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Collective Modes and Linear Response of Spin-Triplet Pairing Models of
Sr _{2}RuO_{4}, UPt_{3} and ^{3}He-A
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Speaker: J. A. Sauls

Department of Physics, Northwestern University, Evanston, IL 60208

July 7-11, 2014

**Abstract:**
The spectrum of Bosonic modes in superconductors reflects the broken symmetries of the ground
state. In conventional superconductors these are Anderson-Bogoliubov (phase) and Amplitude-Higgs (amplitude) modes. The former couples to charge fluctuations and is renormalized to the plasma frequency, while the latter has been observed via Raman spectroscopy through its coupling to CDW phonons in NbSe_{2}.^{1} Strongly correlated fermion superconductors with unconventional pairing correlations, generally exhibit a much richer spectrum of Bosonic collective modes that provide spectroscopic signatures of the broken symmetries of the superconducting ground state. We report theoretical calculations for the spectrum of Bosonic collective modes in spin-triplet superconductors, specifically multi-band models for chiral, ``p-wave’’ spin-triplet (E_{1u} representation) superconductivity in Sr2RuO4, chiral, ``f-wave’’ spin-triplet (E_{2u} representation) superconductivity in UPt_{3} and thin films of superfluid _{3He-A, which is the neutral, 2D isotropic analog of γ-band model for Sr2RuO4, and provides an interesting comparison with Sr2RuO4. In all three cases the order parameter belongs to a higher dimensional representation of the symmetry group of the normal-state, and as a result possesses additional branches of Bosonic collective modes, in particular the number of modes is at least 2N, where N is the dimensionality of the irreducible representation of the ground state. In the case of UPt3, the ground state breaks time-reversal symmetry as well as 2D reflection symmetries, and exhibits gapless Fermionic excitations in low-dimensional regions (line and point nodes) of the Fermi surface. The nodal spectrum plays two important roles - these states are responsible for the finite lifetime of the Bosonic excitations in UPt3 and Sr2RuO4, and they contribute directly to the current reponse to an electromagnetic field (micro-wave and Raman). Results for the mode spectra include (i) the effects of Fermi surface and pairing anisotropy on the mode energies and (ii) their damping by pair-breaking and weak disorder based on microscopic pairing models for UPt3 and Sr2RuO4. (iii) Selection rules for the coupling of the order parameter collective modes to an electromagnetic field for spin-triplet pairing models of the superconducting phases of Sr2RuO4 and UPt3 are discussed, as are (iv) the signatures of broken time-reversal symmetry in the collective mode spectrum and EM response. (v) We show that the double degeneracy of the ``clapping modes’’ of superfluid 3He-A is lifted in anisotropic, chiral p-wave superconductors by tetragonal anisotropy of the Fermi surface and Cooper pair orbital wave functions. The collective modes lead to absorption resonances at frequencies below the pair-breaking threshold of 2Δ(p), and provide a mechanism for circular birefringence and dichroism from microwave to optical frequencies.2
1. M.A. Measson, et al. Phys. Rev. B 89, 060503R (2014).
2. S. K. Yip and J. A. Sauls, J. Low Temp. Phys. 87, 257 (1992).
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Support from the National Science Foundation, Grant DMR-1106315

**Slides:**
[PDF]

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