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Hydrodynamic flow of charge carriers in graphene is an energy flow unlike the usual mass flow in conventional fluids. In neutral graphene, the energy flow is decoupled from the electric current, making it difficult to observe the hydrodynamic effects and measure the viscosity of the electronic fluid by means of electric current measurements. In particular, we show that the hallmark Poiseuille flow in a narrow channel cannot be driven by the electric field irrespective of boundary conditions at the channel edges. Nevertheless one can observe nonuniform current densities similarly to the case of the well-known ballistic-diffusive crossover. The standard diffusive behavior with the uniform current density across the channel is achieved under the assumptions of specular scattering on the channel boundaries. This flow can also be made nonuniform by applying weak magnetic fields. In this case, the curvature of the current density profile is determined by the quasiparticle recombination processes dominated by the disorder-assisted electron-phonon scattering -- the so-called supercollisions.
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We theoretically study the Hofstadter butterfly of a triangular network model in minimally twisted bilayer graphene (mTBLG). The band structure manifests periodicity in energy, mimicking that of Floquet systems. The butterfly diagrams provide fingerprints of the model parameters and reveal the hidden band topology. In a strong magnetic field, we establish that mTBLG realizes low-energy Floquet topological insulators (FTIs) carrying zero Chern number, while hosting chiral edge states in bulk gaps. We identify the FTIs by analyzing the nontrivial spectral flow in the Hofstadter butterfly, and by explicitly computing the chiral edge states. Our theory paves the way for an effective practical realization of FTIs in equilibrium solid state systems.
Hydrodynamics is a general description for the flow of a fluid, and is expected to hold even for fundamental particles such as electrons when inter-particle interactions dominate. While various aspects of electron hydrodynamics were revealed in recent experiments, the fundamental spatial structure of hydrodynamic electrons, the Poiseuille flow profile, has remained elusive. In this work, we provide the first real-space imaging of Poiseuille flow of an electronic fluid, as well as visualization of its evolution from ballistic flow. Utilizing a scanning nanotube single electron transistor, we image the Hall voltage of electronic flow through channels of high-mobility graphene. We find that the profile of the Hall field across the channel is a key physical quantity for distinguishing ballistic from hydrodynamic flow. We image the transition from flat, ballistic field profiles at low temperature into parabolic field profiles at elevated temperatures, which is the hallmark of Poiseuille flow. The curvature of the imaged profiles is qualitatively reproduced by Boltzmann calculations, which allow us to create a phase diagram that characterizes the electron flow regimes. Our results provide long-sought, direct confirmation of Poiseuille flow in the solid state, and enable a new approach for exploring the rich physics of interacting electrons in real space.
Since its first isolation in 2004, graphene has been found to host a plethora of unusual electronic transport phenomena, making it a fascinating system for fundamental studies in condensed-matter physics as well as offering tremendous opportunities for future electronic and sensing devices. However, to fully realise these goals a major challenge is the ability to non-invasively image charge currents in monolayer graphene structures and devices. Typically, electronic transport in graphene has been investigated via resistivity measurements, however, such measurements are generally blind to spatial information critical to observing and studying landmark transport phenomena such as electron guiding and focusing, topological currents and viscous electron backflow in real space, and in realistic imperfect devices. Here we bring quantum imaging to bear on the problem and demonstrate high-resolution imaging of current flow in graphene structures. Our method utilises an engineered array of near-surface, atomic-sized quantum sensors in diamond, to map the vector magnetic field and reconstruct the vector current density over graphene geometries of varying complexity, from mono-ribbons to junctions, with spatial resolution at the diffraction limit and a projected sensitivity to currents as small as 1 {mu}A. The measured current maps reveal strong spatial variations corresponding to physical defects at the sub-{mu}m scale. The demonstrated method opens up an important new avenue to investigate fundamental electronic and spin transport in graphene structures and devices, and more generally in emerging two-dimensional materials and thin film systems.
We show how the weak field magneto-conductance can be used as a tool to characterize epitaxial graphene samples grown from the C or the Si face of Silicon Carbide, with mobilities ranging from 120 to 12000 cm^2/(V.s). Depending on the growth conditions, we observe anti-localization and/or localization which can be understood in term of weak-localization related to quantum interferences. The inferred characteristic diffusion lengths are in agreement with the scanning tunneling microscopy and the theoretical model which describe the pure mono-layer and bilayer of graphene [MacCann et al,. Phys. Rev. Lett. 97, 146805 (2006)].
Collective behavior is one of the most intriguing aspects of the hydrodynamic approach to electronic transport. Here we provide a consistent, unified calculation of the dispersion relations of the hydrodynamic collective modes in graphene. Taking into account viscous effects, we show that the hydrodynamic sound mode in graphene becomes overdamped at sufficiently large momentum scales. Extending the linearized theory beyond the hydrodynamic regime, we connect the diffusive hydrodynamic charge density fluctuations with plasmons.
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