Fluxoid fluctuations in mesoscopic superconducting rings

Abstract

Rings are a model system for studying phase coherence in one dimension. Superconducting rings have states with uniform phase windings that are integer multiples of 2$\pi$ called fluxoid states. When the energy difference between these fluxoid states is of order the temperature so that phase slips are energetically accessible, several states contribute to the ring's magnetic response to a flux threading the ring in thermal equilibrium and cause a suppression or downturn in the ring's magnetic susceptibility as a function of temperature. We review the theoretical framework for superconducting fluctuations in rings including a model developed by Koshnick${}^1$ which includes only fluctuations in the ring's phase winding number called fluxoid fluctuations and a complete model by von Oppen and Riedel${}^2$ that includes all thermal fluctuations in the Ginzburg-Landau framework. We show that for sufficiently narrow and dirty rings the two models predict a similar susceptibility response with a slightly shifted Tc indicating that fluxoid fluctuations are dominant. Finally we present magnetic susceptibility data for rings with different physical parameters which demonstrate the applicability of our models. The susceptibility data spans a region in temperature where the ring transitions from a hysteretic to a non hysteretic response to a periodic applied magnetic field. The magnetic susceptibility data, taken where transitions between fluxoid states are slow compared to the measurement time scale and the ring response was hysteretic, decreases linearly with increasing temperature resembling a mean field response with no fluctuations. At higher temperatures where fluctuations begin to play a larger role a crossover occurs and the non-hysteretic data shows a fluxoid fluctuation induced suppression of diamagnetism below the mean field response that agrees well with the models.

References in corpus (6)

• Superconductivity in one dimension
• Magnetic response of mesoscopic superconducting rings with two order parameters
• Fluctuation Superconductivity in Mesoscopic Aluminum Rings
• Persistent current in small superconducting rings
• Nucleation of superconductivity in a mesoscopic loop of varying width
• Microscopic model for multiple flux transitions in mesoscopic superconducting loops

Cited by in corpus (7)

• Non-sinusoidal current-phase relationship in Josephson junctions from the 3D topological insulator HgTe
• Quantum phase slip phenomenon in ultra-narrow superconducting nanorings
• Deterministic phase slips in mesoscopic superconducting rings
• Cryogen-free variable temperature scanning SQUID microscope
• Imaging phase slip dynamics in micron-size superconducting rings
• Proximity-induced minimum radius of superconducting thin rings closed by the Josephson 0 or pi junction
• Observation of flux qubit states with the help of a superconducting differential double contour interferometer