Higgs and Goldstone Modes in Crystalline Solids

Abstract

In crystalline solids, the acoustic phonon can be described either as a Goldstone or as a non‐Abelian gauge boson. However, the non‐Abelianity of the related gauge group apparently makes the acoustic phonon a frequency‐gapped mode, in contradiction with the other description. In a different perspective, overcoming this contradiction, both 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. In addition, the Higgs mechanism describes all the phonon–phonon interactions, including a possible perturbation of the acoustic phonon's frequency dispersion relation induced by the eventual optical phonon, a peculiar behavior that is able to produce mini‐gaps inside the phonon Brillouin zone.

A reaction-coordinate perspective of magnetic relaxation

“…Here, energy is exchanged through phonons, which are collective, long-range vibrations in a solid, often spanning multiple molecules. 24 The availability of phonons in a system is dependent on the temperature of the system and the nature of the surrounding matrix (e.g. a crystalline vs. frozen solvent glass environment).…”

Parametric Excitation of an Optically Silent Goldstone-Like Phonon Mode

“…Higgs and Goldstone modes are well-studied in superconductors today [10][11][12][13][14][15][16][17][18][19][20][21], and similar manifestations have recently been reported in charge density wave (CDW) systems [22][23][24], antiferromagnets [25][26][27], and excitonic insulators [28]. It has been debated whether the optical and acoustic vibrational modes of solids can be considered Higgs and Goldstone excitations of the crystal lattice [29]. Several complex transition metal oxide compounds have shown signatures of optical Goldstone-like phonon modes that live in their symmetry-broken potential energy landscape [30][31][32][33][34].Coherent control over Raman-active phonons via impulsive stimulated Raman scattering using visible light pulses is well-established [35,36].…”

Manifestation of structural Higgs and Goldstone modes in the hexagonal manganites

“…Such an example would be convenient since the order parameters in structural phase transitions are usually given by the positions of the atoms, which in turn can often be measured unambiguously and remain stable for long times. Indeed, a field-theoretical treatment of both Higgs and Goldstone phonons has recently been developed and would in principle be applicable to such a transition [32].…”