Phase fluctuations in conventional superconductors

Within the Bardeen-Cooper-Schrieffer (BCS) theory, superconductivity is entirely governed by the pairing energy scale, which gives rise to the superconducting energy gap, Δ. However, another important energy scale, the superfluid phase stiffness, J, which determines the resilience of the superconductor to phase-fluctuations is normally ignored. The spectacular success of BCS theory owes to the fact that in conventional superconductors J is normally several orders of magnitude larger than Δ and thus an irrelevant energy scale. However, in certain situations such as in the presence of low carrier density, strong disorder, at low-dimensions or in granular superconductors, J can drastically come down and even become smaller than Δ. In such situations, the temperature and magnetic field evolution of superconducting properties is governed by phase fluctuations, which gives rise to novel electronic states where signatures of electronic pairing continue to exist even when the zero resistance state is destroyed. In this article, we will review the recent experimental developments on the study of phase fluctuations in conventional superconductors.

Inhomogeneous Superconductivity and the ‘Pseudogap’ State of Novel Superconductors

This chapter discusses the high-Tc oxides, which display many unusual properties above Tc, especially for the underdoped compounds. One can observe some features typical for the superconducting state, such as the energy gap, anomalous diamagnetism, and the isotope effect; they coexist with finite resistance. These features are caused by an intrinsic inhomogeneity of the compound. Various energy scales (Tc, Tc*, T*) can be introduced. The system contains a set of superconducting ‘islands’ embedded in a normal metallic matrix. The inhomogeneity is caused by the statistical nature of doping and the pair-breaking effect. The formation of a macroscopic superconducting phase (at T = Tc) corresponds to the transition, which is of a percolative nature. The resistive and Meissner transitions are split. The granular superconductors are inhomogeneous and their properties are similar to those of doped systems. The ordered doping should lead to an increase in the value of the critical temperature.

The Role of the Short Coherence Length in Unconventional Superconductors

A short coherence length is a distinctive feature of many cases of unconventional superconductivity. While in conventional superconductors, it is many orders of magnitude larger than the basic inter-particle distance, a short coherence length is common to superconductors as diverse as the cuprates, the picnites and granular superconductors. We dwell particularly on the last, because their simple chemical structure makes them a favorable material for exploring fundamental phenomena such as the Bardeen-Cooper Schrieffer (BCS)-to-Bose–Einstein condensation cross-over and the effect of the vicinity of a Mott metal-to-insulator transition.

Abnormal behaviour of the resistive transition to the normal state in superconducting Nb-Ti tapes just below Hc2

The results of studying the resistive properties of Nb-Ti tapes in high magnetic fields close to the upper critical field (Hc2) are reported. The voltage-current curves (VCCs) and resistance-current cures (RCCs) show an “abnormal” hysteresis which is opposite in sign to a common thermal one caused by self-heating. Several features were noted: the existence of threshold current below which VCCs are reversible and the presence of excessive voltage noise in the hysteresis region. Earlier the similar behaviour was observed in granular superconductors. The nature of the “granular” properties of Nb-Ti tapes in high magnetic field and the relation with other observed effects, such as the irreversibility field and the apparent anisotropy of the upper critical field are discussed.