Visualization of phase-coherent electron interference in a ballistic graphene Josephson junction

Abstract

Interference of standing waves in electromagnetic resonators forms the basis of many technologies, from telecommunications [1] and spectroscopy [2] to detection of gravitational waves [3]. However, unlike the confinement of light waves in vacuum, the interference of electronic waves in solids is complicated by boundary properties of the crystal, notably leading to electron guiding by atomic-scale potentials at the edges [4–7]. Understanding the microscopic role of boundaries on coherent wave interference is an unresolved question due to the challenge of detecting charge flow with submicron resolution. Here we employ Fraunhofer interferometry to achieve real-space imaging of cavity modes in a graphene Fabry-Pérot (FP) resonator, embedded between two superconductors to form a Josephson junction [8]. By directly visualizing current flow using Fourier methods [9], our measurements reveal surprising redistribution of current on and off resonance. These findings provide direct evidence of separate interference conditions for edge and bulk currents and reveal the ballistic nature of guided edge states. Beyond equilibrium, our measurements show strong modulation of the multiple Andreev reflection amplitude on an off resonance, a direct measure of the gate-tunable change of cavity transparency. These results demonstrate that, contrary to the common belief, electron interactions with realistic disordered edges facilitate electron wave interference and ballistic transport. Graphene provides an appealing platform to explore “electron-optics” due to the ballistic nature of wavelike carriers and ability to engineer transmission of electronic waves in real space using electrostatic 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 materials enables continuous tunability of carrier polarity, positive and negative index of refraction regions can be combined in bipolar structures that form the building blocks of Veselago “electronic lenses” [15], Fabry-Pérot (FP) interferometers [11–15, 17], and whispering gallery mode cavities [19]. Electronic analogs to optical interferometers attract attention because relativistic effects such as hyperlensing and 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, which consists of standing electron waves confined between two reflective interfaces [21, 22]. Despite extensive exploration in the momentum domain, in which Fermi momentum is simply tuned with a gate, little information is available about the real-space distribution of current flow due to the challenge of imaging current paths with submicron resolution. Furthermore, in real devices, atomically sharp potentials at the edges of graphene can confine electron waves into guided edge modes, in analogy to the guiding of light in optical fibers [4–7], as we have demonstrated experimentally in prior work [23]. To investigate the nature of these boundary currents, we measure the interference of standing waves in a graphene Josephson junction and image the real space distribution of supercurrent flow using Fraunhofer interferometry [9]. By visualizing the spatial structure of current-carrying states in the cavity using Fourier methods, our measurements disentangle edge from bulk current flow and highlight the surprising role of the crystal boundaries. In a coherent electron cavity, quantum interference of electron waves replaces classical diffusion as a key feature of electronic transport [21, 22]. In our system, a pair of superconducting electrodes is coupled to a graphene membrane, defining a ballistic cavity between the two graphene-electrode interfaces. As the Fermi wavelength in the cavity is tuned with a gate, the quantized energy levels of the cavity are moved on and off resonance with the Fermi energy of the superconducting leads, thus inducing an oscillatory critical current whose period satisfies the FP interference conditions. Due

Cite this paper

@inproceedings{Allen2015VisualizationOP, title={Visualization of phase-coherent electron interference in a ballistic graphene Josephson junction}, author={Mark T. Allen and Amir Yacoby}, year={2015} }