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Phys Rev Lett. 2015 Oct 9;115(15):157002. doi: 10.1103/PhysRevLett.115.157002. Epub 2015 Oct 9.

Nonrelativistic Dynamics of the Amplitude (Higgs) Mode in Superconductors.

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ISC-CNR and Department of Physics, "Sapienza" University of Rome, P.le A. Moro 5, 00185 Rome, Italy.
Institut Für Physik, BTU Cottbus-Senftenberg, P.O. Box 101344, 03013 Cottbus, Germany.


Despite the formal analogy with the Higgs particle, the amplitude fluctuations of the order parameter in weakly coupled superconductors do not identify a real mode with a Lorentz-invariant dynamics. Indeed, its resonance occurs at 2Δ_{0}, which coincides with the threshold 2E_{gap} for quasiparticle excitations that spoil any relativistic dynamics. Here we investigate the fate of the Higgs mode in the unconventional case where 2E_{gap} becomes larger than 2Δ_{0}, as due to strong coupling or strong disorder. We show that also in this situation, the amplitude fluctuations never identify a real mode at 2Δ_{0}, since such a "bosonic" limit is always reached via strong mixing with the phase fluctuations, which dominate the low-energy part of the spectrum. Our results have direct implications for the interpretation of the subgap optical absorption in disordered superconductors.

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