears only in the strong nonlinear regime, and it is due to an anharmonic term, the same term arising from the gauging of T(3), an approach which did not provide any description of the optical phonon, though. In addition, the Higgs mechanism describes all the phonon-phonon interactions, including a possible perturbation on the acoustic phonon's frequency dispersion relation induced by the eventual optical phonon, a peculiar behavior not described so far in these terms.
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