Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Low Temperature Physics

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

M. Yu. Kagan, Dmitri V. Efremov

Published Dec 4, 2009• 9 citations
Publisher

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.

DOI
10.1007/s10909-009-0047-0

Related papers

BCS-BEC crossover and quantum hydrodynamics in p-wave superfluids with a symmetry of the A1 phase

M. Yu. Kagan, Dmitri V. Efremov

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.

arXiv:1105.4438•Journal of Experimental and Theoretical Physics•Mar 1, 2010•7 citations

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

M. Yu. Kagan, Dmitri V. Efremov

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.

Low Temperature Physics•Aug 1, 2009•0 citations

BCS-BEC crossover in p-wave resonance superfluids

M. Yu. Kagan, S. L. Ogarkov

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.

Journal of Physics Conference Series•Feb 1, 2009•1 citation

Specific features of the BCS-BEC crossover and thermodynamics in the 2D resonant Fermi gas with p-wave pairing

M. Yu. Kagan, S. L. Ogarkov

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.

Laser Physics•Apr 1, 2008•7 citations

Modern trends in Superconductivity and Superfluidity. Selected Chapters

M. Yu. Kagan

In Chapter 1 we start with general Landau scheme of the conservation laws for the hydrodynamics of classical liquids and superfluids. On the basis of Landau scheme we consider hydrodynamics of rotating superfluids with large number of vortices. We study different regimes of slow and fast rotations. In Chapter 4 we consider complicated and yet unresolved problem of chiral anomaly in superfluid 3He-A and present two competing approaches. The first one is based on supersymmetric hydrodynamics, another one on the formal analogy with Dirac equation in QED. In Chapters 6 and 7 we study composed fermions and bosons which correspond to the different bound states consisting of two fermions, two bosons and fermion and boson in ultracold quantum gasses and mixtures. We also elucidate the exact solutions of the Skorniakov-Ter-Martirosian integral equations. We present the basic ideas of Nozieres-Schmitt Rink and Legget theory on BCS-BEC crossover in quantum gasses and construct the phase diagrams for the s-wave and p-wave pairings. In Chapters 9 and 10 we discuss non-phonon mechanisms of superconductivity of the Kohn-Luttinger type for different models in 3D and 2D electron systems at low densities including Fermi-gas, Hubbard and Shubin-Vonsovsky models. We complete the superconductive phase-diagrams of p-wave and d-wave pairing and discuss the possibility to increase Tc already at low density. In Chapters 15 and 16 the mechanisms of electron nanoscale phase-separation in manganite-type oxide materials are analyzed. The instability of magnetic (or charge) homogeneous ordering towards the formation of droplet structures (magnetic polarons) is predicted for a wide parameter range on the phase-diagram. The transport properties of these materials in the phase-separated state are also discussed.

arXiv:1111.5711•Nov 24, 2011•0 citations

BCS – BEC crossover, collective excitations, and hydrodynamics of superfluid quantum liquids and gases

M. Yu. Kagan, Andrei V. Turlapov

Abstract A Fermi gas described within the Bardeen–Cooper–Schrieffer (BCS) theory can be converted into a Bose–Einstein condensate (BEC) of composite molecules (dimers) by adiabatically tuning the interaction. The sequence of states that emerge in the process of such a conversion is referred to as the BCS–BEC crossover. We here review the theoretical and experimental results obtained for the BCS–BEC crossover in three- and quasi-two-dimensional quantum gases in the limiting geometry of traps and on optical lattices. We discuss nontrivial phenomena in the hydrodynamics of superfluid quantum gases and fluids, including the collective excitation spectrum in the BCS–BEC crossover, the hydrodynamics of rotating Bose condensates containing a large number of quantized vortices, and the intriguing problem of the chiral anomaly in the hydrodynamics of superfluid Fermi systems with an anisotropic p-wave pairing. We also analyze spin-imbalanced quantum gases and the potential to realize the triplet p-wave pairing via the Kohn–Luttinger mechanism in those gases. Recent results on two-dimensional Fermi-gas preparation and the observation of fluctuation phenomena related to the Berezinskii–Kosterlitz–Thouless transition in those gases are also reviewed. We briefly discuss the recent experimental discovery of the BCS–BEC crossover and anomalous superconductivity in bilayer graphene and the role of graphene, other Dirac semimetals (for example, bismuth), and 2D optical lattices as potential reference systems that exhibit all of the effects reviewed here.

Physics-Uspekhi•Nov 4, 2018•37 citations
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 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 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.
In Chapter 1 we start with general Landau scheme of the conservation laws for the hydrodynamics of classical liquids and superfluids. On the basis of Landau scheme we consider hydrodynamics of rotating superfluids with large number of vortices. We study different regimes of slow and fast rotations. In Chapter 4 we consider complicated and yet unresolved problem of chiral anomaly in superfluid 3He-A and present two competing approaches. The first one is based on supersymmetric hydrodynamics, another one on the formal analogy with Dirac equation in QED. In Chapters 6 and 7 we study composed fermions and bosons which correspond to the different bound states consisting of two fermions, two bosons and fermion and boson in ultracold quantum gasses and mixtures. We also elucidate the exact solutions of the Skorniakov-Ter-Martirosian integral equations. We present the basic ideas of Nozieres-Schmitt Rink and Legget theory on BCS-BEC crossover in quantum gasses and construct the phase diagrams for the s-wave and p-wave pairings. In Chapters 9 and 10 we discuss non-phonon mechanisms of superconductivity of the Kohn-Luttinger type for different models in 3D and 2D electron systems at low densities including Fermi-gas, Hubbard and Shubin-Vonsovsky models. We complete the superconductive phase-diagrams of p-wave and d-wave pairing and discuss the possibility to increase Tc already at low density. In Chapters 15 and 16 the mechanisms of electron nanoscale phase-separation in manganite-type oxide materials are analyzed. The instability of magnetic (or charge) homogeneous ordering towards the formation of droplet structures (magnetic polarons) is predicted for a wide parameter range on the phase-diagram. The transport properties of these materials in the phase-separated state are also discussed.
Abstract A Fermi gas described within the Bardeen–Cooper–Schrieffer (BCS) theory can be converted into a Bose–Einstein condensate (BEC) of composite molecules (dimers) by adiabatically tuning the interaction. The sequence of states that emerge in the process of such a conversion is referred to as the BCS–BEC crossover. We here review the theoretical and experimental results obtained for the BCS–BEC crossover in three- and quasi-two-dimensional quantum gases in the limiting geometry of traps and on optical lattices. We discuss nontrivial phenomena in the hydrodynamics of superfluid quantum gases and fluids, including the collective excitation spectrum in the BCS–BEC crossover, the hydrodynamics of rotating Bose condensates containing a large number of quantized vortices, and the intriguing problem of the chiral anomaly in the hydrodynamics of superfluid Fermi systems with an anisotropic p-wave pairing. We also analyze spin-imbalanced quantum gases and the potential to realize the triplet p-wave pairing via the Kohn–Luttinger mechanism in those gases. Recent results on two-dimensional Fermi-gas preparation and the observation of fluctuation phenomena related to the Berezinskii–Kosterlitz–Thouless transition in those gases are also reviewed. We briefly discuss the recent experimental discovery of the BCS–BEC crossover and anomalous superconductivity in bilayer graphene and the role of graphene, other Dirac semimetals (for example, bismuth), and 2D optical lattices as potential reference systems that exhibit all of the effects reviewed here.