Collective modes and sound propagation in a p-wave superconductor: Sr${}_2$RuO${}_4$

Abstract

There are five distinct collective modes in the recently discovered p-wave superconductor Sr${}_2$RuO${}_4$; phase and amplitude modes of the order parameter, clapping mode (real and imaginary), and spin wave. The first two modes also exist in the ordinary s-wave superconductors, while the clapping mode with the energy $\sqrt{2}\Delta (T)$ is unique to Sr${}_2$RuO${}_4$ and couples to the sound wave. Here we report a theoretical study of the sound propagation in a two dimensional p-wave superconductor. We identified the clapping mode and study its effects on the longitudinal and transverse sound velocities in the superconducting state. In contrast to the case of ${}^3$He, there is no resonance absorption associated with the collective mode, since in metals $\omega /(v_F|\mathbf{q}|)\ll 1$, where $v_F$ is the Fermi velocity, {\bf q} is the wave vector, and $\omega$ is the frequency of the sound wave. However, the velocity change in the collisionless limit gets modified by the contribution from the coupling to the clapping mode. We compute this contribution and comment on the visibility of the effect. In the diffusive limit, the contribution from the collective mode turns out to be negligible. The behaviors of the sound velocity change and the attenuation coefficient near $T_c$ in the diffusive limit are calculated and compared with the existing experimental data wherever it is possible. We also present the results for the attenuation coefficients in both of the collisionless and diffusive limits at finite temperatures.

RevTex, 12 pages, 2 figures, Replaced by the published version

References in corpus (1)

• Spin waves in a two dimensional p-wave superconductor: Sr${}_2$RuO${}_4$

Cited by in corpus (13)

• Electrodynamics of Correlated Electron Materials
• Evaluation of Spin-Triplet Superconductivity in Sr2RuO4
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• Unconventional quantum oscillations in mesoscopic rings of spin-triplet superconductor Sr2RuO4
• Charge and spin collective modes in a quasi-1D model of Sr2RuO4
• BCS and generalized BCS superconductivity in relativistic quantum field theory. I. formulation
• Leggett modes and multi-band superconductivity in Sr2RuO4
• Sound Propagation in Nematic Fermi Liquid
• Raman Spectra of Triplet Superconductor in Sr${}_2$RuO${}_4$
• Critical Current of the Spin-Triplet Superconducting Phase in Sr${}_2$RuO${}_4$
• Linear spectroscopy of collective modes and the gap structure in two-dimensional superconductors
• Collective modes in unconventional density waves
• Anomalous acoustoelectric effect induced by clapping modes in chiral superconductors