Electric charge is quantized in units of the electron's charge. An experiment explores the suppression of charge quantization caused by quantum fluctuations and supports a long-standing theory that explains this behaviour. See Letter p.58
Because matter is constructed of elementary particles, the electric charge of any object is an integer multiple of the elementary charge, which is equivalent in size to the electron's charge. This concept is known as charge quantization. In 1913, charge quantization (and thus, the existence of elementary particles) was demonstrated by the physicist Robert Millikan, who measured the charges of single electrons in oil drops containing many billions of particles1. However, quantum physics predicts that charge quantization can be destroyed by tiny quantum fluctuations. On page 58, Jezouin et al.2 describe an experiment to control these fluctuations. Their results suggest that the effect of the fluctuations on charge quantization can be explained through particle-like phenomena called Korshunov instantons3.
In the current age of nanoscience, charge quantization has enabled the manipulation of single electrons in nanostructures, with applications in metrology, sensing and thermometry4. These nanostructures consist of conducting, metallic islands that store the single charges, and which are analogues of Millikan's oil drops. The islands are connected to electrodes and to each other by tunnel junctions — barriers between two conducting materials, such as thin layers of an insulator. Other 'gate' electrodes are used to control the discrete charges on the islands.
The most common manifestation of charge quantization in such nanostructures is the presence of Coulomb oscillations3: a periodic dependence of the structure's conductance on the voltage of one of the gate electrodes. However, if the islands are not well isolated, the conductance of the connecting junctions produces quantum fluctuations of charge that suppress the quantization, reducing the visibility of the Coulomb oscillations against the voltage-independent component of conductance.
The aim of Jezouin and colleagues' experiment2 is to fully control these quantum fluctuations. Their set-up is remarkably simple: a single metallic island is connected to two electrodes through separate junctions (Fig. 1). Unlike in previous attempts to control the fluctuations (see, for example, refs 5,6,7), each junction has only one conduction channel (a pathway through which an electron can travel). Therefore, the conduction of each junction is directly related to its transmission probability, the probability that an electron will be transmitted through the junction.
The authors are able to vary and quantify the transmission probability of each junction. To achieve this level of control, the conduction channels are formed in a semiconductor material, the surface of which supports a thin layer of electron gas. The authors' technological advance is to connect this two-dimensional gas to the metallic island.
Using this set-up, the authors measure the visibility of the Coulomb oscillations as two quantities — the transmission probabilities of the two junctions and the temperature — are varied. They find that the visibility of the oscillations is reduced if either of the junctions' transmission probabilities is increased. Furthermore, as the temperature is increased, thermal fluctuations result in an exponential suppression of the oscillations. What is the significance of these two 'scaling laws'?
Unlike classical fluctuations, which tend to destroy the order of a system, quantum fluctuations can actually generate alternative order. For example, large fluctuations in the position of a quantum particle imply that the particle's momentum has a precise value, whereas large fluctuations of momentum imply a precise position. Electric charge and magnetic flux are similarly connected in superconducting nanostructures8, so that increases in charge fluctuation convert charge quantization to flux quantization.
States of quantized flux do not exist in normal, non-superconducting metals. However, in 1987, the physicist Sergey Korshunov unexpectedly discovered that two flux quanta can be transferred between non-quantized flux states without the requirement for superconductivity, owing to the presence of particle-like phenomena called instantons3. Since then, the manifestations of these Korshunov instantons have been thoroughly investigated. In 1999, the concept was extended to arbitrary transmission probabilities9, leading to two specific predictions that describe the influence of instantons on charge quantization.
These predictions are precisely the scaling laws observed by Jezouin and collaborators. The authors' results therefore strongly suggest that charge quantization over the whole range of fluctuation strength is governed by Korshunov instantons, and provide experimental evidence of these long-predicted 'particles'.
The Korshunov instanton is a close relative of another concealed 'particle', the leviton10. Levitons are generated when a carefully engineered voltage pulse, encompassing precisely two flux quanta, is applied to a collection of electrons in a nanojunction. This phenomenon was confirmed11 experimentally in 2013. Whereas the leviton is an excitation of electron systems, the instanton is a property of the electronic ground state that, in the presence of electrostatic (Coulomb) interactions, governs charge quantization.
One puzzle left by the authors' experiment is why the scaling laws are consistent with the theoretical predictions for a single instanton. Theoretical considerations suggest that Jezouin and colleagues' system would involve configurations of many instantons, which would lead to more-complex scaling laws than those observed. Their results may imply that the theory that underlies such systems is simpler than it seems and has unknown symmetries that would cancel out many-instanton configurations. These theories could be tested using more-detailed measurements, especially of the island capacitance. One could also construct more-sophisticated set-ups that combine levitons and instantons. Greater control of these concealed particles could then be achieved by studying their interference.
Charge quantization is a simple concept; however, observing the effect of quantum fluctuations can lead to fascinating discoveries. Chasing exotic particles in nanostructures will help us to understand the complexity of quantum laws of electricity, with the hope of eventually applying this knowledge to quantum information processing.
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