BCS-BEC Crossover and Chiral Anomaly in p-Wave Superfluids with the Symmetry of A1-Phase

Abstract

We solve the Leggett equations for BCS-BEC crossover in the 3D resonance p-wave superfluid with the symmetry of A1-phase. We calculate sound velocity, normal density and specific heat for the BCS-domain (μ>0), BEC-domain (μ<0) as well as close to important point μ=0 in 100% polarized case. We find the indications of quantum phase-transition close to the point μ(T=0)=0. Deep in BCS and BEC-domains the crossover ideas of Leggett and Nozieres, Schmitt-Rink work pretty well.We discuss the spectrum of orbital waves, the paradox of intrinsic angular momentum and complicated problem of chiral anomaly in BCS A1-phase at T=0. We present two different approaches to a chiral anomaly: one based on supersymmetric hydrodynamics, another one on the formal analogy with Dirac equation in quantum electrodynamics (QED theory). We evaluate the damping of nodal fermions due to different decay processes in superclean case at T=0 and find that we are in a ballistic regime ω τ≫1. We propose to use aerogel or nonmagnetic impurities to reach hydrodynamic regime ω τ≪1 at T=0.We discuss the concept of spectral flow and exact cancellations between time-derivatives of anomalous and quasiparticle currents in the equation for the conservation of total linear momentum. We propose to derive and solve a kinetic equation for nodal quasiparticles both in the hydrodynamic and in the ballistic regimes to demonstrate this cancellation explicitly. We briefly discuss the role of the other residual interactions different from damping and invite experimentalists to measure the spectrum and damping of orbital waves in A-phase of 3He at low temperatures.