Bardeen-Cooper-Schrieffer interaction as an infinite-range Penson-Kolb pairing mechanism

Abstract

We demonstrate that the well-known $(k\uparrow ,-k\downarrow )$ Bardeen-Cooper-Schrieffer interaction, when considered in real space, is equivalent to an infinite-range Penson-Kolb pairing mechanism coexisting with an attractive Hubbard term. Driven by this discovery and aiming at exploring the conduction properties, we investigate the dynamics of fermionic particles confined in a ring-shaped lattice. We assume that fermions are simultaneously influenced by the pairing interaction and by an Aharonov-Bohm electromagnetic phase, which is incorporated into the model in a highly non-trivial manner. Remarkably, the aforementioned model shows Richardson integrability for both integer and half-integer values of the applied magnetic flux $\Phi /{\Phi }_0$, thus permitting the exact solution of a genuine many-body problem. We discuss the ground state properties of both two-particle and many-particle systems, drawing comparisons with results from the attractive Hubbard model. Our approach combines exact diagonalization, density matrix renormalization group techniques, and numerical solution of the Richardson equations. This comprehensive analysis allows us to study various key metrics, including the system's conductivity as a function of the interaction strength. In this way, the BCS-BEC transition is investigated in a continuous manner, thus permitting to shed light on fundamental aspects of superconducting pairing. Our findings can be experimentally tested in a condensed matter context or, with greater level of control, using atomtronics platforms.

arXiv comment21 pages, 9 figures; Updated version enhanced with comprehensive new appendices, minor changes and corrections of residual typos

References in corpus (15)

• An Area Law for One Dimensional Quantum Systems
• Roadmap on Atomtronics: State of the art and perspective
• An exactly solvable model of the BCS-BEC crossover
• Does the attractive Hubbard model support larger persistent currents than the repulsive one ?
• A particle-number-conserving solution to the generalized pairing problem
• Imprinting persistent currents in tunable fermionic rings
• h/e-Periodicity in Superconducting Loops
• Probing the BCS-BEC crossover with persistent currents
• Band and filling controlled transitions in exactly solved electronic models
• Exact thermodynamics of an Extended Hubbard Model of single and paired carriers in competition
• The Thermodynamic Limit of Spin Systems on Random Graphs
• Thermodynamic and electromagnetic properties of the eta-pairing superconductivity in the Penson-Kolb model
• On the Bardeen-Cooper-Schrieffer interaction in quantum graphs
• Relative Phase and Josephson Dynamics between Weakly Coupled Richardson Models
• Symmetry and Supersymmetry in Nuclear Pairing: Exact Solutions