Session C2: Novel Electronic Phenomena in Graphene

Creating and Probing Graphene Electron Optics with Local Scanning Probes

Ballistic propagation and the light-like dispersion of graphene charge carriers make graphene an attractive platform for optics-inspired graphene electronics where gate tunable potentials can control electron refraction and transmission. In analogy to optical wave propagation in lenses, mirrors and metamaterials, gate potentials can be used to create a negative index of refraction for Veselago lensing and Fabry-P\'{e}rot interferometers. In circular geometries, gate potentials can induce whispering gallery modes (WGM), similar to optical and acoustic whispering galleries [1] albeit on a much smaller length scale. Klein scattering of Dirac carriers plays a central role in determining the coherent propagation of electron waves in these resonators. In this talk, I examine the probing of electron resonators in graphene confined by linear and circular gate potentials with the scanning tunneling microscope (STM). The tip in the STM tunnel junction serves both as a tunable local gate potential, and as a probe of the graphene states through tunneling spectroscopy. A combination of a back gate potential, $V_{\mathrm{g}}$, and tip potential, $V_{\mathrm{b}}$, creates and controls a circular pn junction that confines the WGM graphene states. The resonances are observed in two separate channels in the tunneling spectroscopy experiment: first, by directly tunneling into the state at the bias energy \textit{eV}$_{\mathrm{b}}$, and, second, by tunneling from the resonance at the Fermi level as the state is gated by the tip potential. The second channel produces a fan-like set of WGM peaks, reminiscent of the fringes seen in planar geometries by transport measurements. The WGM resonances split in a small applied magnetic field, with a large energy splitting approaching the WGM spacing at 0.5 T. These results agree well with recent theory on Klein scattering in graphene electron resonators [2]. [1]. Y. Zhao, J. Wyrick, F. D. Natterer, J. F. Rodriquez-Nieva \textit{et al}., Science \textbf{348}, 672 (2015). [2]. J. F. Rodriguez-Nieva, L. S. Levitov, \textit{arXiv:1508.06609} .   

Electronic Veselago lensing in graphene PN junctions.

Ballistic electrons in a uniform 2D electron gas (2DEG) behave in close analogy to light propagating through an optical medium. In the absence of impurity scattering, electrons follow straight-line trajectories, while the associated de Broglie wavelength can give rise to interference and diffraction. Here we present measurements of ballistic graphene devices in which a graphite gate is used to realize an atomically-smooth junction. We demonstrate unambiguous signatures of negative refraction across a PN junction, paving the way for electron optics inspired by Veselago lensing. Comparison with theoretical simulations reveals the importance of the junction profile towards this effort. Opportunities for future device designs that may take advantage of these effects will be discussed.   

Quantum transport in graphene-based van der Waals heterostructures

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Observation of the hydrodynamic Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene

Interactions between particles in quantum many-body systems can lead to collective behavior described by hydrodynamics. One such system is the electron-hole plasma in graphene near the charge neutrality point which can form a strongly coupled Dirac fluid. This charge neutral plasma of quasi-relativistic fermions is expected to exhibit a substantial enhancement of the thermal conductivity, due to decoupling of charge and heat currents within hydrodynamics. Employing high sensitivity Johnson noise thermometry, we report the breakdown of the Wiedemann-Franz law in graphene, with a thermal conductivity an order of magnitude larger than the value predicted by Fermi liquid theory. This result is a signature of the Dirac fluid, and constitutes direct evidence of collective motion in a quantum electronic fluid. This research is performed in collaboration with J. Crossno, J. K. Shi, K. Wang, X. Liu, A. Harzheim, A. Lucas, S. Sachdev, P. Kim, T. Taniguchi, K. Watanabe, and T. A. Ohki.   

Negative local resistance due to viscous electron backflow in graphene

Theoretical and experimental studies of systems in which particles undergo frequent mutual collisions date back to more than two centuries ago. Transport in such systems is described by hydrodynamic theory that was found very successful in explaining the response of classical liquids and gases to external fields. It has been argued for a long time that collective behavior of charge carriers in solids can be also described by hydrodynamic approach. However, there has been almost no direct evidence to hydrodynamic electron transport so far. This is because the conditions at which the hydrodynamic effects become observable are very strict: the electron-electron scattering length should provide the shortest spatial scale in the problem. First of all, this requires ultra clean systems where the scattering at impurities is diminished. Second, the electron-phonon scattering rate should be smaller than that of electron-electron scattering. Due to weak electron-phonon coupling high mobility graphene devices offer an ideal system to study electron hydrodynamics. To amplify the hydrodynamic effects we employed a special measurement geometry. The idea is that in case of hydrodynamic electron flow, vortices emerge in the spatial electric current distribution near the current injection contact. That results in a development of a negative voltage drop at the nearby contacts. We were able to detect such negative signal over the range of temperatures when the electronic system is in a hydrodynamic regime. Finally, we performed a rheological study of electron liquid in graphene. The electron viscosity was found to be an order of magnitude larger than that of honey which is in good agreement with many-body calculation.