Quantum mechanics predicts that the equilibrium state of a resistive electrical circuit contains a dissipationless current. This persistent current has been the focus of considerable theoretical and experimental work, but its basic properties remain a topic of controversy. The main experimental challenges in studying persistent currents have been the small signals they produce and their exceptional sensitivity to their environment. To address these issues we have developed a new technique for detecting persistent currents which offers greatly improved sensitivity and reduced measurement back action. This allows us to measure the persistent current in metal rings over a wider range of temperature, ring size, and magnetic field than has been possible previously. We find that measurements of both a single ring and arrays of rings agree well with calculations based on a model of non-interacting electrons. An electrical current induced in a resistive circuit will rapidly decay in the absence of an applied voltage. This decay reflects the tendency of the circuit's electrons to dissipate energy and relax to their ground state. However quantum mechanics predicts that the electrons' many-body ground state (and, at finite temperature, their thermal equilibrium state) may itself contain a "persistent" current which flows through the resistive circuit without dissipating energy or decaying. A dissipationless equilibrium current flowing through a resistive circuit is highly counterintuitive, but it has a familiar analog in atomic physics: some atomic species' electronic ground states possess non-zero orbital angular momentum, equivalent to a current circulating around the atom. Theoretical treatments of persistent currents (PC) in resistive metal rings have been developed over a number of decades (see [1,2] and references therein). Calculations which take 1

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 measured the susceptibility of many rings, one ring at a time, by using a scanning superconducting quantum interference device that can isolate magnetic signals that are seven orders of magnitude smaller than 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.

We present scanning superconducting quantum interference device microscopy data on the superconductors Sr 2 RuO 4 ͑T c = 1.5 K͒ and PrOs 4 Sb 12 ͑T c = 1.8 K͒. In both of these materials, superconductivity-related timereversal 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 p x Ϯ ip y 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 ϳ0.1% and ϳ0.2% of the expected magnitude, respectively. Alternatively, if the magnetization is of the expected order, the typical domain size is limited to ϳ30 nm for random domains or ϳ500 nm for periodic domains.

. Although vortex matter has been studied extensively 1,6,7 , the static and dynamic properties of an individual vortex have not. Here, we use magnetic force microscopy (MFM) to image and manipulate individual vortices in a detwinned YBa 2 Cu 3 O 6.991 single crystal, directly measuring the interaction of a moving vortex with the local disorder potential. We find an unexpected and marked enhancement of the response of a vortex to pulling when we wiggle it transversely. In addition, we find enhanced vortex pinning anisotropy that suggests clustering of oxygen vacancies in our sample and demonstrates the power of MFM to probe vortex structure and microscopic defects that cause pinning.

We have fabricated and characterized micro-SQUID susceptometers for use in low-temperature scanning probe microscopy systems. The design features the following: a 4.6 mum diameter pickup loop; an integrated field coil to apply a local field to the sample; an additional counterwound pickup-loop/field-coil pair to cancel the background signal from the applied field in the absence of the sample; modulation coils to allow setting the SQUID at its optimum bias point (independent of the applied field), and shielding and symmetry that minimizes coupling of magnetic fields into the leads and body of the SQUID. We use a SQUID series array preamplifier to obtain a system bandwidth of 1 MHz. The flux noise at 125 mK is approximately 0.25 mu Phi 0/ sqrt Hz above 10 kHz, with a value of 2.5 mu Phi 0/ sqrt Hz at 10 Hz. The nominal sensitivity to electron spins located at the center of the pickup loop is approximately 200 muB/ sqrt Hz above 10 kHz, in the white-noise frequency region.