One-dimensional Cooper pairing

• Published in: Physica. C, Superconductivity Superconductivity, 2011-09, Vol.471 (17), p.497-503
• Main Authors: Mendoza, R., Fortes, M., de Llano, M., Solís, M.A.
• Format: Article
• Language: English
• Subjects: Attraction; BCS; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Cooper pairing; Coordinate measuring machines; Dispersions; Exact sciences and technology; Excitation; Linear mode; Nonconventional mechanisms (spin fluctuations, polaron and bipolaron theory, rvb theory, anyon mechanism, marginal fermi liquid, luttinger liquid, etc.); Pair excitation energy; Physics; Roton mode; Strength; Superconductivity; Theory and models of superconducting state; Three dimensional; Wavenumber
• ISSN: 0921-4534; 1873-2143
• DOI: 10.1016/j.physc.2011.05.252

► Exact solutions for electron pairing in a 1D Fermi gas under different separable interactions. ► Energy dispersion relations for arbitrary values of center-of-mass momenta and interaction strengths. ► Results reveal linear and roton-like modes. ► Effects due to finite range parameters in the interaction. We study electron pairing in a one-dimensional (1D) fermion gas at zero temperature under zero- and finite-range, attractive, two-body interactions. The binding energy of Cooper pairs (CPs) with zero total or center-of-mass momentum (CMM) increases with attraction strength and decreases with interaction range for fixed strength. The excitation energy of 1D CPs with nonzero CMM display novel, unique properties. It satisfies a dispersion relation with two branches: a phonon-like linear excitation for small CP CMM; this is followed by roton-like quadratic excitation minimum for CMM greater than twice the Fermi wavenumber, but only above a minimum threshold attraction strength. The expected quadratic-in-CMM dispersion in vacuo when the Fermi wavenumber is set to zero is recovered for any coupling. This paper completes a three-part exploration initiated in 2D and continued in 3D.