Detecting transition radiation from a magnetic moment

Cathodoluminescence Nanoscopy: State of the Art and Beyond

Cathodoluminescence (CL) nanoscopy is proven to be a powerful tool to explore nanoscale optical properties, whereby free electron beams achieve a spatial resolution far beyond the diffraction limit of light. With developed methods for the control of electron beams and the collection of light, the dimension of information that CL can access has been expanded to include polarization, momentum, and time, holding promise to provide invaluable insights into the study of materials and optical near-field dynamics. With a focus on the burgeoning field of CL nanoscopy, this perspective outlines the recent advancements and applications of this technique, as illustrated by the salient experimental works. In addition, as an outlook for future research, several appealing directions that may bring about developments and discoveries are highlighted.

Interfacial Cherenkov radiation from ultralow-energy electrons

Cherenkov radiation occurs only when a charged particle moves with a velocity exceeding the phase velocity of light in that matter. This radiation mechanism creates directional light emission at a wide range of frequencies and could facilitate the development of on-chip light sources except for the hard-to-satisfy requirement for high-energy particles. Creating Cherenkov radiation from low-energy electrons that has no momentum mismatch with light in free space is still a long-standing challenge. Here, we report a mechanism to overcome this challenge by exploiting a combined effect of interfacial Cherenkov radiation and umklapp scattering, namely the constructive interference of light emission from sequential particle-interface interactions with specially designed (umklapp) momentum-shifts. We find that this combined effect is able to create the interfacial Cherenkov radiation from ultralow-energy electrons, with kinetic energies down to the electron-volt scale. Due to the umklapp scattering for the excited high-momentum Bloch modes, the resulting interfacial Cherenkov radiation is uniquely featured with spatially separated apexes for its wave cone and group cone.

Free-electron Brewster-transition radiation

We reveal a mechanism to enhance particle-matter interactions by exploiting the pseudo-Brewster effect of gain materials, presenting an enhancement of at least four orders of magnitude for light emission. This mechanism is enabled by the emergence of an unprecedented phase diagram that maps all phenomena of free-electron transition radiation into three distinct phases in a gain-thickness parameter space, namely, the conventional, intermediate, and Brewster phases, when an electron penetrates a dielectric slab with a modest gain and a finite thickness. Essentially, our revealed mechanism corresponds to the free-electron transition radiation in the Brewster phase, which also features ultrahigh directionality, always at the Brewster angle, regardless of the electron velocity. Counterintuitively, we find that the intensity of this free-electron Brewster-transition radiation is insensitive to the Fabry-Pérot resonance condition and, thus, the variation of slab thickness, and moreover, a weaker gain could lead to a stronger enhancement for light emission.

Generation of Perfect Electron Vortex Beam with a Customized Beam Size Independent of Orbital Angular Momentum

The electron vortex beam (EVB)-carrying quantized orbital angular momentum (OAM) plays an essential role in a series of fundamental research. However, the radius of the transverse intensity profile of a doughnut-shaped EVB strongly depends on the topological charge of the OAM, impeding its wide applications in electron microscopy. Inspired by the perfect vortex in optics, herein, we demonstrate a perfect electron vortex beam (PEVB), which completely unlocks the constraint between the beam size and the beam's OAM. We design nanoscale holograms to generate PEVBs carrying different quanta of OAM but exhibiting almost the same beam size. Furthermore, we show that the beam size of the PEVB can be readily controlled by only modifying the design parameters of the hologram. The generation of PEVB with a customized beam size independent of the OAM can promote various in situ applications of free electrons carrying OAM in electron microscopy.

Highly Active and Durable Single-Atom Tungsten-Doped NiS0.5 Se0.5 Nanosheet @ NiS0.5 Se0.5 Nanorod Heterostructures for Water Splitting

Developing robust and highly active non-precious electrocatalysts for the hydrogen/oxygen evolution reaction (HER/OER) is crucial for the industrialization of hydrogen energy. In this study, a highly active and durable single-atom W-doped NiS_0.5 Se_0.5 nanosheet @ NiS_0.5 Se_0.5 nanorod heterostructure (W-NiS_0.5 Se_0.5 ) electrocatalyst is prepared. W-NiS_0.5 Se_0.5 exhibits excellent catalytic activity for the HER and OER with ultralow overpotentials (39 and 106 mV for the HER and 171 and 239 mV for the OER at 10 and 100 mA cm^-2 , respectively) and excellent long-term durability (500 h), outperforming commercial precious-metal catalysts and many other previously reported transition-metal-based compounds (TMCs). The introduction of single-atom W delocalizes the spin state of Ni, which results in an increase in the Ni d-electron density. This causes the optimization of the adsorption/desorption process of H and a significant reduction in the adsorption free energy of the rate-determining step (O* → OOH*), thus accelerating the thermodynamics and kinetics of the HER and OER. This work provides a rational feasible strategy to design single-atom catalysts for water splitting and to develop advanced TMC electrocatalysts by regulating delocalized spin states.

Relativistic Quantum Dynamics of Twisted Electron Beams in Arbitrary Electric and Magnetic Fields

Relativistic quantum dynamics of twisted (vortex) Dirac particles in arbitrary electric and magnetic fields are constructed for the first time. This allows us to change the controversial contemporary situation when the nonrelativistic approximation is used for relativistic twisted electrons. The relativistic Hamiltonian and equations of motion in the Foldy-Wouthuysen representation are derived. A critical experiment for a verification of the results obtained is proposed. The new important effect of a radiative orbital polarization of a twisted electron beam in a magnetic field resulting in a nonzero average projection of the intrinsic orbital angular momentum on the field direction is predicted.

Orbital-Angular-Momentum Mode Selection by Rotationally Symmetric Superposition of Chiral States with Application to Electron Vortex Beams

A general orbital-angular-momentum (OAM) mode selection principle is put forward involving the rotationally symmetric superposition of chiral states. This principle is not only capable of explaining the operation of vortex generating elements such as spiral zone plate holograms, but more importantly, it enables the systematic and flexible generation of structured OAM waves in general. This is demonstrated both experimentally and theoretically in the context of electron vortex beams using rotationally symmetric binary amplitude chiral sieve masks.

Is the angular momentum of an electron conserved in a uniform magnetic field?

We show that an electron moving in a uniform magnetic field possesses a time-varying "diamagnetic" angular momentum. Surprisingly this means that the kinetic angular momentum of the electron may vary with time, despite the rotational symmetry of the system. This apparent violation of angular momentum conservation is resolved by including the angular momentum of the surrounding fields.

Imaging the dynamics of free-electron Landau states

Landau levels and states of electrons in a magnetic field are fundamental quantum entities underlying the quantum Hall and related effects in condensed matter physics. However, the real-space properties and observation of Landau wave functions remain elusive. Here we report the real-space observation of Landau states and the internal rotational dynamics of free electrons. States with different quantum numbers are produced using nanometre-sized electron vortex beams, with a radius chosen to match the waist of the Landau states, in a quasi-uniform magnetic field. Scanning the beams along the propagation direction, we reconstruct the rotational dynamics of the Landau wave functions with angular frequency ~100 GHz. We observe that Landau modes with different azimuthal quantum numbers belong to three classes, which are characterized by rotations with zero, Larmor and cyclotron frequencies, respectively. This is in sharp contrast to the uniform cyclotron rotation of classical electrons, and in perfect agreement with recent theoretical predictions.

Landau states are associated with the quantised orbits of charged particles in magnetic fields. By manipulating electron vortex beams in a magnetic field, this study reconstructs the internal quantum dynamics of free-electron Landau states, which differs strongly from the classical cyclotron rotation.