Leggett Modes Accompanying Crystallographic Phase Transitions

TL;DR

This paper reveals the existence of Leggett-like collective modes in crystallographic phase transitions, analogous to those in multi-band superconductors, demonstrated through the example of Cd$_2$Nb$_2$O$_7$.

Contribution

It introduces the concept of structural Leggett modes in crystallography, expanding the understanding of collective excitations in phase transitions.

Findings

Structural Leggett modes can occur as antiphase Goldstone modes.

A new amplitude channel mode, an antiphase Higgs mode, is predicted.

These modes are illustrated in the pyrochlore ferroelectric Cd$_2$Nb$_2$O$_7$.

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 insights on structural phase transitions. Here, we show that the Leggett mode, a collective mode observed in multi-band 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, \href{https://doi.org/10.1143/PTP.36.901}{Prog.\ Theor.\ Phys.\ \textbf{36}, 901 (1966)}. That is, they are antiphase Goldstone modes (anti-phasons). 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 multi-band 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$_7$.