Leggett Modes Accompanying Crystallographic Phase Transitions

Abstract

Higgs and Goldstone modes, well known in high-energy physics, have been realized in a number of condensed matter physics contexts, including superconductivity and magnetism. The Goldstone-Higgs concept is also applicable to and gives rise to new insight on structural phase transitions. Here, we show that the Leggett mode, a collective mode observed in multiband superconductors, also has an analog in crystallographic phase transitions. Such structural Leggett modes can occur in the phase channel as in the original work of Leggett [Prog. Theor. Phys. 36, 901 (1966)PTPKAV0033-068X10.1143/PTP.36.901]. That is, they are antiphase Goldstone modes (antiphasons). In addition, a new collective mode can also occur in the amplitude channel, an out-of phase (antiphase) Higgs mode, that should be observable in multiband superconductors as well. We illustrate the existence and properties of these structural Leggett modes using the example of the pyrochlore relaxor ferroelectric Cd_{2}Nb_{2}O_{7}.