Session B24: From Ballistic to Hydrodynamic Flow in Graphene

Electron optics with ballistic graphene junctions

Electrons transmitted across a ballistic semiconductor junction undergo refraction, analogous to light rays across an optical boundary. A \textit{pn} junction theoretically provides the equivalent of a negative index medium, enabling novel electron optics such as negative refraction and perfect (Veselago) lensing. In graphene, the linear dispersion and zero-gap bandstructure admit highly transparent \textit{pn} junctions by simple electrostatic gating, which cannot be achieved in conventional semiconductors. Robust demonstration of these effects, however, has not been forthcoming. Here we employ transverse magnetic focusing to probe propagation across an electrostatically defined graphene junction. We find perfect agreement with the predicted Snell's law for electrons, including observation of both positive and negative refraction. Resonant transmission across the \textit{pn} junction provides a direct measurement of the angle dependent transmission coefficient, and we demonstrate good agreement with theory. Comparing experimental data with simulation reveals the crucial role played by the effective junction width, providing guidance for future device design. Efforts toward sharper \textit{pn} junction and possibility of zero field Veselago lensing will also be discussed.   

Ballistic miniband conduction in a graphene superlattice

Heterostructures of graphene and hexagonal boron nitride can be prepared with very low disorder, such that electrons travel along ballistic trajectories over lengths that are accessible to direct measurements. I will discuss such transport experiments in this system which exhibit ballistic conduction phenomena, particularly the transverse electron focusing (or magnetic focusing) effect. Through electron focusing, we demonstrate ballistic conduction in the 14 nm period moire superlattice formed by the relative alignment of graphene and hexagonal boron nitride crystals. Quasiparticles in five successive minibands are shown to traverse skipping orbits extended over hundreds of superlattice periods. This experiment reveals the effective charge and Fermi momentum of quasiparticles as well as saddle points in the dispersion. We identify a crossover to hydrodynamic transport owing to the Coulomb interaction. A theory of nearly free Dirac fermions that obey semiclassical equations of motion describes the system well, and we quantitatively determine the interlayer interaction parameter and the superlattice-reconstructed miniband structure. M. Lee, J. R. Wallbank, et al., Science 353, 1526 (2016).   

Higher-Than-Ballistic Conduction in Viscous Electron Fluids

Strongly interacting electrons can move in a neatly coordinated way, reminiscent of the movement of viscous fluids. This talk will argue that in viscous flows interactions facilitate transport, allowing conductance to exceed the fundamental Sharvin-Landauer quantum-ballistic limit. The effect is particularly striking for the flow through a viscous point contact, a constriction exhibiting the quantum-mechanical ballistic transport at $T=0$ but governed by electron hydrodynamics at elevated temperatures. Conductance grows as a square of the constriction width, i.e. faster than the linear width dependence for noninteracting fermions. The crossover between the ballistic and viscous regimes occurs when the mean free path for e-e collisions becomes comparable to the constriction width. Further, we will discuss the negative nonlocal response, a signature effect of viscous transport. This response exhibits an interesting nonmonotonic behavior vs. $T$ at the viscous-to-balistic transition. The response is negative but small in the highly viscous regime at elevated temperatures. The value grows as the temperature is lowered and the system becomes less viscous, reaching the most negative values in the crossover region where the mean free path is comparable to the distance between contacts. Subsequently, it reverses sign at even lower temperatures, becoming positive as the system enters the ballistic regime. This peculiar behavior provides a clear signature of the ballistic-to-viscous transition and enables a direct measurement of the electron-electron collision mean free path.   

Valley-symmetric quasi-1D transport in ballistic graphene

We present our recent studies on gate-defined valley-symmetric one-dimensional (1D) carrier guiding in ballistic monolayer graphene [1] and valley-symmetry-protected topological 1D transport in ballistic bilayer graphene [2]. Successful carrier guiding was realized in ballistic monolayer graphene even in the absence of a band gap by inducing a high distinction (\textasciitilde more than two orders of magnitude) in the carrier density between the region of a quasi-1D channel and the rest of the top-gated regions. Conductance of a channel shows quantized values in units of 4$e^{2}$/$h$, suggesting that the valley symmetry is preserved. For the latter, the topological 1D conduction was realized between two closely arranged insulating regions with inverted band gaps, induced under a pair of split dual gating with polarities opposite to each other. The maximum conductance along the boundary channel showed 4$e^{2}$/$h$, again with the preserved valley symmetry. The 1D topological carrier guiding demonstrated in this study affords a promising route to robust valleytronic applications and sophisticated valley-associated functionalities based on 2D materials. [1]. M. Kim, J.-H. Choi, S.-H. Lee, K. Watanabe, T. Taniguchi, S.-H. Jhi, and H.-J. Lee, Nature Physics \textbf{12}, 1022 (2016). [2]. J. Lee, K. Watanabe, T. Taniguchi, and H.-J. Lee, submitted.   

Hydrodynamic transport in graphene near the charge neutrality point

Understanding the dynamics of many interacting particles is a formidable task in physics, complicated by many coupled degrees of freedom. A strongly interacting complex microscopic dynamics can often be simplified by a hydrodynamic description of momentum, energy, and charge transport on long length and time scales. For an electronic system at high enough temperature, the enhanced inelastic collisions between charge carriers dramatically accelerate the relaxation towards local thermal equilibrium and yields a hydrodynamic collective behavior. Near the charge neutrality point of the graphene, the electron-electron and electron-hole scattering rates grow linearly with temperature, and the electron-hole plasma of Dirac fermions develops. Here, interactions between particles in quantum many-body systems can lead to the collective behavior described by hydrodynamics of 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 the 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. We will also discuss recent development of magneto-thermal conduction in graphene in the hydrodynamic transport regime.