The theory of unconventional superconductors continues to provide profound puzzles. The crossover between the weakly coupled Bardeen-Cooper-Schrieffer (BCS) state and the strong-pairing Bose-Einstein condensate (BEC) provides a useful perspective on how to address these questions. This paper describes a self-consistent framework for thinking about the crossover regime in between these two limits. The review discusses to what extent this BCS-BEC theory applies to a range of classes of superconducting materials including the cuprates, iron pnictides, twisted bilayer graphene, and interfacial superconductivity among others.
In this paper, we have investigated the effect of weak random disorder in the Bardeen–Cooper–Schrieffer to Bose–Einstein condensation (BCS–BEC) crossover region. The disorder is included in the mean field formalism through Nozières–Smith-Rink (NSR) theory of superconducting fluctuations. A self-consistent numerical solution of the coupled equations involving the superfluid gap parameter and density as a function of the disorder strength, albeit unaffected in the BCS phase, yields a depleted order parameter in the BEC regime and an interesting nonmonotonic behaviour of the condensate fraction in the vicinity of the unitary region, and a gradual depletion thereafter, as the pairing interaction is continuously tuned across the BCS–BEC crossover. The unitary regime thus demonstrates a robust paradigm of superfluidity even when the disorder is introduced. To support the above feature and shed light on a lingering controversial issue, we have computed the behaviour of the sound mode across the crossover that distinctly reveals a suppression of the sound velocity. We also find the Landau critical velocity that shows similar nonmonotonicity as that of the condensate fraction data, thereby supporting a stable superfluid scenario in the unitary limit.
The BCS-BEC crossover is studied in a systematic way in the broken-symmetry phase between zero temperature and the critical temperature. This study bridges two regimes where quantum and thermal fluctuations are, respectively, important. The theory is implemented on physical grounds, by adopting a fermionic self-energy in the broken-symmetry phase that represents fermions coupled to superconducting fluctuations in weak coupling and to bosons described by the Bogoliubov theory in strong coupling. This extension of the theory beyond mean field proves important at finite temperature, to connect with the results in the normal phase. The order parameter, the chemical potential, and the single-particle spectral function are calculated numerically for a wide range of coupling and temperature. This enables us to assess the quantitative importance of superconducting fluctuations in the broken-symmetry phase over the whole BCS-BEC crossover. Our results are relevant to the possible realizations of this crossover with high-temperature cuprate superconductors and with ultracold fermionic atoms in a trap.
We investigate magnetic properties and effects of pairing fluctuations in the Bardeen-Cooper-Schrieffer--Bose-Einstein condensation (BCS-BEC) crossover regime of an ultracold Fermi gas. Recently, Liu and Hu [Europhys. Lett. 75, 364 (2006)], and Parish et al. [Nat. Phys. 3, 124 (2007)], pointed out that the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR), which has been extensively used to successfully clarify various physical properties of cold Fermi gases, unphysically gives negative spin susceptibility in the BCS-BEC crossover region. The same problem also exists in the ordinary non-self-consistent
T-matrix approximation. In this paper, we clarify that this serious problem comes from incomplete treatment in term of pseudogap phenomena originating from strong pairing fluctuations, as well as effects of spin fluctuations on the spin susceptibility. Including these two key issues, we construct an extended
T-matrix theory which can overcome this problem. The resulting positive spin susceptibility agrees well with the recent experiment on a
6Li Fermi gas done by Sanner et al. [Phys. Rev. Lett. 106, 010402 (2011)]. We also apply our theory to a polarized Fermi gas to examine the superfluid phase transition temperature
Tc, as a function of the polarization rate. Since the spin susceptibility is an important physical quantity, especially in singlet Fermi superfluids, our results would be useful in considering how singlet pairs appear above and below
Tc in the BCS-BEC crossover regime of cold Fermi gases.
The BCS-BEC crossover is studied in a systematic way in the broken-symmetry phase between zero temperature\nand the critical temperature. This study bridges two regimes where quantum and thermal fluctuations\nare, respectively, important. The theory is implemented on physical grounds, by adopting a fermionic selfenergy\nin the broken-symmetry phase that represents fermions coupled to superconducting fluctuations in weak\ncoupling and to bosons described by the Bogoliubov theory in strong coupling. This extension of the theory\nbeyond mean field proves important at finite temperature, to connect with the results in the normal phase. The\norder parameter, the chemical potential, and the single-particle spectral function are calculated numerically for\na wide range of coupling and temperature. This enables us to assess the quantitative importance of superconducting\nfluctuations in the broken-symmetry phase over the whole BCS-BEC crossover. Our results are relevant\nto the possible realizations of this crossover with high-temperature cuprate superconductors and with\nultracold fermionic atoms in a trap.
We discuss the derivation of a low-energy effective field theory of phase (Goldstone) and amplitude (Higgs) modes of the pairing field from a microscopic theory of attractive fermions. The coupled equations for Goldstone and Higgs fields are critically analyzed in the Bardeen–Cooper–Schrieffer (BCS)-to-Bose–Einstein condensate (BEC) crossover—both in three spatial dimensions and in two spatial dimensions. The crucial role of pair fluctuations is investigated, and the beyond-mean-field Gaussian theory of the BCS–BEC crossover is compared with available experimental data of the two-dimensional ultracold Fermi superfluid.