Importance of phase fluctuations in superconductors with small superfluid density

Abstract

THE superconducting state of a metal is characterized by a complex order parameter with an amplitude and a phase. In the BCS-Eliashberg mean-field theory1, which is a very good approximation for conventional metals, the phase of the order parameter is un-important for determining the value of the transition temperature Tc and the change of many physical properties brought about by the transition. Here we argue that superconductors with low super-conducting carrier density (such as the organic and high-Tc oxide superconductors) are characterized by a relatively small phase 'stiffness9 and poor screening, both of which imply a significantly larger role for phase fluctuations. As a consequence, in these mat-erials the transition to the superconducting state may not display typical mean-field behaviour, and phase fluctuations, both classical and quantum, may have a significant influence on low-temperature properties. For some quasi-two-dimensional materials, notably underdoped high-temperature superconductors, the onset of long-range phase order controls the gross value of Tc as well as its systematic variation from one material to another.