Comparison of Different Pairing Fluctuation Approaches to BCS-BEC Crossover

Abstract

The subject of BCS - Bose Einstein condensation (BEC) crossover is particularly exciting because of its realization in ultracold Fermi gases and its possible relevance to high temperature superconductors. In the paper we review that body of theoretical work on this subject which represents a natural extension of the seminal papers by Leggett and by Nozieres and Schmitt-Rink (NSR). The former addressed only the ground state, now known as the "BCS-Leggett" wave-function and the key contributions of the latter pertain to calculations of the superfluid transition temperature $T_c$. These two papers have given rise to two main and, importantly, distinct, theoretical schools in the BCS-BEC crossover literature. The first of these extends the BCS-Leggett ground state to finite temperature and the second extends the NSR scheme away from $T_c$ both in the superfluid and normal phases. It is now rather widely accepted that these extensions of NSR produce a different ground state than that first introduced by Leggett. Our analysis shows how the NSR-based approach views the bosonic contributions more completely but it treats the fermions as "quasi-free". By contrast, the BCS-Leggett based approach treats the fermionic contributions more completely but it treats the bosons as "quasi-free". The NSR based schemes approach the crossover between BCS and BEC by starting from the BEC limit and the BCS-Leggett based scheme approaches this crossover by starting from the BCS limit. Ultimately, one would like to combine these two schemes. In this paper we review the strengths and weaknesses of both approaches. To reach a full understanding, it is important in the future to invest effort in investigating in more detail the T=0 aspects of NSR-based theory and the $T\ne 0$ aspects of BCS-Leggett theory.

23 pages, 6 figures

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Cited by in corpus (34)

• When Superconductivity Crosses Over: From BCS to BEC
• Pseudogaps in strongly interacting Fermi gases
• Ground-state thermodynamic quantities of homogeneous spin-$1/2$ fermions from the BCS region to the unitarity limit
• Population imbalance and pairing in the BCS-BEC crossover of three-component ultracold fermions
• Fermi gas throughout the BCS-BEC crossover: Comparative study of t-matrix approaches with various degrees of self-consistency
• Comparative Study of BCS-BEC Crossover Theories above $T_c$: the Nature of the Pseudogap in Ultra-Cold Atomic Fermi Gases
• Quantum Geometric Contributions to the BKT Transition: Beyond Mean Field Theory
• Establishing the Presence of Coherence in Atomic Fermi Superfluids: Spin-Flip and Spin-Preserving Bragg Scattering at Finite Temperatures
• Pseudogap phenomena in ultracold atomic Fermi gases
• Electrical Conductivity of Dense Quark Matter with Fluctuations and Magnetic Field Included
• Low-temperature thermodynamics of the unitary Fermi gas: superfluid fraction, first sound and second sound
• The pseudogap regime in the unitary Fermi gas
• BCS-BEC Crossover in Symmetric Nuclear Matter at Finite Temperature: Pairing Fluctuation and Pseudogap
• Theories of Linear Response in BCS Superfluids and How They Meet Fundamental Constraints
• BCS-BEC crossover at finite temperature in spin-orbit coupled Fermi gases
• BCS-BEC crossover of atomic Fermi superfluid in a spherical bubble trap
• Viscosity-entropy ratio of the unitary Fermi gas from zero-temperature elementary excitations
• Momentum-resolved spectroscopy of a Fermi liquid
• Establishing Conservation Laws in Pair Correlated Many Body theories: T matrix Approaches
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• BEC-BCS crossover in a p+ip-wave pairing Hamiltonian coupled to bosonic molecular pairs
• Finite temperature vortices in a rotating Fermi gas
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• A Holographic Model for Pseudogap in BCS-BEC Crossover (I): Pairing Fluctuations, Double-Trace Deformation and Dynamics of Bulk Bosonic Fluid
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