All forms of waves can contain phase singularities. In the case of optical waves, a light beam with a phase singularity carries orbital angular momentum, and such beams have found a range of applications in optical manipulation, quantum information and astronomy. Here we report the generation of an electron beam with a phase singularity propagating in free space, which we achieve by passing a plane electron wave through a spiral phase plate constructed naturally from a stack of graphite thin films. The interference pattern between the final beam and a plane electron wave in a transmission electron microscope shows the 'Y'-like defect pattern characteristic of a beam carrying a phase singularity with a topological charge equal to one. This fundamentally new electron degree of freedom could find application in a number of research areas, as is the case for polarized electron beams.

The wave–particle duality of electrons was demonstrated in a kind of two-slit interference experiment using an electron microscope equipped with an electron biprism and a position-sensitive electron-counting system. Such an experiment has been regarded as a pure thought experiment that can never be realized. This article reports an experiment that successfully recorded the actual buildup process of the interference pattern with a series of incoming single electrons in the form of a movie.

Evidence for the Aharonov-Bohm effect was obtained with magnetic fields shielded from the electron wave. A toroidal ferromagnet was covered with a superconductor layer to confine the field, and further with a copper layer for complete shielding from the electron wave. The expected relative phase shift was detected with electron holography between two electron beams, one passing through the hole of the toroid, and the other passing outside. The experiment gave direct evidence for flux quantization also. P ACS num bers: 03,65.Bz, 41.80.DdThe Aharonov-Bohm (AB) effect' has recently received much attention as an unusual but important quantum effect. The predicted effect is the production of a relative phase shift between two electron beams enclosing a magnetic flux even if they do not touch the magnetic flux. Such an effect is inconceivable in classical physics and directly demonstrates the gauge principle of electromagnetism.Although the affirmative experimental test was offered4 soon after its prediction, Bocchieri et aI. 5 and Roy questioned the validity of the test, attributing the phase shift to leakage fields. The authors' recent experiment using a toroidal magnet established the existence of the AB effect, under the condition of complete confinement of the magnetic field in the magnet; electron holography confirmed quantitatively the expected relative phase shift between the two beams. Bocchieri, Loinger, and Siragusa still argued that the phase shift could be due to the Lorentz-force effect on the portion of the electron beam going through the magnet. 9The present experiment'0 is designed to provide a crucial test of the AB effect. A tiny toroidal magnet covered entirely with a superconductor layer and further with a copper layer is fabricated. The two layers prevent the incident electron wave from penetrating the magnet. In addition, the magnetic field is confined to the toroidal magnet by the Meissner effect of the covering superconductor.Then the relative phase shift between two electron beams, one passing through a region enclosed by the toroid and the other passing outside the toroid, is measured by means of electron holography.The experimental results detected the predicted relative phase shift, giving conclusive evidence for the AB effect. This experiment also demonstrated the flux quantization. " Tiny toroidal samples were fabricated by use of photolithography.

The microscopic mechanism of the matching effect in a superconductor, which manifested itself as the production of peaks or cusps in the critical current at specific values of the applied magnetic field, was investigated with Lorentz microscopy to allow direct observation of the behavior of vortices in a niobium thin film having a regular array of artificial defects. Vortices were observed to form regular and consequently rigid lattices at the matching magnetic field, at its multiples, and at its fractions. The dynamic observation furthermore revealed that vortices were most difficult to move at the matching field, whereas excess vortices moved easily.