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$_7$.
Highlights
Spontaneous symmetry breaking is a ubiquitous phenomenon in physics, and is responsible for various collective modes, most famously the well-known Goldstone and Higgs modes
We show that the Leggett mode, a collective mode observed in multiband superconductors, has an analog in crystallographic phase transitions
A new collective mode can occur in the amplitude channel, an out-of phase Higgs mode, that should be observable in multiband superconductors as well
Summary
Spontaneous symmetry breaking is a ubiquitous phenomenon in physics, and is responsible for various collective modes, most famously the well-known Goldstone and Higgs modes. The former refers to fluctuations of the phase of an order parameter, the latter to fluctuations of its amplitude. Its structural phase transition arises from an instability associated with a doubly degenerate Γ−3 phonon [11] This defines a Mexican-hat free-energy surface with the top of the hat representing the high-temperature cubic phase and the brim representing the lower symmetry distorted phase. We begin by developing a minimal Landau model that describes a structural phase transition that is accompanied by a new collective mode, the antiphase Higgs mode (the amplitude analog of the Leggett mode) that should be observable in multiband superconductors. We conclude by discussing the relevance of our work to other materials, in particular, those that involve modes at nonzero wave vectors
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