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Low Temperature Physics

BCS-BEC crossover and nodal-points contribution in p-wave resonance superfluids

M. Yu. Kagan, Dmitri V. Efremov

Published Aug 1, 2009• 0 citations
Publisher

Abstract

We solve the Leggett equations for BCS-BEC crossover of the resonance p-wave superfluid. We calculate sound velocity, specific heat and the normal density for the BCS domain (μ>0), the BEC domain (μ<0), and for the interesting interpolation point (μ=0) in the 100%-polarized A1 phase in 3D. We are especially interested in the quasiparticle contribution coming from the zeros of the superfluid gap in the A1 phase. We discuss the spectrum of orbital waves and the superfluid hydrodynamics at temperature T→0. In this context we elucidate the difficult problem of the chiral anomaly and mass-current nonconcervation appearing in the BCS domain. We present the different approaches taken to solve this problem. To clarify this problem experimentally we propose an experiment for measurement of the anomalous current in the superfluid A1 phase in the presence of aerogel for He3 and in the presence of Josephson tunneling structures for ultracold gases in magnetic traps.

DOI
10.1063/1.3224735

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We solve the Leggett equations for BCS-BEC crossover of the resonance p-wave superfluid. We calculate sound velocity, specific heat and the normal density for the BCS domain (μ>0), the BEC domain (μ<0), and for the interesting interpolation point (μ=0) in the 100%-polarized A1 phase in 3D. We are especially interested in the quasiparticle contribution coming from the zeros of the superfluid gap in the A1 phase. We discuss the spectrum of orbital waves and the superfluid hydrodynamics at temperature T→0. In this context we elucidate the difficult problem of the chiral anomaly and mass-current nonconcervation appearing in the BCS domain. We present the different approaches taken to solve this problem. To clarify this problem experimentally we propose an experiment for measurement of the anomalous current in the superfluid A1 phase in the presence of aerogel for He3 and in the presence of Josephson tunneling structures for ultracold gases in magnetic traps.
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.
We solve the Leggett equations for the BCS-BEC crossover in a three dimensional resonance p -wave superfluid with the symmetry of the A 1 phase. We calculate the sound velocity, the normal density, and the specific heat for the BCS domain (μ > 0), for the BEC domain (μ < 0), and close to the important point μ = 0 in the 100% polarized case. We find the indications of a quantum phase transition close to the point μ( T = 0) = 0. Deep in the BCS and BEC domains, the crossover ideas of Leggett, Nozieres, and Schmitt-Rink work quite well. We discuss the spectrum of orbital waves, the paradox of intrinsic angular momentum and the complicated problem of chiral anomaly in the BCS A 1 phase at T = 0. We present two different approaches to the chiral anomaly, based on supersymmetric hydrodynamics and on the formal analogy with the Dirac equation in quantum electrodynamics. We evaluate the damping of nodal fermions due to different decay processes in the superclean case at T = 0 and find that a ballistic regime ωτ ≫ 1 occurs. We propose to use aerogel or nonmagnetic impurities to reach the hydrodynamic regime ωτ ≪ 1 at T = 0. We discuss the concept of the spectral flow and exact cancelations between time derivatives of anomalous and quasiparticle currents in the equation for the total linear momentum conservation. We propose to derive and solve the kinetic equation for the nodal quasiparticles in both the hydrodynamic and ballistic regimes to demonstrate this cancelation 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 the A phase of 3 He at low temperatures.
We consider 3D and 2D fully (100%) polarized resonance superfluid Fermi-gas with p-wave pairing in the regime of BCS-BEC crossover. For low temperatures T « T cp ( T cp is a p-wave critical temperature) we evaluate the contribution of the superfluid fermionic quasiparticles and bosonic collective waves (phonons) in the specific heat ( C v ) and the normal density (ρ n ) in the BCS-regime for the chemical potential μ > 0, in BEC-regime for μ < 0 and in the interesting intermediate regime for μ → 0. We discuss an experimental possibility to observe a chiral anomaly (which leads to mass-current non-conservation at T = 0) in 3D A1-phase in ballistic regime as well as a topological term with a charge Q = 1 in the 2D fully polarized axial phase in BCS-regime.
The 2D resonant Fermi gas with p -wave pairing is considered n the BCS-BEC regime. For the 2D analog of the superfluid A1 phase, the Leggett equations [1] for superfluid gap Δ and chemical potential μ are analytically solved at T = 0 and the spectrum of the collective excitations (acoustic waves) is analyzed in the BCS regime (μ > 0), where the triplet Cooper pairs emerge; in the BEC regime (μ < 0), where the triplet local pairs (molecules) emerge; and in the transition region, where μ → 0. At low temperatures, the contribution of the superfluid Fermi quasiparticles of the resonant gas to heat capacity C v and the density of normal component ρ n is also calculated. At μ = 0, the fermionic contribution to ρ n and C v are represented as power functions of temperature (ρ n ∼ T 3 and C v ∼ T 2 ). However, similar power contributions to these quantities are related to phonons (bosonic acoustic oscillations). The possibility of the experimental observation of the nontrivial topological term with the charge Q = 1 in the BCS regime of the 2D A1 phase is briefly discussed.
The thermodynamic potential is calculated for a uniform superfluid gas of fermi atoms from the mean field BCS equations including corrections from induced interactions, Hartree-Fock energies and quasiparticle selfenergies. The entropy, specific heat and sound modes are calculated as function of temperature, density and interaction strength from the BCS to the unitarity limit and around the BCS-BEC crossover. The second sound speed is of particular interest as it is a clear signal of a superfluid component and it determines the critical temperature.
This review is written at the time of the twentieth anniversary of the discovery of high-temperature superconductors, which nearly coincides with the important discovery of the superfluid phases of ultracold trapped fermionic atoms. We show how these two subjects have much in common. Both have been addressed from the perspective of the BCS—Bose–Einstein condensation (BEC) crossover scenario, which is designed to treat short coherence length superfluids with transition temperatures which are “high” with respect to the Fermi energy. A generalized mean field treatment of BCS–BEC crossover at general temperatures T, based on the BCS–Leggett ground state, has met with remarkable success in the fermionic atomic systems. Here we summarize this success in the context of four different cold atom experiments, all of which provide indications, direct or indirect, for the existence of a pseudogap. This scenario also provides a physical picture of the pseudogap phase in the underdoped cuprates which is a central focus of high Tc research. We summarize successful applications of BCS–BEC crossover to key experiments in high Tc systems, including the phase diagram, specific heat, and vortex core STM data, along with the Nernst effect, and exciting recent data on the superfluid density in very underdoped samples.