One-dimensional Cooper pairing

✍ Scribed by R. Mendoza; M. Fortes; M. de Llano; M.A. Solís

• Publisher: Elsevier Science
• Year: 2011
• Tongue: English
• Weight: 444 KB
• Volume: 471
• Category: Article
• ISSN: 0921-4534
• DOI: 10.1016/j.physc.2011.05.252

✦ Synopsis

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.