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Register a new userCreating and Probing Electron Whispering Gallery Modes in Graphene
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Designing high-finesse resonant cavities for electronic waves faces challenges due to short electron coherence lengths in solids. Previous approaches, e.g. the seminal nanometer-sized quantum corrals, depend on careful positioning of adatoms at clean surfaces. Here we demonstrate an entirely different approach, inspired by the peculiar acoustic phenomena in whispering galleries. Taking advantage of graphenes unique properties, namely gate-tunable light-like carriers, we create Whispering Gallery Mode (WGM) resonators defined by circular pn-junctions, induced by a scanning tunneling probe. We can tune the resonator size and the carrier concentration under the probe in a back-gated graphene device over a wide range, independently and in situ. The confined modes, revealed through characteristic resonances in the tunneling spectrum, originate from Klein scattering at pn junction boundaries. The WGM-type confinement and resonances are a new addition to the quantum electron-optics toolbox, paving the way to real-world electronic lenses and resonators.
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Structural and electronic properties of oligothiophene nano-wires and rings synthesized on a Au(111) surface are investigated by scanning tunneling microscopy. The spectroscopic data of the linear and cyclic oligomers show remarkable differences which, to a first approximation, can be accounted by considering electronic states confinement to one-dimensional (1D) boxes having respectively fixed and periodic boundary conditions. A more detailed analysis shows that polythiophene must be treated as a ribbon (i.e. having an effective width) rather than a purely 1D structure. A fascinating consequence is that the molecular nano-rings act as whispering gallery mode resonators for electrons, opening the way for new applications in quantum-electronics.
Quasiclassical approach and geometric optics allow to describe rather accurately whispering gallery modes in convex axisymmetric bodies. Using this approach we obtain practical formulas for the calculation of eigenfrequencies and radiative Q-factors in dielectrical spheroid and compare them with the known solutions for the particular cases and with numerical calculations. We show how geometrical interpretation allows expansion of the method on arbitrary shaped axisymmetric bodies.
We put forward a concept to create highly collimated, non-dispersive electron beams in pseudo-relativistic Dirac materials such as graphene or topological insulator surfaces. Combining negative refraction and Klein collimation at a parabolic pn junction, the proposed lens generates beams, as narrow as the focal length, that stay focused over scales of several microns and can be steered by a magnetic field without losing collimation. We demonstrate the lens capabilities by applying it to two paradigmatic settings of graphene electron optics: We propose a setup for observing high-resolution angle-dependent Klein tunneling, and, exploiting the intimate quantum-to-classical correspondence of these focused electron waves, we consider high-fidelity transverse magnetic focusing accompanied by simulations for current mapping through scanning gate microscopy. Our proposal opens up new perspectives for next-generation graphene electron optics experiments.
We demonstrate that yttrium iron garnet microspheres support optical whispering gallery modes similar to those in non-magnetic dielectric materials. The direction of the ferromagnetic moment tunes both the resonant frequency via the Voigt effect as well as the degree of polarization rotation via the Faraday effect. An understanding of the magneto-optical coupling in whispering gallery modes, where the propagation direction rotates with respect to the magnetization, is fundamental to the emerging field of cavity optomagnonics.
Theory predicts that Coherent Synchrotron Radiation (CSR) in electron storage rings should appear in whispering gallery modes. In an idealized model these are resonances of the vacuum chamber that are characterized by their high frequencies and concentration of the field near the outer wall of the chamber. The resonant modes imply a series of sharp peaks in the frequency spectrum of CSR, and very long wake fields which lead to interbunch communication. Theory and experimental evidence for this behavior will be reviewed.
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