Low-dimensional BEC

Abstract

The Bose-Einstein condensation (BEC) temperature T-c of Cooper pairs (CPs) created front a general interfermion interaction is determined for a linear, as well as the usually assumed quadratic, energy vs center-of-mass momentum dispersion relation. This explicit T-c is then compared with a widely applied implicit one of Wen & Kan (1988) in d = 2 + epsilon dimensions, for small epsilon, for a geometry of an infinite stack of parallel (e.g., copper-oxygen) planes as in, say, a cuprate superconductor, and with a new result for linear-dispersion CPs. The implicit formula gives T-c values only slightly lower than those of the explicit formula for typical cuprate parameters.