Sensing a Small But Persistent Current

A magnetic field can create tiny currents that flow continuously in an ordinary metal ring, despite its electrical resistance. The idea that a normal, nonsuperconducting metal ring can sustain a persistent current—one that flows forever without dissipating energy—seems preposterous. Metal wires have an electrical resistance, and currents passing through resistors dissipate energy. Besides, time-reversal symmetry should forbid a current choosing one direction over the other around the ring.

It is well known from embryological studies of living mammals that the process of detachment of the middle ear bones is repeated during early ontogeny ( 10,11). In recent decades, evolutionary developmental biology studies have elucidated the driving forces for this process. The partial resorption of Meckel's cartilage and disconnection of the middle ear ossicles from the mandible in modern mammals are controlled by complex regulatory networks; mutant mouse studies have shown that changes in these networks can alter the timing of resorption and ossifi cation, causing morphological transformations such as the permanent connection of middle ear ossicles and mandible (12)(13)(14). From an evolutionary biologist's viewpoint, the "reevolution" of an ancestral character state appears unlikely, but in the case of Maotherium's DMME, a simple temporal change causing premature ossifi cation of Meckel's cartilage during embryo development fi xed the ancestral condition in the adult.
The approach of Ji et al. exemplifi es recent studies that have combined paleontology and developmental biology to gain deep insight into evolutionary processes ( 15). These studies have shown that mammalian evolution was much more complex than had been thought a few years ago. Developmental processes played a central role in evolutionary changes in mammals, as recently shown for patterns of rodent teeth ( 16). The middle ear and mandible of Maotherium demonstrate that besides orderly evolution from primitive to derived characters, reversals to more primitive conditions are also to be expected. In the case of the DMME, the labile phase with multiple reversals appears to have ended with the evolution of the coiled cochlea in the inner ear of more derived ancestors of therian mammals (marsupials and placentals) ( 17).
T he idea that a normal, nonsuperconducting metal ring can sustain a persistent current-one that fl ows forever without dissipating energy-seems preposterous. Metal wires have an electrical resistance, and currents passing through resistors dissipate energy. Besides, timereversal symmetry should forbid a current choosing one direction over the other around the ring.
The latter argument is indeed correct. The persistent current exists only in the presence of a magnetic fi eld piercing the ring, which breaks time-reversal symmetry. All physical properties of a metal ring vary periodically with the magnetic flux through the ring ( 1), with period equal to the magnetic fl ux quantum, Φ 0 = h/e, where h is Planck's constant and e is the charge of an electron. Among those properties is the ring's persistent current ( 2), and this current exists even in realistic metal rings containing atomic defects, grain boundaries, and other kinds of static disorder ( 3). The current is extremely small and notoriously diffi cult to measure. Two recent studies, one by These studies help resolve some of the discrepancies that have arisen in previous studies spanning nearly 20 years.
Several factors conspire to render detection of the persistent currents extremely diffi cult. The current fl ows only around a closed ring, so the effect is lost if a device like an ammeter is put into the circuit to measure it directly. The very small magnetic moment produced by the current must be measured instead. Theory predicts that the magnitude of the persistent current is roughly equal to the charge of a single electron divided by the time it takes an electron to diffuse around the ring. Experimentalists have kept this time small by using rings with diameters ranging from half a micrometer to a few micrometers. The persistent current diminishes rapidly as the temperature is raised, so temperatures are kept near 1 K. The sign of the persistent current in a real sample depends on the details of the disorder (the defects that scatter electrons and create resistance), and varies randomly from ring to ring, so many rings must be used as samples to get a good estimate of the typical current. Finally, spu-rious magnetic moments that can arise from contamination on the surface of the sample can easily swamp the magnetic moment created by the persistent current.
The fi rst two persistent-current experiments used very different strategies. In 1990, Lévy and co-workers measured an array of 10 million copper rings; their strategy was to add together many small signals to create a much larger, measurable signal ( 6). However, because the persistent current in each ring has a random sign, the total signal was proportional only to the square root of the number of rings ( 7).
It turns out that there is a second kind of persistent current, whose period is half of the magnetic fl ux quantum, Φ 0 /2 = h/2e. The "h/2e" persistent currents are normally much smaller than the "h/e" persistent currents, but they have the same sign in every ring, so the total signal is proportional to the number of rings. Lévy et al. did indeed observe the h/2e persistent current, but both the magnitude and the sign of their results disagreed with the theoretical predictions of that time ( 8,9). A possible resolution of that discrepancy has been proposed recently ( 10).
In 1991, Webb and co-workers measured the persistent current in three individual Department of Physics, Michigan State University, East Lansing, MI 48824, USA. E-mail: birge@pa.msu.edu PERSPECTIVES gold rings ( 11). They observed a persistent current with fl ux periodicity of h/e, but with a magnitude at least 30 times greater than predicted by theory. Later experiments by Webb's group on an array of 30 rings gave results closer to the theoretical prediction ( 12), but still left several questions unanswered. Experiments on semiconducting rings ( 13) have given results in closer agreement with theory.
The fi eld received a huge boost in the past year from two experiments. Bluhm et al. used a scanning microscope to measure the persistent currents in 33 gold rings, one ring at a time ( 4). Magnetic fi elds were detected with superconducting quantum interference devices, or SQUIDs. The ability of the microscope to spatially scan over the sample led to several improvements over previous measurements, including a better understanding of the background signals and better statistics from measuring many individual rings. Nevertheless, the small magnitude of the signals required 12 hours of signal averaging to obtain each data point. The observed h/e-periodic persistent currents varied randomly in sign from ring to ring, as expected, and had an overall magnitude in good agreement with theory.
Bleszynski-Jayich et al. used a much different technology to improve the measurement sensitivity and enable measurements in high magnetic fi elds. They adapted methods from nanoelectromechanical systems. Specifi cally, they fabricated the rings on the ends of ultrasmall mechanical cantilevers, as shown schematically in the fi gure. The cantilevers oscillate at a frequency determined by their stiffness and mass, and this oscillation frequency can be measured with extremely high precision.
When the cantilevers are placed in a large magnetic field, the interaction of the persistent current with the fi eld leads to a very small torque on the cantilever, which in turn changes its oscillation frequency ever so slightly. Using this technique, Bleszynski-Jayich et al. achieved a sensitivity about 100 times greater than the SQUIDbased measurements. The large magnetic fi eld suppressed any background signal caused by contamination from impurity spins, and the large range of fi eld enabled the experimentalists to obtain a statistical sampling of the persistent current in a single ring. They measured the h/e persistent currents in a single ring and in arrays containing 242, 990, and 1680 rings.
The total signal is proportional to the square root of the number of rings, confi rming the randomness of the sign discussed above. Both the overall magnitude of the persistent current and its temperature dependence agree extremely well with theory ( 14). The h/2e persistent currents, however, are not visible in this experiment because of the presence of the large magnetic fi eld.
It is safe to say that the h/e persistent currents in isolated metal rings are now well understood. So where do we go from here? Bleszynski-Jayich et al. propose coupling small rings to more complicated circuits, to see how the latter infl uence the former. The h/2e puzzle remains, at least until the recent hypothesis ( 10) can be checked experimentally.

Victor S. Batista
Laser pulses can be shaped to control energy transfer at the molecular scale in light-harvesting systems.

B ||
A ring cycle of currents. Persistent currents fl ow through an ordinary metal ring penetrated by a magnetic fi eld. Bleszynski-Jayich et al. fabricated either a single ring or an array of rings near the tip of a nanomechanical cantilever that serves as an oscillator (the rings vary in diameter from 0.6 to 1.6 µm, while the cantilevers are 450 µm long and 40 to 80 µm wide). The magnetic fi eld perpendicular to the plane of the rings, B II , produces magnetic fl ux through the rings, which causes the persistent currents to appear. The interaction of the persistent current with the magnetic fi eld parallel to the plane, B || , causes a torque on the cantilever, which changes its oscillation frequency slightly. The vibration amplitude is highly exaggerated in the fi gure. 10.1126/science.1180577 C ontrolling energy transfer at the molecular scale has been a longstanding goal since the development of high-power lasers in the 1960s. Appreciable advances toward this goal have been made with demonstrations of laser-controlled energy fl ow in natural and artifi cial light-harvesting antennas ( 1,2). Based on closed-loop control experiments ( 3,4), these techniques can effi ciently shape femtosecond laser pulses to control and optimize a variety of molecular processes. However, the details of the resulting control mechanisms are diffi cult to extract from a cursory examination of the shaped pulses. On page 263 of this issue, Kuroda et al. ( 5) report an important contribution toward understanding shaped laser pulses that control energy transfer at the molecular scale. The reported insights on the control mechanism are valuable to understand laser control, in general, in a variety of molecular systems with common relaxation processes.
The goal of Kuroda et al. was to elucidate how to optimize the fl ow of energy in donoracceptor dendrimer aggregates in liquids, as monitored by the radiative fl uorescence of