Is Superfluid 3He-A a Precursor to Magnetically Ordered Solid 3He?

39th CNLS Annual Conference - Strongly Correlated Quantum Materials, Eldorado Hotel Conference Center, Santa Fe, NM

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>=Y1,−1(p)|↑↑>+Y1,+1(p)|↓↓>+Y1,0(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>=Y1,+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 3He, 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 pPCP=21 bar, the A phase is stabilized in a window of temperatures, TAB < T < Tc, separated from the B phase by a pressure and temperature dependent first-order transition at TAB(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 3He 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 Tc(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/2kf=0.82. This wavevector corresponds to a reciprocal lattice vector of bcc solid 3He at melting pressure. The results provide a quantitative strong-coupling theory for the stability of the A phase, and imply that liquid 3He 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 3He.

Research supported by the US National Science Foundation Grant NSF DMR-1508730.

Slides: [PDF]

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Last update: April 28, 2019