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Journal of Superconductivity and Novel Magnetism

Quartet Structures of Particles and Quasiparticles in the BCS Model

J. D. Fan, Y. M. Malozovsky

Published Feb 8, 2010• 5 citations
Publisher
DOI
10.1007/s10948-010-0746-4

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We investigate the quartet correlations in four-component fermionic systems at the thermodynamic limit within a variational many-body theory. The Bardeen-Cooper-Schrieffer (BCS)--type variational wave function is extended to the systems with the coexistence of pair and quartet correlations at zero temperature. Special attention is paid to the application of the present framework to an $\ensuremath{\alpha}$-particle condensation in symmetric nuclear matter, where the coexistence of deuteron and $\ensuremath{\alpha}$ condensations is anticipated. We also discuss how physical properties, such as quasiparticle dispersion, can be modified by the pair and quartet correlations and show a hierarchical structure of in-medium cluster formations in infinite nuclear matter. The present results may also contribute to the interdisciplinary understanding of fermionic condensations beyond the BCS paradigm in many-body systems.
We theoretically investigate a quartet superfluid state in fermionic matter by using the quartet Bardeen-Cooper-Schrieffer (BCS) variational theory and the Green's function method. We demonstrate that the quartet BCS theory with the multiple-infinite-product ansatz successfully reproduces an exact four-body result in a one-dimensional four-component Fermi gas at the dilute limit, in contrast to the single-infinite-product ansatz. To see the validity of the quartet BCS state, we derive the self-consistent equation for the quartet superfluid order parameter within the generalized imaginary-time Nambu-Gor'kov formalism, which is found to be consistent with the quartet BCS variational equation. Moreover, by numerically computing the momentum-resolved single-particle spectral function in a one-dimensional system, we discuss how the single-particle spectra evolve with increasing the strength of the four-body cluster formation. We show that a coherent BCS-like quasiparticle branch on the weak-coupling side evolves into a strongly damped, continuum-dominated spectrum in the strong-coupling side, while nonzero quartet superfluid order parameter persists throughout the crossover regime. Our results would be useful for understanding beyond-BCS pairing effects and four-body cluster formations in fermionic systems in an interdisciplinary way.
The formal implications of a quartet coherent-state ansatz for proton-neutron pairing are analyzed. Its nonlinear annihilation operators, which generalize the BCS linear quasiparticle operators, are computed in the quartetting case. Their structure is found to generate nontrivial relationships between the many-body correlation functions. The intrinsic structure of the quartet coherent state is detailed as it hints to the precise correspondence between the quartetting picture and the symmetry restored pair condensate picture for the proton-neutron pairing correlations.