One-dimensional Cooper pairing |
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Authors: | R Mendoza M Fortes M de Llano MA Solís |
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Institution: | 1. Instituto de F?´sica, UNAM, Apdo. Postal 20-364, 01000 México D.F., Mexico;2. Instituto de Investigaciones en Materiales, UNAM, Apdo. Postal 70-360, 04510 México D.F., Mexico |
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Abstract: | 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. |
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