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• W2963973216 abstract "Abstract: Interference of standing waves in electromagnetic resonators forms thebasisofmanytechnologies, fromtelecommunications[1]andspectroscopy[2]tode-tection of gravitational waves [3]. However, unlike the connement of light wavesin vacuum, the interference of electronic waves in solids is complicated by boundaryproperties of the crystal, notably leading to electron guiding by atomic-scale poten-tials at the edges [4–7]. Understanding the microscopic role of boundaries on co-herent wave interference is an unresolved question due to the challenge of detectingcharge ow with submicron resolution. Here we employ Fraunhofer interferometryto achieve real-space imaging of cavity modes in a graphene Fabry-P erot (FP) res-´onator, embedded between two superconductors to form a Josephson junction [8].By directly visualizing current ow using Fourier methods [9], our measurements re-veal surprising redistribution of current on and off resonance. These ndings providedirect evidence of separate interference conditions for edge and bulk currents andreveal the ballistic nature of guided edge states. Beyond equilibrium, our measure-mentsshowstrongmodulationofthemultipleAndreevreectionamplitudeonanoffresonance, a direct measure of the gate-tunable change of cavity transparency. Theseresults demonstrate that, contrary to the common belief, electron interactions withrealistic disordered edges facilitate electron wave interference and ballistic transport.Graphene provides an appealing platform to explore “electron-optics” due to the ballistic nature ofwavelike carriers and ability to engineer transmission of electronic waves in real space using electro-static potentials [10–17]. In particular, the electronic analog to refractive index is the Fermi energy,which is tunable via electrostatic gating [11,18]. Because the gapless spectrum of Dirac materialsenables continuous tunability of carrier polarity, positive and negative index of refraction regions canbe combined in bipolar structures that form the building blocks of Veselago “electronic lenses” [15],Fabry-P ´erot (FP) interferometers [11–15,17], and whispering gallery mode cavities [19]. Electronicanalogs to optical interferometers attract attention because relativistic effects such as hyperlensingand phase-coherent Klein transmission provide capabilities beyond conventional optics [10–17,20].Here we investigate the simplest analog to an optical interferometer, the electron FP resonator, whichconsists of standing electron waves conned between two reective interfaces [21,22]. Despite ex-tensiveexplorationinthemomentumdomain,inwhichFermimomentumissimplytunedwithagate,little information is available about the real-space distribution of current ow due to the challenge ofimaging current paths with submicron resolution. Furthermore, in real devices, atomically sharp po-tentialsattheedgesofgraphenecanconneelectronwavesintoguidededgemodes,inanalogytotheguidingoflightinopticalbers[4–7],aswehavedemonstratedexperimentallyinpriorwork[23]. Toinvestigate the nature of these boundary currents, we measure the interference of standing waves in agraphene Josephson junction and image the real space distribution of supercurrent ow using Fraun-hofer interferometry [9]. By visualizing the spatial structure of current-carrying states in the cavityusing Fourier methods, our measurements disentangle edge from bulk current ow and highlight thesurprising role of the crystal boundaries.In a coherent electron cavity, quantum interference of electron waves replaces classical diffusionas a key feature of electronic transport [21,22]. In our system, a pair of superconducting electrodesis coupled to a graphene membrane, dening a ballistic cavity between the two graphene-electrodeinterfaces. As the Fermi wavelength in the cavity is tuned with a gate, the quantized energy levels ofthe cavity are moved on and off resonance with the Fermi energy of the superconducting leads, thusinducing an oscillatory critical current whose period satises the FP interference conditions. Due" @default.
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• W2963973216 date "2015-06-22" @default.
• W2963973216 modified "2023-09-23" @default.
• W2963973216 title "Visualization of phase-coherent electron interference in a ballistic graphene Josephson junction" @default.
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