Speaker: **James A. Sauls**

Department of Physics, Northwestern University, Evanston, IL 60208

April 29, 2019

**Abstract:**
I present a strong-coupling theory for the stability and thermodynamics of the chiral p-wave phase of superfluid based on next-to-leading order corrections to the weak-coupling BCS theory of superconductivity. The resulting analysis suggests a deep connection between the stability of the A phase, Mott physics and the anti-ferromagnetically ordered phase of solid at the solidification pressure.
Liquid is a strongly correlated Fermi liquid with heavy quasiparticles that become superconducting at low temperatures. There are two broken symmetry phases, both of which are spin-triplet, p-wave BCS condensates. The bulk of the pressure-temperature phase diagram is occupied by the time-reversal invariant B phase, a condensate of entangled spin-triplet, p-wave Cooper pairs with a pair amplitude |B>=Y_{1,−1}(p)|↑↑>+Y_{1,+1}(p)|↓↓>+Y_{1,0}(p)|↑↓>+|↓↑>. This is the ground state predicted by Balian and Werthamer in 1963 based on weak-coupling BCS theory for p-wave pairing valid for any pressure. By contrast, the high pressure A phase is a condensate of anti-ferromagnetically ordered, chiral p-wave Cooper pairs, |A>=Y_{1,+1}(p) (|↑↑>+|↓↓>). Thus, the A phase breaks time-reversal and mirror reflection symmetries, as well as gauge, spin and orbital rotational symmetries.
Despite our detailed understanding of the physical properties of the phases of superfluid ^{3}He, a quantitative theory of the pairing mechanism, phase diagram and thermodynamics of the high-pressure superfluid phases has been elusive. Above the tri-critical pressure of p_{PCP}=21 bar, the A phase is stabilized in a window of temperatures, T_{AB} < T < T_{c}, separated from the B phase by a pressure and temperature dependent first-order transition at T_{AB}(p). The stability of the A phase requires a microscopic pairing theory based on strong-correlation physics that goes beyond weak-coupling BCS theory. The "feedback" model proposed by Anderson and Brinkman in which spin-triplet pairing correlations modify the spin-fluctuation-mediated pairing interaction based on paramagnon exchange was a key insight pointing towards a mechanism to stabilize the equal-spin-pairing A phase over the B phase. However, paramagnon exchange theory fails to provide quantitative predictions for the stability of the A phase, specifically the pressure-temperature phase diagram.
I present a strong-coupling theory of superfluid ^{3}He based on a generalized fluctuation-mediated theory of paring, combined with next-to-leading order corrections to weak-coupling pairing theory based on quasiparticle-quasparticle interactions that accurately describes the thermodynamic potentials for the A and B phases at all pressures and temperatures below T_{c}(p).
The interaction potentials that describe the quasiparticle scattering amplitudes exhibit a broad ferromagnetic spin-fluctuation peak near q=0, reminiscent of paramagnon theory, but also resonances corresponding to antiferromagnetic spin-fluctuations and density fluctuations at wavevector Q/2k_{f}=0.82. This wavevector corresponds to a reciprocal lattice vector of bcc solid ^{3}He at melting pressure. The results provide a quantitative strong-coupling theory for the stability of the A phase, and imply that liquid ^{3}He at high pressures is an *almost localized Fermi liquid* near a Mott transition, and suggests that the equal-spin pairing A phase is the precursor of the UUDD phase of solid ^{3}He.

^{†} Research supported by the US National Science Foundation Grant NSF DMR-1508730.

**Slides:**
[PDF]

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