Influence of Resonances on the Noise Performance of SQUID Susceptometers

Scanning Superconducting Quantum Interference Device (SQUID) Susceptometry simultaneously images the local magnetic fields and susceptibilities above a sample with sub-micron spatial resolution. Further development of this technique requires a thorough understanding of the current, voltage, and flux ( IVΦ ) characteristics of scanning SQUID susceptometers. These sensors often have striking anomalies in their current–voltage characteristics, which we believe to be due to electromagnetic resonances. The effect of these resonances on the performance of these SQUIDs is unknown. To explore the origin and impact of the resonances, we develop a model that qualitatively reproduces the experimentally-determined IVΦ characteristics of our scanning SQUID susceptometers. We use this model to calculate the noise characteristics of SQUIDs of different designs. We find that the calculated ultimate flux noise is better in susceptometers with damping resistors that diminish the resonances than in susceptometers without damping resistors. Such calculations will enable the optimization of the signal-to-noise characteristics of scanning SQUID susceptometers

Fluxoid fluctuations in mesoscopic superconducting rings

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

Meissner response of a bulk superconductor with an embedded sheet of reduced penetration depth

We calculate the change in susceptibility resulting from a thin sheet with reduced penetration depth embedded perpendicular to the surface of an isotropic superconductor, in a geometry applicable to scanning Superconducting QUantum Interference Device (SQUID) microscopy, by numerically solving Maxwell's and London's equations using the finite element method. The predicted stripes in susceptibility agree well in shape with the observations of Kalisky et al. of enhanced susceptibility above twin planes in the underdoped pnictide superconductor Ba(Fe1-xCox)2As2 (Ba-122). By comparing the predicted stripe amplitudes with experiment and using the London relation between penetration depth and superfluid density, we estimate the enhanced Cooper pair density on the twin planes, and the barrier force for a vortex to cross a twin plane. Fits to the observed temperature dependence of the stripe amplitude suggest that the twin planes have a higher critical temperature than the bulk, although stripes are not observed above the bulk critical temperature.Comment: 16 pages, 9 figure

SuperScreen: An open-source package for simulating the magnetic response of two-dimensional superconducting devices

Quantitative understanding of the spatial distribution of magnetic fields and Meissner screening currents in two-dimensional (2D) superconductors and mesoscopic thin film superconducting devices is critical to interpreting the results of magnetic measurements of such systems. Here, we introduce SuperScreen, an open-source Python package for simulating the response of 2D superconductors to trapped flux and applied time-independent or quasi-DC magnetic fields for any value of the effective magnetic penetration depth, $\Lambda$. Given an applied magnetic field, SuperScreen solves the 2D London equation using an efficient matrix inversion method to obtain the Meissner currents and magnetic fields in and around structures composed of one or more superconducting thin films of arbitrary geometry. SuperScreen can be used to model screening effects and calculate self- and mutual-inductance in superconducting devices, and simulate the magnetic response of inhomogeneous 2D superconductors.Comment: 20 pages, 8 figures. GitHub repository: https://github.com/loganbvh/superscreen/ . Supplementary Jupyter notebooks: https://github.com/loganbvh/superscreen-paper . Submitted to Computer Physics Communication

Persistent currents in normal metal rings

The authors have measured the magnetic response of 33 individual cold mesoscopic gold rings, one ring at a time. The response of some sufficiently small rings has a component that is periodic in the flux through the ring and is attributed to a persistent current. Its period is close to h/e, and its sign and amplitude vary between rings. The amplitude distribution agrees well with predictions for the typical h/e current in diffusive rings. The temperature dependence of the amplitude, measured for four rings, is also consistent with theory. These results disagree with previous measurements of three individual metal rings that showed a much larger periodic response than expected. The use of a scanning SQUID microscope enabled in situ measurements of the sensor background. A paramagnetic linear susceptibility and a poorly understood anomaly around zero field are attributed to defect spins.Comment: Journal version. 4+ pages, 3 figures. See http://stanford.edu/group/moler/publications.html for the auxiliary document containing additional data and discussion (Ref. 29). Changes w.r.t. v1: Clarified some details in introduction and regarding experimental procedures, shortened abstract, added references and fixed some typo