Fluctuation Superconductivity in Mesoscopic Aluminum Rings

Fluctuations are important near phase transitions, where they can be difficult to describe quantitatively. Superconductivity in mesoscopic rings is particularly intriguing because the critical temperature is an oscillatory function of magnetic field. There is an exact theory for thermal fluctuations in one-dimensional superconducting rings, which are therefore expected to be an excellent model system. We measure the susceptibility of many rings, one ring at a time, using a scanning SQUID that can isolate magnetic signals from seven orders of magnitude larger background applied flux. We find that the fluctuation theory describes the results and that a single parameter characterizes the ways in which the fluctuations are especially important at magnetic fields where the critical temperature is suppressed.Comment: Reprinted with permission from AAA

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

A Terraced Scanning Superconducting Quantum Interference Device Susceptometer with Sub-Micron Pickup Loops

Superconducting Quantum Interference Devices (SQUIDs) can have excellent spin sensitivity depending on their magnetic flux noise, pick-up loop diameter, and distance from the sample. We report a family of scanning SQUID susceptometers with terraced tips that position the pick-up loops 300 nm from the sample. The 600 nm - 2 um pickup loops, defined by focused ion beam, are integrated into a 12-layer optical lithography process allowing flux-locked feedback, in situ background subtraction and optimized flux noise. These features enable a sensitivity of ~70 electron spins per root Hertz at 4K.Comment: See http://stanford.edu/group/moler/publications.html for an auxiliary document containing additional fabrication details and discussio

Limits on Superconductivity-Related Magnetization in Sr2_2RuO4_4 and PrOs4_4Sb12_{12} from Scanning SQUID Microscopy

We present scanning SQUID microscopy data on the superconductors Sr2RuO4 (Tc = 1.5 K) and PrOs$_4$Sb$_{12}$ (Tc = 1.8 K). In both of these materials, superconductivity-related time-reversal symmetry-breaking fields have been observed by muon spin rotation; our aim was to visualize the structure of these fields. However in neither Sr$_2$RuO$_4$ nor PrOs$_4$Sb$_{12}$ do we observe spontaneous superconductivity-related magnetization. In Sr$_2$RuO$_4$, many experimental results have been interpreted on the basis of a $px \pm ipy$ superconducting order parameter. This order parameter is expected to give spontaneous magnetic induction at sample edges and order parameter domain walls. Supposing large domains, our data restrict domain wall and edge fields to no more than ~0.1% and ~0.2% of the expected magnitude, respectively. Alternatively, if the magnetization is of the expected order, the typical domain size is limited to ~30 nm for random domains, or ~500 nm for periodic domains.Comment: 8 pages, 7 figures. Submitted to Phys. Rev.

A possibility of persistent voltage observation in a system of asymmetric superconducting rings

A possibility to observe the persistent voltage in a superconducting ring of different widths of the arms is experimentally investigated. It was earlier found that switching of the arms between superconducting and normal states by ac current induces the dc voltage oscillation in magnetic field with a period corresponding to the flux quantum inside the ring. We use systems with a large number of asymmetric rings connected in series in order to investigate the possibility to observe this quantum phenomenon near the superconducting transition where thermal fluctuations switch ring segments without external influence and the persistent current is much smaller than in the superconducting state.Comment: 7 pages, 4 figure

Universal Signatures of Fractionalized Quantum Critical Points

Groundstates of certain materials can support exotic excitations with a charge that's a fraction of the fundamental electron charge. The condensation of these fractionalized particles has been predicted to drive novel quantum phase transitions, which haven't yet been observed in realistic systems. Through numerical and theoretical analysis of a physical model of interacting lattice bosons, we establish the existence of such an exotic critical point, called XY*. We measure a highly non-classical critical exponent eta = 1.49(2), and construct a universal scaling function of winding number distributions that directly demonstrates the distinct topological sectors of an emergent Z_2 gauge field. The universal quantities used to establish this exotic transition can be used to detect other fractionalized quantum critical points in future model and material systems.Comment: 12 pages, 3 figures (+ supplemental

Multiple Current States of Two Phase-Coupled Superconducting Rings

The states of two phase-coupled superconducting rings have been investigated. Multiple current states have been revealed in the dependence of the critical current on the magnetic field. The performed calculations of the critical currents and energy states in a magnetic field have made it possible to interpret the experiment as the measurement of energy states into which the system comes with different probabilities because of the equilibrium and non-equilibrium noises upon the transition from the resistive state to the superconducting state during the measurement of the critical currentComment: 5 pages, 5 figure

Partition asymptotics from one-dimensional quantum entropy and energy currents

We give an alternative method to that of Hardy-Ramanujan-Rademacher to derive the leading exponential term in the asymptotic approximation to the partition function p(n,a), defined as the number of decompositions of a positive integer 'n' into integer summands, with each summand appearing at most 'a' times in a given decomposition. The derivation involves mapping to an equivalent physical problem concerning the quantum entropy and energy currents of particles flowing in a one-dimensional channel connecting thermal reservoirs, and which obey Gentile's intermediate statistics with statistical parameter 'a'. The method is also applied to partitions associated with Haldane's fractional exclusion statistics.Comment: Published versio