Structural Phase Transitions in Crystals: Phonons as Higgs and Goldstone Excitations

It has recently been indicated that optical and acoustic phonons can be identified with Higgs and Goldstone excitations of the crystal lattice arising from the spontaneous breaking of a global, continuous symmetry. Herein, this view is supported considering structural phase transitions induced by temperature, from the face-centered-cubic (fcc) phase of cobalt, and from the body-centered-cubic (bcc) phase of zirconium and titanium, to their hexagonal-close-packet (hcp) phase. The Higgs field potential is identified with the Ginzburg–Landau free energy difference calculated and available in the literature for the concerned structural phase transitions. In all the considered cases, the ensuing spontaneous symmetry breaking makes the optical phonon (identified with the Higgs mode) to arise only in the less symmetric hcp phase. This demonstrates Higgs excitations to be associated not only with quantum phase transitions, but also with structural phase transitions in natural crystals.